Posted by: SATYASRINIVAS | July 5, 2007

quotes

Miles and Miles apart that
lies between us
there’s never a time I don’t stop thinking about you,
All night I lie awake and think about what it would be like to feel your lips against mine,
Can you dream of me the way I dream of you?
there will be that day
that day of meeting each other
the joy of happiness that will stream down our faces when we are holding each other tightly,
every time I talk to you
my body is singing with butterflies,
through miles and miles apart
life holds us patience
there will be that day
when its just me and you
living in the arms of each other
i promise you
through miles and miles apart
that beautiful day of us being together…will come.
Love is an ideal thing, marriage a real thing; a confusion of the real with the ideal never goes unpunished. – Goethe.

A man falls in love through his eyes, a woman through her ears. – Woodrow Wyatt

I like not only to be loved, but to be told that I am loved. – George Elliot

LOVE: The irresistable desire to be irresistibly desired. – Mark Twain

The first duty of love – is to listen. – Paul Tillich

One word frees us of all the weight and pain in life. That word is love. – Sophocles

How on earth are you ever going to explain in terms of chemistry and physics so important a biological phenomenon as first love?” – Albert Einstien

Life is a flower of which love is the honey. – Victor Hugo

Love is friendship set to music. – E. Joseph Crossmann

At the touch of love, everyone becomes a poet. – Plato

Love is a great beautifier. – Louisa May Alcott

In our life there is a single color, as on an artist`s palette, which provides the meaning of life and art. It is the color of love. – Marc Chagall

Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. THAT’S relativity. – Einstein.

I feel something in my heart, it’s like a little flame, every time I see you, this flame lights up, this flame is special for you, because I LOVE YOU!

Love is being stupid together.

Love is not just looking at each other, it’s looking in the same direction.

Never frown, even when you are sad, because you never know who is falling in love with your smile.

No one is too young for love, because love doesn’t come from your mind, which knows your age, but from your heart, which knows no age.

Love conquers all. – Virgil.
…………………………………………………………………..
Never live in the past but always learn from it.
       – unknown
He who knows all the answers has not yet been asked all the questions.
       – unknown
Wisdom is supreme; therefore make a full effort to get wisdom.
Esteem her and she will exalt your; embrace her and she will honor you.
       – Proverbs 4:7-8
Education is the power to think clearly, the power to act well in the world’s work, and the power to appreciate life.
       – Brigham Young
The sublimity of wisdom is to do those things living that are desired when dying.
       – unknown
The foolish man seeks happiness in the distance, the wise grows it under his feet.
       – James Oppenheim
The wisest mind has something yet to learn.
       – George Santayana
The secret of health for both mind and body is not to mourn for the past, worry about the future, or anticipate troubles but to live in the present moment wisely and earnestly.
       – Buddha
Luck is what happens when preparation meets opportunity.
       – Darrell Royal, in James A. Michener, Sports in America, 1976.
Do not believe in anything simply because you have heard it.
Do not believe in anything simply because it is spoken and rumored by many.
Do not believe in anything simply because it is found written in your religious books.
Do not believe in anything merely on the authority of your teachers and elders.
Do not believe in traditions because they have been handed down for many generations.
But after observation and analysis, when you find that anything agrees with reason and is conducive to the good and benefit of one and all, then accept it and live up to it.
       – Buddha
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

Posted by: SATYASRINIVAS | July 5, 2007

Dr. Abdul Kalaam’s Speech

Dr. Abdul Kalaam’s Speech

I have three visions for India.

In 3000 years of our history people from all over the world have come and
invaded us, captured our lands, conquered our minds. From Alexander onwards.
The Greeks, the Turks, the Moguls, the Portuguese, the British, the French, the
Dutch, all of them came and looted us, took over what was ours.

Yet we have not done this to any other nation. We have not conquered anyone. We
have not grabbed their land, their culture, and their history and tried to
enforce our way of life on them. Why? Because we respect the freedom of others.
That is why my first vision is that of FREEDOM. I believe that India got its
first vision of this in 1857, when we started the war of independence. It is
this freedom that we must protect and nurture and build on. If we are not free,
no one will respect us.

My second vision for India is DEVELOPMENT. For fifty years we have been a
developing nation. It is time we see ourselves as a developed nation. We are
among top 5 nations of the world in terms of GDP. We have 10 percent growth
rate in most areas. Our poverty levels are falling. Our achievements are being
globally recognized today. Yet we lack the self-confidence to see ourselves as
a developed nation, self-reliant and self-assured. Isn’t this incorrect?

I have a THIRD vision. India must STAND UP to the world. Because I believe that
unless India stands up to the world, no one will respect us. Only strength
respects strength. We must be strong not only as a military power but also as
an economic power. Both must go hand-in-hand.

My good fortune was to have worked with three great minds. Dr.Vikram Sarabhai
of the Dept. of space, Professor Satish Dhawan, who succeeded him and Dr. Brahm
Prakash, father of nuclear material. I was lucky to have worked with all three
of them closely and consider this the great opportunity of my life.

I see four milestones in my career:

ONE: Twenty years I spent in ISRO. I was given the opportunity to be the
project director for India’s first satellite launch vehicle, SLV3. The one that
launched Rohini. These years played a very important role in my life of
Scientist.

TWO: After my ISRO years, I joined DRDO and got a chance to be the part of
India’s guided missile program. It was my second bliss when Agni met its
mission requirements in 1994.

THREE: The Dept. of Atomic Energy and DRDO had this tremendous partnership in
the recent nuclear tests, on May 11 and 13. This was the third bliss. The joy
of participating with my team in these nuclear tests and proving to the world
that India can make it, that we are no longer a developing nation but one of
them. It made me feel very proud as an Indian. The fact that we have now
developed for Agni a re-entry structure, for which we have developed this new
material. A Very light material called carbon-carbon.

FOUR: One day an orthopaedic surgeon from Nizam Institute of Medical Sciences
visited my laboratory. He lifted the material and found it so light that he
took me to his hospital and showed me his patients. There were these little
girls and boys with heavy metallic calipers weighing over three Kg. each,
dragging their feet around. He said to me: Please remove the pain of my
patients. In three weeks, we made these Floor reaction Orthosis 300 gram
callipers and took them to the orthopedic centre. The children didn’t believe
their eyes. From dragging around a three kg load on their legs, they could now
move around! Their parents had tears in their eyes. That was my fourth bliss!

Why is the media here so negative? Why are we in India so embarrassed to
recognize our own strengths, our achievements? We are such a great nation. We
have so many amazing success stories but we refuse to acknowledge them.

Why? We are the first in milk production. We are number one in Remote sensing
satellites. We are the second largest producer of wheat. We are the second
largest producer of rice. Look at Dr. Sudarshan; he has transferred the tribal
village into a self-sustaining, self-driving unit. There are millions of such
achievements but our media is only obsessed in the bad news and failures and
disasters.

I was in Tel Aviv once and I was reading the Israeli newspaper. It was the day
after a lot of attacks and bombardments and deaths had taken place. The Hamas
had struck. But the front page of the newspaper had the picture of a Jewish
gentleman who in five years had transformed his desert land into an orchid and
a granary. It was this inspiring picture that everyone woke up to. The gory
details of killings, bombardments, deaths, were inside in the newspaper, buried
among other news. In India we only read about death, sickness, terrorism,
crime. Why are we so NEGATIVE?

Another question: Why are we, as a nation so obsessed with foreign things? We
want foreign TVs. We want foreign shirts. We want foreign technology. Why this
obsession with everything imported. Do we not realize that self-respect comes
with self-reliance? I was in Hyderabad giving this lecture, when a 14 years old
girl asked me for my autograph. I asked her what her goal in life is: She
replied: I want to live in a developed India. For her, you and I will have to
build this developed India. You must proclaim. India is not an under-developed
nation; it is a highly developed nation.

Do you have 10 minutes?

Allow me to come back with vengeance. Got 10 minutes for your country? If yes,
then read; otherwise, choice is yours. YOU say that our government is
inefficient. YOU say that our laws are too old. YOU say that the municipality
does not pick up the garbage. YOU say that the phones don’t work, the railways
are a joke, the airline is the worst in the world, and mails never reach their
destination. YOU say that our country has been fed to the dogs and is the
absolute pits. YOU say, say and say. What do YOU do about it?

Take a person on his way to Singapore. Give him a name – YOURS. Give him a face
– YOURS. YOU walk out of the airport and you are at your International best. In
Singapore you don’t throw cigarette butts on the roads or eat in the stores.
YOU are as proud of their Underground Links as they are. You pay $5 (approx.
Rs.60) to drive through Orchard Road (equivalent of Mahim causeway or Pedder
Road) between 5 PM and 8 PM. YOU comeback to the parking lot to punch your
parking ticket if you have over stayed in a restaurant or a shopping mall
irrespective of your status identity.

In Singapore you don’t say anything, DO YOU? YOU wouldn’t dare to eat in public
during Ramadan, in Dubai. YOU would not dare to go out without your head
covered in Jeddah. YOU would not dare to buy an employee of the telephone
exchange in London at 10 pounds (Rs.650) a month to, “see to it that my STD and
ISD calls are billed to someone else. ” YOU would not dare to speed beyond 55
mph (88 kmph) in Washington and then tell the traffic
cop, “Jaanta hai sala main kaun hoon (Do you know who I am?). I am so and so’s
son. Take your two bucks and get lost.” YOU wouldn’t chuck an empty coconut
shell anywhere other than the garbage pail on the beaches in Australia and New
Zealand. Why don’t YOU spit Paan on the streets of Tokyo? Why don’t YOU use
examination jockeys or buy fake certificates in Boston? We are still talking of
the same YOU. YOU who can respect and conform to a foreign system in other
countries but cannot in your own. You who will throw papers and cigarettes on
the road the moment you touch Indian ground. You can be an involved and
appreciative citizen in an alien country why cannot you be the same here in
India.

Once in an interview, the famous Ex-municipal commissioner of Bombay
Mr.Tinaikar had a point to make. “Rich people’s dogs are walked on the streets
to leave their affluent droppings all over the place,” he said. “And then the
same people turn around to criticize and blame the authorities for inefficiency
and dirty pavements. What do they expect the officers to do? Go down with a
broom every time their dog feels the pressure in his bowels? In America every
dog owner has to clean up after his pet has done the job. Same in Japan. Will
the Indian citizen do that here?”

He’s right. We go to the polls to choose a government and after that forfeit
all responsibility. We sit back wanting to be pampered and expect the
government to do everything for us whilst our contribution is totally negative.
We expect the government to clean up but we are not going to stop chucking
garbage all over the place or are we going to stop to pick a up a stray piece
of paper and throw it in the bin. We expect the railways to provide clean
bathrooms but we are not going to learn the proper use of bathrooms. We want
Indian Airlines and Air India to provide the best of food and toiletries but we
are not going to stop pilfering at the least opportunity. This applies even to
the staff who is known not to pass on the service to the public. When it comes
to burning social issues like those related to women, dowry, girl child and
others, we make loud drawing room protestations and continue to do the reverse
at home. Our excuse?

“It’s the whole system which has to change, how will it matter if I alone
forego my sons’ rights to a dowry.”

So who’s going to change the system? What does a system consist of? Very
conveniently for us it consists of our neighbors, other households, other
cities, other communities and the government.

But definitely not me and YOU.

When it comes to us actually making a positive contribution to the system we
lock ourselves along with our families into a safe cocoon and look into the
distance at countries far away and wait for a Mr. Clean to come along & work
miracles for us with a majestic sweep of his hand.

Or we leave the country and run away. Like lazy cowards hounded by our fears we
run to America to bask in their glory and praise their system. When New York
becomes insecure we run to England. When England experiences unemployment, we
take the next flight out to the Gulf. When the Gulf is war struck, we demand to
be rescued and brought home by the Indian government.

Everybody is out to abuse and rape the country. Nobody thinks of feeding the
system. Our conscience is mortgaged to money.

Dear Indians, The article is highly thought inductive, calls for a great deal
of introspection and pricks one’s conscience too…. I am echoing J.F.
Kennedy’s words to his fellow Americans to relate to Indians.
“ASK WHAT WE CAN DO FOR INDIA AND DO WHAT HAS TO BE DONE TO MAKE INDIA WHAT
AMERICA AND OTHER WESTERN COUNTRIES ARE TODAY”
End of Speech

Lets do what India needs from us. Forward this mail to each Indian.

Posted by: SATYASRINIVAS | June 4, 2007

APTITUDE2

1) What is the average speed of the car ?

a) The car covered 25% of distance at 45 Km per Hour.
b) The car covered the remaining 75% of distance at 55 Km /
Hour.
Let the total distance be 100X
Time taken for first 25x = 25X/45
Time taken to cover remaining 75X = 75X/55
Total time taken = 25X/45 + 75X/55 =
LCM of 45 and 55 = 495
= 275X+675X/ 495 = 950X/495
So average speed = 100X/ ( 950X/495) = 49500/950 Km per
hour.

————————————————————————-

2)What is the remainder when factorial 11 divided by 17 ?

 

11*10*9*8*7*6*5*4*3*2 Mod 17
11*10 Mod 17 = 8
9*8 Mod 17= 4
7*6 Mod 17= 8
5*4*3*2 Mod 17 = 1
Now the remaining balances are 8*4*8*1
64 mod 17 = 13
13* 4 Mod 17= 1
Hence the Answer is 1

——————————————————————————

3)What is the remainder when difference of the 5th power
and the 4th power of 59 is divided by 11? ( 59^5-59^4)

59^5-59^4 mod 11
59^4( 59-1)
= 58*59^4
58 mod 11= 3
59 mod 11= 4
so we are left with 3*4^4 which is equal to 3*(4^2)^2
4^2 mod 11= 5
so we are left with 3*5*5 =75
75 mod 11= 9

———————————————————–

4)At what time after 4.00 p.m. is the minutes hand of a clock exactly aligned with the hour hand?

Answer

4:21:49.5

Assume that X minutes after 4.00 PM minute hand exactly aligns with and hour hand.

For every minute, minute hand travels 6 degrees.
Hence, for X minutes it will travel 6 * X degrees.

For every minute, hour hand

travels 1/2 degrees.
Hence, for X minutes it will travel X/2 degrees.

At 4.00 PM, the angle between minute hand and hour hand is 120 degrees. Also, after X minutes, minute hand and hour hand are exactly aligned. So the angle with respect to 12 i.e. Vertical Plane will be same. Therefore,

6 * X = 120 + X/2
12 * X = 240 + X
11 * X = 240
X = 21.8182
X = 21 minutes 49.5 seconds

Hence, at 4:21:49.5 minute hand is exactly aligned with the hour hand.

———————————————————-

5)If a rook and a bishop of a standard chess set are randomly placed on a chessboard, what is the probability that one is attacking the other?

Note that both are different colored pieces.
SubmAnswer

The probability of either the Rook or the Bishop attacking the other is 0.3611

A Rook and a Bishop on a standard chess-board can be arranged in 64P2 = 64*63 = 4032 ways

Now, there are 2 cases – Rook attacking Bishop and Bishop attacking Rook. Note that the Rook and the Bishop never attack each other simultaneously. Let’s consider both the cases one by one.

Case I – Rook attacking Bishop
The Rook can be placed in any of the given 64 positions and it always attacks 14 positions. Hence, total possible ways of the Rook attacking the Bishop = 64*14 = 896 ways

Case II – Bishop attacking Rook
View the chess-board as a 4 co-centric hollow squares with the outermost square with side 8 units and the innermost square with side 2 units.

If the bishop is in one of the outer 28 squares, then it can attack 7 positions. If the bishop is in one of the 20 squares at next inner-level, then it can attack 9 positions. Similarly if the bishop is in one of the 12 squares at next inner-level, then it can attack 11 positions. And if the bishop is in one of the 4 squares at next inner-level (the innermost level), then it can attack 13 positions.

Hence, total possible ways of the Bishop attacking the Rook
= 28*7 + 20*9 + 12*11 + 4*13
= 560 ways

Thus, the required probability is
= (896 + 560) / 4032
= 13/36
= 0.3611

Posted by: SATYASRINIVAS | June 4, 2007

formulae11

Apollonius theorem ; In a triangle ABC , if AD
is the median to the side BC , then
AB^2 + AC^2 = 2(AD^2 + BD^2) or 2(AD^2 + DC^2) .
Note BD=DC=BC/2.

—————————————————————————————-

Let the sides be A,B,C.

Semiperimeter = (A+B+C)/2

Area =(S*(S-A)*(S-B)*(S-C))^0.5

Inradius = Area/ Semiperimeter

Circumradius= A.B.C/ 4.Area

—————————————————————————————–

if n is number of sides.
For any regular polynomial, each angle =((n-2)*180)/n and
Total sum of the angles = (n-2)*180 or Each angle* n

——————————————————————————

Wrong Weight*(100 + Profit %)/100 = Correct Weight

———————————————————————————-

1. 1st January 0001 and every 400 years after that is a Monday.
That is 1st Jan of year 0001, 401, 801,1201,1601,2001 is
Monday.
2. An year divisible by 4 is a leap year, but century years are not
leap years unless they are divisible by 400. So 2000 is a Leap
Year but 1900, 1800, 1700 are not not leap year.
3. Odd days is the remainder obtained when the number of days
is divided by 7. Example: If it is Sunday today , after 50 days it will
be: 50/7 gives remained 1. Add 1 day to Sunday to get answer
as Monday.
4. A non leap year has 1 odd day and a leap year has 2 odd
days.
5. A normal Century has 5 odd days and leap century has 6 odd
days.
6. January, March, May, July, Aug, Oct and December have 3 odd
days each. April, June, Sept and Nov have 2 odd days each. Feb
has 0 odd days if it is not a leap year and has 1 odd day if it is a
leap year.
6. Number of leap years between any two given years is equal to
the quotient when the difference between the two given years is
divided by 4. Example Number of Leap years between 1947 to
1901 = 1947-1901= 46. 46 /4 = 11.5. So number of leap years=11.

 

What was the day on 15 Aug 1947 ?

Odd year for 1601-1900 : 5+5+5=15 or 1 odd day
1947-1901= 46. No of odd days =46 or 4
Number of leap years = 46/4=11. No. of odd days =11 or 4
Odd days till July end : 3+0+3+2+3+2+3= 16 or 2
Day is August = 15 or 1
Total Odd days =1+4+4+2+1= 12 or 5 odd days.
So 15th Aug 1947 was Friday.

——————————————————————–

Arithmetic series

Sn= n(2a +(n-1)d) / 2
Tn= a + (n-1)d

A.M*HM=GM^2

geometric progression

Tn=ar^(n-1)

Sn= a[ (1-r^n)/ (1-r) ] where r<1

Sn= a[ (r^n-1)/ (r-1) ] where r>1

S(infinity)= a/ (1-r) when r<1

——————————————————————

Right angle triangle:The square of the shortest side is less than the product of the
sum and the difference of the longest and the third side.

Posted by: SATYASRINIVAS | May 31, 2007

quntspoint to remember

COMMON ADMISSION TEST – MBA ENTRANCE

Quantitative Ability – POINTS TO REMEMBER

  1. If an equation (i.e. f(x) = 0) contains all positive co-efficients of any powers of x, it has no positive roots.

Eg: x3+3x2+2x+6=0 has no positive roots

  1. For an equation, if all the even powers of x have same sign coefficients and all the odd powers of x have the opposite sign coefficients, then it has no negative roots.

  1. For an equation f(x)=0 , the maximum number of positive roots it can have is the number of sign changes in f(x) ; and the maximum number of negative roots it can have is the number of sign changes in f(-x)

  1. Complex roots occur in pairs, hence if one of the roots of an equation is 2+3i, another has to be 2-3i and if there are three possible roots of the equation, we can conclude that the last root is real. This real root could be found out by finding the sum of the roots of the equation and subtracting (2+3i)+(2-3i)=4 from that sum.

ü For a cubic equation ax3+bx2+cx+d=o

    • Sum of the roots = – b/a
    • Sum of the product of the roots taken two at a time = c/a
    • Product of the roots = -d/a

ü For a bi-quadratic equation ax4+bx3+cx2+dx+e = 0

    • Sum of the roots = – b/a
    • Sum of the product of the roots taken three at a time = c/a
    • Sum of the product of the roots taken two at a time = -d/a
    • Product of the roots = e/a

  1. If an equation f(x)= 0 has only odd powers of x and all these have the same sign coefficients or if f(x) = 0 has only odd powers of x and all these have the same sign coefficients, then the equation has no real roots in each case (except for x=0 in the second case)

  1. Consider the two equations

a1x+b1y=c1

a2x+b2y=c2

Then,

ü If a1/a2 = b1/b2 = c1/c2, then we have infinite solutions for these equations.

ü If a1/a2 = b1/b2 <> c1/c2, then we have no solution.

ü If a1/a2 <> b1/b2, then we have a unique solution.

  1. Roots of x2 + x + 1=0 are 1, w, w2 where 1 + w + w2=0 and w3=1

  1. |a| + |b| = |a + b| if a*b>=0

else, |a| + |b| >= |a + b|

  1. The equation ax2+bx+c=0 will have max. value when a<0 and min. value when a>0. The max. or min. value is given by (4ac-b2)/4a and will occur at x = -b/2a

ü If for two numbers x + y=k (a constant), then their PRODUCT is MAXIMUM if x=y (=k/2). The maximum product is then (k2)/4.

ü If for two numbers x*y=k (a constant), then their SUM is MINIMUM if
x=y (=root(k)). The minimum sum is then 2*root (k).

  1. Product of any two numbers = Product of their HCF and LCM. Hence product of two numbers = LCM of the numbers if they are prime to each other.

  1. For any 2 numbers a, b where a>b

ü a>AM>GM>HM>b (where AM, GM ,HM stand for arithmetic, geometric , harmonic means respectively)

ü (GM)^2 = AM * HM

  1. For three positive numbers a, b, c

ü (a + b + c) * (1/a + 1/b + 1/c)>=9

  1. For any positive integer n

ü 2<= (1 + 1/n)^n <=3

  1. a2 + b2 + c2 >= ab + bc + ca

If a=b=c, then the case of equality holds good.

  1. a4 + b4 + c4 + d4 >= 4abcd (Equality arises when a=b=c=d=1)

  1. (n!)2 > nn

  1. If a + b + c + d=constant, then the product a^p * b^q * c^r * d^s will be maximum if a/p = b/q = c/r = d/s

  1. If n is even, n(n+1)(n+2) is divisible by 24

  1. x^n -a^n = (x-a)(x^(n-1) + x^(n-2) + …….+ a^(n-1) ) ……Very useful for finding multiples. For example (17-14=3 will be a multiple of 17^3 – 14^3)

  1. e^x = 1 + (x)/1! + (x^2)/2! + (x^3)/3! + ……..to infinity

Note: 2 < e < 3

  1. log(1+x) = x – (x^2)/2 + (x^3)/3 – (x^4)/4 ………to infinity [Note the alternating sign . .Also note that the logarithm is with respect to base e]

  1. (m + n)! is divisible by m! * n!

  1. When a three digit number is reversed and the difference of these two numbers is taken, the middle number is always 9 and the sum of the other two numbers is always 9.

  1. Any function of the type y=f(x)=(ax-b)/(bx-a) is always of the form x=f(y)

  1. To Find Square of a 3-Digit Number

Let the number be XYZ

Step No.

Operation to be Performed

1

Last digit = Last digit of Sq(Z)

2

Second last digit = 2*Y*Z + any carryover from STEP 1

3

Third last digit 2*X*Z+ Sq(Y) + any carryover from STEP 2

4

Fourth last digit is 2*X*Y + any carryover from STEP 3

5

Beginning of result will be Sq(X) + any carryover from Step 4

Eg) Let us find the square of 431

Step No.

Operation to be Performed

1

Last digit = Last digit of Sq(1) = 1

2

Second last digit = 2*3*1 + any carryover from STEP 1=6+0=6

3

Third last digit 2*4*1+ Sq(3) + any carryover from STEP 2 = 8+9+0 = 17 i.e. 7 with carry over of 1

4

Fourth last digit is 2*4*3 + any carryover from STEP 3 = 24+1 = 25 i.e. 5 with carry over of 2

5

Beginning of result will be Sq(4) + any carryover from Step 4 = 16+2 = 18

THUS SQ(431) = 185761

If the answer choices provided are such that the last two digits are different, then, we need to carry out only the first two steps only.

ü The sum of first n natural numbers = n(n+1)/2

ü The sum of squares of first n natural numbers is n(n+1)(2n+1)/6

ü The sum of cubes of first n natural numbers is (n(n+1)/2)2/4

ü The sum of first n even numbers= n (n+1)

ü The sum of first n odd numbers= n2

  1. If a number ‘N’ is represented as a^x * b^y * c^z… where {a, b, c, …} are prime numbers, then

ü the total number of factors is (x+1)(y+1)(z+1) ….

ü the total number of relatively prime numbers less than the number is
N * (1-1/a) * (1-1/b) * (1-1/c)….

ü the sum of relatively prime numbers less than the number is
N/2 * N * (1-1/a) * (1-1/b) * (1-1/c)….

ü the sum of factors of the number is {a^(x+1)} * {b^(y+1)} * …../(x * y *…)

ü Total no. of prime numbers between 1 and 50 is 15

ü Total no. of prime numbers between 51 and 100 is 10

ü Total no. of prime numbers between 101 and 200 is 21

ü The number of squares in n*m board is given by m*(m+1)*(3n-m+1)/6

ü The number of rectangles in n*m board is given by n+1C2 * m+1C2

  1. If ‘r’ is a rational no. lying between 0 and 1, then, r^r can never be rational.

  1. Certain nos. to be remembered

ü 210 = 45 = 322 = 1024

ü 38 = 94 = 812 = 6561

ü 7 * 11 * 13 = 1001

ü 11 * 13 * 17 = 2431

ü 13 * 17 * 19 = 4199

ü 19 * 21 * 23 = 9177

ü 19 * 23 * 29 = 12673

  1. Where the digits of a no. are added and the resultant figure is 1 or 4 or 7 or 9, then, the no. could be a perfect square.

  1. If a no. ‘N’ has got k factors and a^l is one of the factors such that l>=k/2, then, a is the only prime factor for that no.

  1. To find out the sum of 3-digit nos. formed with a set of given digits

This is given by (sum of digits) * (no. of digits-1)! * 1111…1 (i.e. based on the no. of digits)

Eg) Find the sum of all 3-digit nos. formed using the digits 2, 3, 5, 7 & 8.

Sum = (2+3+5+7+8) * (5-1)! * 11111 (since 5 digits are there)

= 25 * 24 * 11111

=6666600

  1. Consider the equation x^n + y^n = z^n

As per Fermat’s Last Theorem, the above equation will not have any solution whenever n>=3.

  1. Further as per Fermat, where ‘p’ is a prime no. and ‘N’ is co-prime to p, then,
    N^(p-1) – 1 is always divisible by p.

  1. 145 is the 3-digit no. expressed as sum of factorials of the individual digits i.e.

145 = 1! + 4! + 5!

ü Where a no. is of the form a^n – b^n, then,

· The no. is always divisible by a – b

· Further, the no. is divisible by a + b when n is even and not divisible by
a + b when n is odd

ü Where a no. is of the form a^n + b^n, then,

· The no. is usually not divisible by a – b

· However, the no. is divisible by a + b when n is odd and not divisible by
a + b when n is even

  1. The relationship between base 10 and base ‘e’ in log is given by
    log10N = 0.434 logeN

  1. WINE and WATER formula

Let Q – volume of a vessel, q – qty of a mixture of water and wine be removed each time from a mixture, n – number of times this operation is done and A – final qty of wine in the mixture, then,

A/Q = (1-q / Q)^n

  1. Pascal’s Triangle for computing Compound Interest (CI)

The traditional formula for computing CI is

CI = P*(1+R/100)^N – P

Using Pascal’s Triangle,

Number of Years (N)

——————-

1 1

2 1 2 1

3 1 3 3 1

4 1 4 6 4 1

1 …. …. … … ..1

Eg: P = 1000, R=10 %, and N=3 years. What is CI & Amount?

Step 1:

Amount after 3 years = 1 * 1000 + 3 * 100 + 3 * 10 + 1 * 1 = Rs.1331

The coefficients – 1,3,3,1 are lifted from the Pascal’s triangle above.

Step 2:

CI after 3 years = 3*100 + 3*10 + 3*1 = Rs.331 (leaving out first term in step 1)

If N =2, we would have had,

Amt = 1 * 1000 + 2 * 100 + 1 * 10 = Rs.1210

CI = 2 * 100 + 1* 10 = Rs.210

  1. Suppose the price of a product is first increased by X% and then decreased by Y% , then, the final change % in the price is given by:

Final Difference% = X – Y – XY/100

Eg) The price of a T.V set is increased by 40 % of the cost price and then is decreased by 25% of the new price. On selling, the profit made by the dealer was Rs.1000. At what price was the T.V sold?

Applying the formula,

Final difference% = 40 – 25 – (40*25/100) = 5 %.

So if 5 % = 1,000

Then, 100 % = 20,000.

Hence, C.P = 20,000

& S.P = 20,000+ 1000= 21,000

  1. Where the cost price of 2 articles is same and the mark up % is same, then, marked price and NOT cost price should be assumed as 100.

ü Where ‘P’ represents principal and ‘R’ represents the rate of interest, then, the difference between 2 years’ simple interest and compound interest is given by P * (R/100)2

ü The difference between 3 years’ simple interest and compound interest is given by (P * R2 *(300+R))/1003

ü If A can finish a work in X time and B can finish the same work in Y time then both of them together can finish that work in (X*Y)/ (X+Y) time.

ü If A can finish a work in X time and A & B together can finish the same work in S time then B can finish that work in (XS)/(X-S) time.

ü If A can finish a work in X time and B in Y time and C in Z time then all of them working together will finish the work in (XYZ)/ (XY +YZ +XZ) time

ü If A can finish a work in X time and B in Y time and A, B & C together in S time then

· C can finish that work alone in (XYS)/ (XY-SX-SY)

· B+C can finish in (SX)/(X-S); and

· A+C can finish in (SY)/(Y-S)

  1. In case ‘n’ faced die is thrown k times, then, probability of getting atleast one more than the previous throw = nC5/n5

ü When an unbiased coin is tossed odd no. (n) of times, then, the no. of heads can never be equal to the no. of tails i.e. P (no. of heads=no. of tails) = 0

ü When an unbiased coin is tossed even no. (2n) of times, then,
P (no. of heads=no. of tails) = 1-(2nCn/22n)

  1. Where there are ‘n’ items and ‘m’ out of such items should follow a pattern, then, the probability is given by 1/m!

Eg)1. Suppose there are 10 girls dancing one after the other. What is the probability of A dancing before B dancing before C?

Here n=10, m=3 (i.e. A, B, C)

Hence, P (A>B>C) = 1/3!

= 1/6

Eg)2. Consider the word ‘METHODS’. What is the probability that the letter ‘M’ comes before ‘S’ when all the letters of the given word are used for forming words, with or without meaning?

P (M>S) = 1/2!

= 1/2

  1. CALENDAR

ü Calendar repeats after every 400 years.

ü Leap year- it is always divisible by 4, but century years are not leap years unless they are divisible by 400.

ü Century has 5 odd days and leap century has 6 odd days.

ü In a normal year 1st January and 2nd July and 1st October fall on the same day. In a leap year 1st January 1st July and 30th September fall on the same day.

ü January 1, 1901 was a Tuesday.

52.

ü For any regular polygon, the sum of the exterior angles is equal to 360 degrees, hence measure of any external angle is equal to 360/n (where n is the number of sides)

ü For any regular polygon, the sum of interior angles =(n-2)*180 degrees

So measure of one angle is (n-2)/n *180

ü If any parallelogram can be inscribed in a circle, it must be a rectangle.

ü If a trapezium can be inscribed in a circle it must be an isosceles trapezium (i.e. oblique sides equal).

  1. For an isosceles trapezium, sum of a pair of opposite sides is equal in length to the sum of the other pair of opposite sides (i.e. AB+CD = AD+BC, taken in order)

ü For any quadrilateral whose diagonals intersect at right angles, the area of the quadrilateral is

0.5*d1*d2, where d1, d2 are the length of the diagonals.

ü For a cyclic quadrilateral, area = root((s-a) * (s-b) * (s-c) * (s-d)), where
s=(a + b + c + d)/2

Further, for a cyclic quadrilateral, the measure of an external angle is equal to the measure of the interior opposite angle.

ü Area of a Rhombus = Product of Diagonals/2

  1. Given the coordinates (a, b); (c, d); (e, f); (g, h) of a parallelogram , the coordinates of the meeting point of the diagonals can be found out by solving for

[(a + e)/2, (b + f)/2] = [(c + g)/2, (d + h)/2]

  1. Area of a triangle

ü 1/2*base*altitude

ü 1/2*a*b*sin C (or) 1/2*b*c*sin A (or) 1/2*c*a*sin B

ü root(s*(s-a)*(s-b)*(s-c)) where s=(a+b+c)/2

ü a*b*c/(4*R) where R is the circumradius of the triangle

ü r*s ,where r is the inradius of the triangle

  1. In any triangle

ü a=b*cos C + c*cos B

ü b=c*cos A + a*cos C

ü c=a*cos B + b*cos A

ü a/sin A=b/sin B=c/sin C=2R, where R is the circumradius

ü cos C = (a^2 + b^2 – c^2)/2ab

ü sin 2A = 2 sin A * cos A

ü cos 2A = cos^2 (A) – sin^2 (A)

  1. The ratio of the radii of the circumcircle and incircle of an equilateral triangle is 2:1

  1. Appollonius Theorem

In a triangle ABC, if AD is the median to side BC, then

AB2 + AC2 = 2(AD2 + BD2) or 2(AD2 + DC2)

ü In an isosceles triangle, the perpendicular from the vertex to the base or the angular bisector from vertex to base bisects the base.

ü In any triangle the angular bisector of an angle bisects the base in the ratio of the other two sides.

  1. The quadrilateral formed by joining the angular bisectors of another quadrilateral is always a rectangle.

  1. Let W be any point inside a rectangle ABCD, then,

WD2 + WB2 = WC2 + WA2

  1. Let a be the side of an equilateral triangle, then, if three circles are drawn inside this triangle such that they touch each other, then each circle’s radius is given by a/(2*(root(3)+1))

ü Distance between a point (x1, y1) and a line represented by the equation
ax + by + c=0 is given by |ax1+by1+c|/Sq(a2+b2)

ü Distance between 2 points (x1, y1) and (x2, y2) is given by
Sq((x1-x2)2+ (y1-y2)2)

  1. Where a rectangle is inscribed in an isosceles right angled triangle, then, the length of the rectangle is twice its breadth and the ratio of area of rectangle to area of triangle is 1:2.

references

pagalguy.com

esnips.com

—–>back to top

Posted by: SATYASRINIVAS | May 30, 2007

maths tips(1)

Hi people,

Wanted to share some shortcuts that would be helpful in quant as well as DI sections. The shortcuts have been compiled from various threads of PG itself.

Dunno whether this is the right thread for this purpose but well, let me post.

If any parallelogram can be inscribed in a circle , it must be a rectangle.

If a quadrilateral circumscribes a circle , the sum of a pair of opposite sides is equal to the sum of the other pair .

The ratio of the radii of the circumcircle and incircle of an equilateral triangle is 2:1 .

for similar cones , ratio of radii = ratio of their bases.

the quadrilateral formed by joining the angular bisectors of another f a quadrilateral is always a rectangle.

Let W be any point inside a rectangle ABCD .
Then
WD^2 + WB^2 = WC^2 + WA^2

Let a be the side of an equilateral triangle . then if three circles be drawn inside
this triangle touching each other then each’s radius = a/(2*(root(3)+1))

Area of a regular hexagon : root(3)*3/2*(side)*(side)

the area of a regular n-sided polygon of side ‘a’ is given by
area=(n/4)*a^2*cot(180/n)

In any triangle
a=b*CosC + c*CosB
b=c*CosA + a*CosC
c=a*CosB + b*CosA
————————————————————

————————————————————
If a+b+c+d=constant , then the product a^p * b^q * c^r * d^s will be maximum
if a/p = b/q = c/r = d/s .
————————————————————
e^x = 1 + (x)/1! + (x^2)/2! + (x^3)/3! + ……..to infinity
————————————————————
(m+n)! is divisible by m! * n!
————————————————————
for squares of numbers between 25 and 50.
let the number be 25+k
first calculate (25-k)^2 and to it add k*100
2)for squares of numbers between 50 and 75.
again let the number 50+k
calculate k^2 and to it add 2500+100*k
————————————————————
3)for squares of numbers between 75 and 100
let the number be 100-k
calculate k^2 and to it add (100-2*k)*100
these formulas are basically a derivation from the formulas (a+b)^2 and (a-b)^2.
————————————————————
2^2n -1 is always divisible by 3
2^2n -1 = (3-1)^2n -1
= 3M +1 -1
= 3M, thus divisible by 3
———————————-
if a number ‘n’ is represented as
n=a^x * b^y * c^z ….
where, {a,b,c,.. } are prime numbers then
Quote:
(a) the total number of factors is (x+1)(y+1)(z+1) ….
(b) the total number of relatively prime numbers less than the number is n * (1-1/a) * (1-1/b) * (1-1/c)…. ???????????????????
(c) the sum of relatively prime numbers less than the number is n/2 * n * (1-1/a) * (1-1/b) * (1-1/c)….
(d) the sum of factors of the number is {a^(x+1)} * {b^(y+1)} * …../(x*y*…)
—————————————–
what is the highest power of 10 in 203!ANS : express 10 as product of primes; 10 = 2*5
divide 203 with 2 and 5 individually
203/2 = 101
101/2 = 50
50/2 = 25
25/2 = 12
12/2 = 6
6/2 = 3
3/2 = 1
thus power of 2 in 203! is, 101 + 50 + 25 + 12 + 6 + 3 + 1 = 198
divide 203 with 5
203/5 = 40
40/5 = 8
8/5 = 1
thus power of 5 in 203! is, 49
so the power of 10 in 203! factorial is 49
——————————————————
n how many ways, 729 can be expressed as a difference of 2 squares?
ANS: 729 = a^2 – b^2
= (a-b)(a+b),
since 729 = 3^5,
total ways of getting 729 are, 1*729, 3*243, 9*81, 27*27.
So 4 ways
Funda is that, all four ways of expressing can be used to findout distinct a,b values,
for example take 9*81
now since 9*81 = (a-b)(a+b) by solving the system a-b = 9 and a+b = 81 we can have 45,36 as soln.
————————————–
if x%a=y%a = r then
(x-y)%r =0 (% stands for modulo operator)
———————————————
total number of primes between 1 and 100 – 25
———————————————-
Reminder Funda
(a) (a + b + c) % n = (a%n + b%n + c%n) %n
EXAMPLE: The reminders when 3 numbers 1221, 1331, 1441 are divided by certain number 9 are 6, 8, 1 respectively. What would be the reminder when you divide 3993 with
9? ( never seen such question though )
the reminder would be (6 + 8 + 1) % 9 = 6
————————————————–
(a*b*c) % n = (a%n * b%n * c%n) %n
————————————–
when a number is divided by 11,7,4 the reminders are 5,6,3 respectively. what would be the reminders when the same number is divided by 4,7,11 respectively?
ANS : whenever such problem is given,
we need to write the numbers in top row and rems in the bottom row like this
11 7 4
| \ \
5 6 3
( coudnt express here properly )
now the number is of the form, LCM ( 11,7,4 ) + 11*(3*7 + 6) + 5
that is 302 + LCM(11,7,4) and thus the rems when the same number is divided by 4,7,11 respectively are,
302 mod 4 = 2
75 mod 7 = 5
10 mod 11 = 10

————————————————————
Plz tell me the answer to remainder when 2^156 / 13 .

2^156/13 = 2^(6*26)/13 (156 = 26 x 6)
= 64^26/13 = (65-1)^26/13 (since 65 is multiple of 13)
= (-1)^26=1
u just have to bring close to the multiple of the number which divides the numerator..(like 65 in this case)…..
———————————————————–
In how many ways can 2310 be expressed as a product of 3 factors?
ANS: 2310 = 2*3*5*7*11
When a number can be expressed as a product of n distinct primes,
then it can be expressed as a product of 3 numbers in (3^(n-1) + 1)/2 ways
(I guess this is incorrect)
————————————————————-
Multiplication by 7: Going from right to left, we use
this rule: Double each number and add half the
neighbor (digit to the right, dropping any fraction);
add 5 if the number (not the neighbor) is odd. And of
course, we have to deal with carries:
3852 x 7 = 26964
Starting at the right (2), we double the first number
(it has no neighbor) and write down the right-most
digit of that (4) and we have no carry. Then we double
the next number (2×5=10), add five (+5=15), and add
half the neighbor (+1=16), and write down the right
digit (6) of that and carry the 1. Then we double the
next number (2×8=16), and add half the neighbor
(+2=1, and add the carry (+1=19). Then we double the
next number (2×3=6), add five (+5=11), add half the
neighbor (+4=15), and add the carry (+1=16). Now we
double a zero off to the left of our 3852
(Trachtenberg wrote the zero out there: 03852) and add
half the neighbor (0+1=1), and add the carry (+1=2).
And we have our answer.
Notice that the carries are smaller than they were in
normal multiplication by 7. The above rule is not
simple, but once mastered, it is easy to use. It
should be about as fast as multiplying normally (which
requires memorizing the multiplication table).
Multiplication by other small numbers (3 through 12)
uses similar rules.
————————————-
Square 2-digit

Rule:
1. Square the second digit
2. Multiply the two digits and double
3. Square the first digit

example
49
81 L.D. 1 cy=8
4*9*2=72 +8 = 80 cy=8
4*4=16 + 8=24
ans=2401
——————————————-
Multiply just-under numbers

Example:
98
x 99
100 – 98 = 2 picture 98 2
100 – 99 = 1 picture 99 1
97 98 – 1 (upper left – lower right)
02 2 x 1 (multiply two right numbers)
9702
98 x 99 = 9702
99*94
99 1
94 6
(99-6)1*6=9306
————————————————————
Multiply just-over numbers

Example:
104
x106
104 -100 = 4 picture 104 4
106 -100 = 6 picture 106 6
110 104+6 (upper left + lower right)
24 4 x 6 (multiply two right numbers)
11024
104 x 106 = 11024
————————————————————–
Multiply just over and just under numbers
97*104
97 -3
104 4
101 -12
100 88 (subtract 1 from the result of cross addition. take the complement of the right multiplication)
10088
103*96
103 3
96 -4
99 -12
9888
————————————————————
38*32=1216.ie,3*4=12 and 8*2=16.only criteria is that the units digit number should add to 10 and that the ten’s digit number shud b the same
————————————————————
3)multiply 57 by 63
method :
5 7
| \ / |
| / \ |
6 3
__________
35 9 1
There are 3 steps:
a)Multiply vertically on the right: 7 x 3 = 21
This gives the last figure of the answer 1 and 2 as carry.
b) Multiply crosswise and add: (5 x 3 + 6 x 7) + 2(carry) = 59
This gives the middle figure 9 and 5 as carry.
c) Multiply vertically on the left: (5 x 6) + 5(carry) = 35.
This gives the first figure of the answer.

for 3 digits
127*93
12 7
9 3
118 1 1
——————————————————
Square just-under numbers

Example:
96^2
100 – 96 is 4
92 96 – 4 is 92
16 4 squared is 16
9216
962 = 9216
—————————————
Square just-over numbers

Example:
106^2
106 – 100 is 6
112 106 + 6
36 6^2
Ans: 11236
—————————————-
Square of number between 50 and 60
Example:
56^2
31 25 + last digit (25+6)
36 sqare of last digit (62)
3136
562 = 3136
———————–
Find remainder when 2222^5555 + 5555^2222 is divided by 7
2222 mod 7=3
5555 mod 7 = 4
so prob reduces to 3^5555 +4^2222 remainder 7
now this can b written as 243^1111 + 16^1111 remainder 7
now use direct formula tht x^n + y^n is divisible by x+y if n is odd
given expression is divisible by 243+16=259
so it is also divisible by 7
and hence remainder=0

anoter method:
Well fermat’s rule states that
a^(p-1) whenever divided by p where p is a prime no. and a is coprime to p, then the remainder would be 1.
as the divisor is 7 and both 2222 and 5555 are coprime to 7 thus any1 of them raised to the power of 6 or a multiple of it would give remainder as 1
2222^5555 + 5555^2222 is equivqlent to
3^5555 + 4^2222 which is
3^(6k+5) + 4^(6m+2)
which is 3^5 + 4^2 (since 3^6 and 4^6 will give 1 as remainder)
——————————————————–
Some pythagorean triplets:
3,4,5 (3^2=4+5)
5,12,13 (5^2=12+13)
7,24,25 (7^2=24+25)
8,15,17 (8^2 / 2 = 15+17 )
9,40,41 (9^2=40+41)
11,60,61 (11^2=60+61)
12,35,37 (12^2 / 2 = 35+37)
16,63,65 (16^2 /2 = 63+65)
20,21,29(EXCEPTION)
—————————————————-
For a set of fractions ( num<den), if the difference between the numerator and the denominator is the same, then the fraction with the largest numerator is the largest and the one with the smallest numerator is the smallest
e.g. 21/27, 23/29, 19/26
largest: 23/29
smallest: 19/26
———————————————————–
For a set of fractions ( num>den), if the difference between the numerator and the denominator is the same, then the fraction with the smallest numerator is the largest and the one with the largest numerator is the smallest
e.g. 27/21, 29/23, 26/19
smallest: 29/23
largest: 26/19
——————————————————————-
i guess we could find sqrt for numbers whose nearby sqrt we already know.
steps are :-
1. take the difference from the nearest smaller perfect square. for eg. sqrt (39) nearest perfect square is 36(whose sqrt we know as 6). and the difference is 39-36=3.
2. divide the difference with product of 2 and sq root of the number which we know.
ie difference 3/(2* sqrt(36) )
3/(2*6)=.25
3.sum the above with the sqrt which we know
ie .25+6=6.25
also works for subtraction
sqrt(33) = 6-.25 = 5.75 (aprox)
4. there is a great chance of getting the answer right with even the first decimal
is correct in most of the cases.

——————————————————————
Finding square root:
Splitting the difference:
Sqrt(3125) : group the digits taking two at a time from the left (like in the usual way of finding sq roots)
First pair: 31
1)We know 5*5 =25
2)rough estimate sqrt is 50
3)divide 3125by 50 =62.5
4)subtracton: 62.5-50 =12.5
5)divide 12.5 by 2 =6.25
round it off downwards :6
rough estimate 50+6=56

try this one:
sqrt(93560)
9,35,60
roughly :300
div 93560 by 300
311.8667-300=11.87
11.87/2=5.935
approx 6
ans 306
sqrt(3847214
38 47 21 48
approx 6000
38472148/6000
6412.014-6000=412.014
412.114/2=206.05
6206.05…(has considerable error)
In most cases error is just 1%
——————————————————————
————————————–
when a number is divided by 11,7,4 the reminders are 5,6,3 respectively. what would be the reminders when the same number is divided by 4,7,11 respectively?
ANS : whenever such problem is given,
we need to write the numbers in top row and rems in the bottom row like this
11 7 4
| \ \
5 6 3
( coudnt express here properly )
now the number is of the form, LCM ( 11,7,4 ) + 11*(3*7 + 6) + 5
that is 302 + LCM(11,7,4) and thus the rems when the same number is divided by 4,7,11 respectively are,
302 mod 4 = 2
75 mod 7 = 5
10 mod 11 = 10

————————————————————
Plz tell me the answer to remainder when 2^156 / 13 .

2^156/13 = 2^(6*26)/13 (156 = 26 x 6)
= 64^26/13 = (65-1)^26/13 (since 65 is multiple of 13)
= (-1)^26=1
u just have to bring close to the multiple of the number which divides the numerator..(like 65 in this case)…..
———————————————————–
In how many ways can 2310 be expressed as a product of 3 factors?
ANS: 2310 = 2*3*5*7*11
When a number can be expressed as a product of n distinct primes,
then it can be expressed as a product of 3 numbers in (3^(n-1) + 1)/2 ways
(I guess this is incorrect)
————————————————————-
Multiplication by 7: Going from right to left, we use
this rule: Double each number and add half the
neighbor (digit to the right, dropping any fraction);
add 5 if the number (not the neighbor) is odd. And of
course, we have to deal with carries:
3852 x 7 = 26964
Starting at the right (2), we double the first number
(it has no neighbor) and write down the right-most
digit of that (4) and we have no carry. Then we double
the next number (2×5=10), add five (+5=15), and add
half the neighbor (+1=16), and write down the right
digit (6) of that and carry the 1. Then we double the
next number (2×8=16), and add half the neighbor
(+2=1, and add the carry (+1=19). Then we double the
next number (2×3=6), add five (+5=11), add half the
neighbor (+4=15), and add the carry (+1=16). Now we
double a zero off to the left of our 3852
(Trachtenberg wrote the zero out there: 03852) and add
half the neighbor (0+1=1), and add the carry (+1=2).
And we have our answer.
Notice that the carries are smaller than they were in
normal multiplication by 7. The above rule is not
simple, but once mastered, it is easy to use. It
should be about as fast as multiplying normally (which
requires memorizing the multiplication table).
Multiplication by other small numbers (3 through 12)
uses similar rules.
————————————-
Square 2-digit

Rule:
1. Square the second digit
2. Multiply the two digits and double
3. Square the first digit

example
49
81 L.D. 1 cy=8
4*9*2=72 +8 = 80 cy=8
4*4=16 + 8=24
ans=2401
——————————————-
Multiply just-under numbers

Example:
98
x 99
100 – 98 = 2 picture 98 2
100 – 99 = 1 picture 99 1
97 98 – 1 (upper left – lower right)
02 2 x 1 (multiply two right numbers)
9702
98 x 99 = 9702
99*94
99 1
94 6
(99-6)1*6=9306
————————————————————
Multiply just-over numbers

Example:
104
x106
104 -100 = 4 picture 104 4
106 -100 = 6 picture 106 6
110 104+6 (upper left + lower right)
24 4 x 6 (multiply two right numbers)
11024
104 x 106 = 11024
————————————————————–
Multiply just over and just under numbers
97*104
97 -3
104 4
101 -12
100 88 (subtract 1 from the result of cross addition. take the complement of the right multiplication)
10088
103*96
103 3
96 -4
99 -12
9888
————————————————————
38*32=1216.ie,3*4=12 and 8*2=16.only criteria is that the units digit number should add to 10 and that the ten’s digit number shud b the same
————————————————————
3)multiply 57 by 63
method :
5 7
| \ / |
| / \ |
6 3
__________
35 9 1
There are 3 steps:
a)Multiply vertically on the right: 7 x 3 = 21
This gives the last figure of the answer 1 and 2 as carry.
b) Multiply crosswise and add: (5 x 3 + 6 x 7) + 2(carry) = 59
This gives the middle figure 9 and 5 as carry.
c) Multiply vertically on the left: (5 x 6) + 5(carry) = 35.
This gives the first figure of the answer.

for 3 digits
127*93
12 7
9 3
118 1 1
——————————————————
Square just-under numbers

Example:
96^2
100 – 96 is 4
92 96 – 4 is 92
16 4 squared is 16
9216
962 = 9216
—————————————
Square just-over numbers

Example:
106^2
106 – 100 is 6
112 106 + 6
36 6^2
Ans: 11236
—————————————-
Square of number between 50 and 60
Example:
56^2
31 25 + last digit (25+6)
36 sqare of last digit (62)
3136
562 = 3136
———————–
Find remainder when 2222^5555 + 5555^2222 is divided by 7
2222 mod 7=3
5555 mod 7 = 4
so prob reduces to 3^5555 +4^2222 remainder 7
now this can b written as 243^1111 + 16^1111 remainder 7
now use direct formula tht x^n + y^n is divisible by x+y if n is odd
given expression is divisible by 243+16=259
so it is also divisible by 7
and hence remainder=0

anoter method:
Well fermat’s rule states that
a^(p-1) whenever divided by p where p is a prime no. and a is coprime to p, then the remainder would be 1.
as the divisor is 7 and both 2222 and 5555 are coprime to 7 thus any1 of them raised to the power of 6 or a multiple of it would give remainder as 1
2222^5555 + 5555^2222 is equivqlent to
3^5555 + 4^2222 which is
3^(6k+5) + 4^(6m+2)
which is 3^5 + 4^2 (since 3^6 and 4^6 will give 1 as remainder)
——————————————————–
Some pythagorean triplets:
3,4,5 (3^2=4+5)
5,12,13 (5^2=12+13)
7,24,25 (7^2=24+25)
8,15,17 (8^2 / 2 = 15+17 )
9,40,41 (9^2=40+41)
11,60,61 (11^2=60+61)
12,35,37 (12^2 / 2 = 35+37)
16,63,65 (16^2 /2 = 63+65)
20,21,29(EXCEPTION)
—————————————————-
For a set of fractions ( num<den), if the difference between the numerator and the denominator is the same, then the fraction with the largest numerator is the largest and the one with the smallest numerator is the smallest
e.g. 21/27, 23/29, 19/26
largest: 23/29
smallest: 19/26
———————————————————–
For a set of fractions ( num>den), if the difference between the numerator and the denominator is the same, then the fraction with the smallest numerator is the largest and the one with the largest numerator is the smallest
e.g. 27/21, 29/23, 26/19
smallest: 29/23
largest: 26/19
——————————————————————-
i guess we could find sqrt for numbers whose nearby sqrt we already know.
steps are :-
1. take the difference from the nearest smaller perfect square. for eg. sqrt (39) nearest perfect square is 36(whose sqrt we know as 6). and the difference is 39-36=3.
2. divide the difference with product of 2 and sq root of the number which we know.
ie difference 3/(2* sqrt(36) )
3/(2*6)=.25
3.sum the above with the sqrt which we know
ie .25+6=6.25
also works for subtraction
sqrt(33) = 6-.25 = 5.75 (aprox)
4. there is a great chance of getting the answer right with even the first decimal
is correct in most of the cases.

——————————————————————
Finding square root:
Splitting the difference:
Sqrt(3125) : group the digits taking two at a time from the left (like in the usual way of finding sq roots)
First pair: 31
1)We know 5*5 =25
2)rough estimate sqrt is 50
3)divide 3125by 50 =62.5
4)subtracton: 62.5-50 =12.5
5)divide 12.5 by 2 =6.25
round it off downwards :6
rough estimate 50+6=56

try this one:
sqrt(93560)
9,35,60
roughly :300
div 93560 by 300
311.8667-300=11.87
11.87/2=5.935
approx 6
ans 306
sqrt(3847214
38 47 21 48
approx 6000
38472148/6000
6412.014-6000=412.014
412.114/2=206.05
6206.05…(has considerable error)
In most cases error is just 1%
——————————————————————
——————————————
We all know the traditional formula to compute interest…
CI = P*(1+R/100)^N – P
The calculation get very tedious when N>2 (more than 2 years). The method suggested below is elegant way to get CI/Amount after ‘N’ years.
You need to recall the good ol’ Pascal’s Triange in following way:
Code:

Number of Years (N)
——————-
1 1
2 1 2 1
3 1 3 3 1
4 1 4 6 4 1
. 1 …. …. … … 1

Example: P = 1000, R=10 %, and N=3 years. What is CI & Amount?
Step 1: 10% of 1000 = 100, Again 10% of 100 = 10 and 10% of 10 = 1
We did this three times b’cos N=3.
Step 2:
Now Amount after 3 years = 1 * 1000 + 3 * 100 + 3 * 10 + 1 * 1 = Rs.1331/-
The coefficents – 1,3,3,1 are lifted from the pascal’s triangle above.
Step 3:
CI after 3 years = 3*100 + 3*10 + 3*1 = Rs.331/- (leaving out first term in step 2)
If N =2, we would have had, Amt = 1 * 1000 + 2 * 100 + 1 * 10 = Rs. 1210/-
CI = 2 * 100 + 1* 10 = Rs. 210/-
This method is extendable for any ‘N’ and it avoids calculations involving higher powers on ‘N’ altogether!
A variant to this short cut can be applied to find depreciating value of some property. (Example, A property worth 100,000 depreciates by 10% every year, find its value after ‘N’ years).
Pascal’s triangle works in all cases but the problem being that it’s lot easier if P(Principal) and R(Rate of interest) are multiples of 10.The problem arises when either the principal or rate of interest or both are not multiples of 10.The calculation becomes a li’l bit complicated …or at least that’s what i think…in the example below R is not 10 and still it works…
For example:P=700,R=8%,N=3
(8/100)*700=56
(8/100)*56=4.48
(8/100)*4.48=0.3584
So CI=(1*700+3*56+3*4.48+1*0.3584)-700=181.7984
and if you would hav calculated in the original method
C.I=700(1+8/100)^3 – 700=700(1.08*1.08*1.0-700=181.7984
——————————————
When interest is calculated as CI, the number of years for the Amount to double (two times the principal) can be found with this following formula:
R * N ~ 72 (approximately equal to).
Exampe, if R=6% p.a. then it takes roughly 12 years for the Principal to double itself.
Note: This is just a approximate formula (when R takes large values, the error % in formula increases).
When interest is calculated as SI, number of years for amt to double can be found as:
N * R = 100 . BTW this formula is exact!

———————————————–
Let’s say we want to find 14.25% of 3267.
What will 10% of 3267 be… 326.7
And 1%… obviously 32.67. Then what would 4% be… 128 for 32 and 2.68 for 0.67…, i.e. 130.6
Thus, 14% will be 326.7 + 130.6, i.e. 457.3
If I want an even more accurate answer, if 1% is 32.6, then 0.25% will be 1/4 of 32.6, i.e 8.15
14.25% of 3267 will be 465.4
Knowing reciprocal percentage equivalent, I should have thought of an even better factorisation as 14.28% – 0.03% and since 14.28% is nothing but 1/7, the answer can directly be found by dividing 3267 by 7, i.e. 466.7

————————————————
a% of b = b% of a
so, sometimes if 4% of 25 is to be found, finding 25% of 4 would be a more sensible way
—————————————————

Percentage Table

SUBTRACTED ADDED
4 4.16(1/24) 3.86(1/26)
5 5.26(1/19) 4.76(1/21)
10 11.11(1/9) 9.09(1/11)
12.5 14.28(1/7) 11.11(1/9)
15 17.55 13
20 25 16.67(1/6)
25 33.33 20(1/5)
30 42.8 23
40 66.67(2/3) 28
50 100 33.33(1/3)
60 150 37.5(3/
when subtracted then add this% when added the subtarct this%

neha’s table of percentages.
first its uses: the info is xtremely important when dealing with problems of type..
say price increased by x% how much shud consumption decrease so that expenditure remains same.
also since most of the time speed dist..problems are in the end ratio proportion kind
this info will be xtremely useful..
so the info given is if increase is 25% decrease reqd to negate it is 20%.
In fact the table need not be memorized.the whole work can be done mentally without much problem..
the trick is to use 100 as a base and work on it..
for eg ..imagine price and consumption both as 100
now price increases by 25%..therefore ratio of new price/old price = 125/100
=> ratio of new consumption/old consumption = inverse of prev ratio = 100/125
=>change (decrease)= (125-100)/125 = 25/125= 20%
ive unnecessarily gone to such detail with the calc ..with xperience this is very simple..
for eg: 4% decrease
here’s how one shud work it out.
4% decrease =>96/100 invert it=>100/96=>change 4/96 = > 1/24
this is as given in the table.
nother one 5% increase => 105/100=>100/105=>5/105=>1/21

————————————————-

Problem : 2485/179379 = ?
1. Take the denominator(179379)
2. See what percentage would give you same no of digits as numerator. In this case 1% of 179379 = 1793.79.
3. Now you need another~ 600 to get to 2400 which is 30% (.3% w.r.t original denominator) of 1793.79 ~ 1800.
4. This gives us all together 1.3% of denominator or .013 as quotient.

———————————————————-

The sum of terms from x to y where x and y are non negative intergers and y > x is
(sqr(y) – sqr(x) + x + y )/2

d/dx of (x+a)(x+b)(x+c)(x+d) = (x+b)(x+c)(x+d)d/dx(x+a) + (x+a)(x+c)(x+d)d/dx(x+b) + (x+b)(x+a)(x+d)d/dx(x+c) + (x+b)(x+c)(x+a)d/dx(x+d)

Cheers

VIVEK

references

pagalguy.com

esnips.com

——>back to top

Posted by: SATYASRINIVAS | May 26, 2007

Aptitude1

Aptitude Questions
1.One of the following is my secret word:AIM DUE MOD OAT TIE.With the list in front of you, if I were to tell you any one of my secret word, then you would be able to tell me the number of vowels in my secret word.Which is my secret word?
Ans.TIE

2.In the following figure:A B C
D
E F G
H
I
Each of the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 is:
a)Represented by a different letter in the figure above.
b)Positioned in the figure above so that each of A + B + C,C + D +E,E + F + G, and G + H + I is equal to 13.
Which digit does E represent?

Ans.E is 4
3.One of Mr. Horton,his wife,their son,and Mr. Horton’s mother is a doctor and another is a lawyer.
a)If the doctor is younger than the lawyer, then the doctor and the lawyer are not blood relatives.
b)If the doctor is a woman, then the doctor and the lawyer are blood relatives.
c)If the lawyer is a man, then the doctor is a man.
Whose occupation you know?

Ans.Mr. Horton:he is the doctor.
4.Here is a picture of two cubes:

a)The two cubes are exactly alike.
b)The hidden faces indicated by the dots have the same alphabet on them.
Which alphabet-q, r, w, or k is on the faces indicated by the dots?

Ans.q

5.In the following figure:
A D
B G E
C F
Each of the seven digits from 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is:
a)Represented by a different letter in the figure above.
b)Positioned in the figure above so that A*B*C,B*G*E, and D*E*F are equal.
Which digit does G represent?

Ans.G represents the digit 2.
6.Mr. and Mrs. Aye and Mr. and Mrs. Bee competed in a chess tournament.Of the three games played:
a)In only the first game werethe two players married to each other.
b)The men won two games and the women won one game.
c)The Ayes won more games than the Bees.
d)Anyone who lost game did not play the subsequent game.
Who did not lose a game?

Ans.Mrs.Bee did not lose a game.
7.Three piles of chips–pile I consists one chip, pile II consists of chips, and pile III consists of three chips–are to be used in game played by Anita and Brinda.The game requires:
a)That each player in turn take only one chip or all chips from just one pile.
b)That the player who has to take the last chip loses.
c)That Anita now have her turn.
From which pile should Anita draw in order to win?

Ans.Pile II
8.Of Abdul, Binoy, and Chandini:
a)Each member belongs to the Tee family whose members always tell the truth or to the El family whose members always lie.
b)Abdul says ”Either I belong or Binoy belongs to a different family from the other two.”
Whose family do you name of?

Ans.Binoy’s family–El.
9.In a class composed of x girls and y boys what part of the class is composed of girls

A.y/(x + y)
B.x/xy
C.x/(x + y)
D.y/xy

Ans.C

10.What is the maximum number of half-pint bottles of cream that can be filled with a 4-gallon can of cream(2 pt.=1 qt. and 4 qt.=1 gal)

A.16
B.24
C.30
D.64

Ans.D

11.If the operation,^ is defined by the equation x ^ y = 2x + y,what is the value of a in 2 ^ a = a ^ 3

A.0
B.1
C.-1
D.4

Ans.B

12.A coffee shop blends 2 kinds of coffee,putting in 2 parts of a 33p. a gm. grade to 1 part of a 24p. a gm.If the mixture is changed to 1 part of the 33p. a gm. to 2 parts of the less expensive grade,how much will the shop save in blending 100 gms.

A.Rs.90
B.Rs.1.00
C.Rs.3.00
D.Rs.8.00

Ans.C

13.There are 200 questions on a 3 hr examination.Among these questions are 50 mathematics problems.It is suggested that twice as much time be spent on each maths problem as for each other question.How many minutes should be spent on mathematics problems

A.36
B.72
C.60
D.100

Ans.B

14.In a group of 15,7 have studied Latin, 8 have studied Greek, and 3 have not studied either.How many of these studied both Latin and Greek

A.0
B.3
C.4
D.5

Ans.B

15.If 13 = 13w/(1-w) ,then (2w)2 =

A.1/4
B.1/2
C.1
D.2

Ans.C

16. If a and b are positive integers and (a-b)/3.5 = 4/7, then
(A) b a
(C) b = a
(D) b >= a
Ans. A17. In june a baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak this team raised its average to 50% .How many games must the team have won in a row to attain this average?
A. 12
B. 20
C. 24
D. 30
Ans. C

18. M men agree to purchase a gift for Rs. D. If three men drop out how much more will each have to contribute towards the purchase of the gift/
A. D/(M-3)
B. MD/3
C. M/(D-3)
D. 3D/(M2-3M)
Ans. D

19. A company contracts to paint 3 houses. Mr.Brown can paint a house in 6 days while Mr.Black would take 8 days and Mr.Blue 12 days. After 8 days Mr.Brown goes on vacation and Mr. Black begins to work for a period of 6 days. How many days will it take Mr.Blue to complete the contract?
A. 7
B. 8
C. 11
D. 12

Ans.C

20. 2 hours after a freight train leaves Delhi a passenger train leaves the same station travelling in the same direction at an average speed of 16 km/hr. After travelling 4 hrs the passenger train overtakes the freight train. The average speed of the freight train was?
A. 30
B. 40
C.58
D. 60
Ans. B

21. If 9x-3y=12 and 3x-5y=7 then 6x-2y = ?
A.-5
B. 4
C. 2
D. 8
Ans. D
22. There are 5 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe

Ans 5c1/ 9c1

23. What is the selling price of a car? If the cost of the car is Rs.60 and a profit of 10% over selling price is earned

Ans: Rs 66/-

24. 1/3 of girls , 1/2 of boys go to canteen .What factor and total number of classmates go to canteen.

Ans: Cannot be determined.

25. The price of a product is reduced by 30% . By what percentage should it be increased to make it 100%

Ans: 42.857%

26. There is a square of side 6cm . A circle is inscribed inside the square. Find the ratio of the area of circle to square.
Ans. 11/14
27. There are two candles of equal lengths and of different thickness. The thicker one lasts of six hours. The thinner 2 hours less than the thicker one. Ramesh lights the two candles at the same time. When he went to bed he saw the thicker one is twice the length of the thinner one. How long ago did Ramesh light the two candles .

Ans: 3 hours.
28. If M/N = 6/5,then 3M+2N = ?
29. If p/q = 5/4 , then 2p+q= ?
30. If PQRST is a parallelogram what it the ratio of triangle PQS & parallelogram PQRST .
Ans: 1:2
31. The cost of an item is Rs 12.60. If the profit is 10% over selling price what is the selling price ?
Ans: Rs 13.86/-
32. There are 6 red shoes & 4 green shoes . If two of red shoes are drawn what is the probability of getting red shoes
Ans: 6c2/10c2
33. To 15 lts of water containing 20% alcohol, we add 5 lts of pure water. What is % alcohol.
Ans : 15%
34. A worker is paid Rs.20/- for a full days work. He works 1,1/3,2/3,1/8.3/4 days in a week. What is the total amount paid for that worker ?
Ans : 57.50
35. If the value of x lies between 0 & 1 which of the following is the largest?
(a) x
(b) x2
(c) -x
(d) 1/x

Ans : (d)
36. If the total distance of a journey is 120 km .If one goes by 60 kmph and comes back at 40kmph what is the average speed during the journey?
Ans: 48kmph
37. A school has 30% students from Maharashtra .Out of these 20% are Bombey students. Find the total percentage of Bombay?
Ans: 6%
38. An equilateral triangle of sides 3 inch each is given. How many equilateral triangles of side 1 inch can be formed from it?
Ans: 9
39. If A/B = 3/5,then 15A = ?
Ans : 9B
40. Each side of a rectangle is increased by 100% .By what percentage does the area increase?
Ans : 300%
41. Perimeter of the back wheel = 9 feet, front wheel = 7 feet on a certain distance, the front wheel gets 10 revolutions more than the back wheel .What is the distance?
Ans : 315 feet.
42. Perimeter of front wheel =30, back wheel = 20. If front wheel revolves 240 times. How many revolutions will the back wheel take?
Ans: 360 times
43. 20% of a 6 litre solution and 60% of 4 litre solution are mixed. What percentage of the mixture of solution
Ans: 36%
44City A’s population is 68000, decreasing at a rate of 80 people per year. City B having population 42000 is increasing at a rate of 120 people per year. In how many years both the cities will have same population?
Ans: 130 years
45Two cars are 15 kms apart. One is turning at a speed of 50kmph and the other at 40kmph . How much time will it take for the two cars to meet?
Ans: 3/2 hours
46A person wants to buy 3 paise and 5 paise stamps costing exactly one rupee. If he buys which of the following number of stamps he won’t able to buy 3 paise stamps.
Ans: 9
47There are 12 boys and 15 girls, How many different dancing groups can be formed with 2 boys and 3 girls.
48Which of the following fractions is less than 1/3
(a) 22/62
(b) 15/46
(c) 2/3
(d) 1
Ans: (b)
49There are two circles, one circle is inscribed and another circle is circumscribed over a square. What is the ratio of area of inner to outer circle?
Ans: 1 : 2
50Three types of tea the a,b,c costs Rs. 95/kg,100/kg and70/kg respectively.
How many kgs of each should be blended to produce 100 kg of mixture worth Rs.90/kg,
given that the quntities of band c are equal
a)70,15,15
b)50,25,25
c)60,20,20
d)40,30,30
Ans. (b)
51. in a class, except 18 all are above 50 years.
15 are below 50 years of age. How many people are there
(a) 30
(b) 33
(c) 36
(d) none of these.
Ans. (d)
52. If a boat is moving in upstream with velocity of 14 km/hr and goes downstream with a velocity of 40 km/hr, then what is the speed of the stream ?

(a) 13 km/hr
(b) 26 km/hr
(c) 34 km/hr
(d) none of these
Ans. A
53. Find the value of ( 0.75 * 0.75 * 0.75 – 0.001 ) / ( 0.75 * 0.75 – 0.075 + 0.01)

(a) 0.845
(b) 1.908
(c) 2.312
(d) 0.001
Ans. A
54. A can have a piece of work done in 8 days, B can work three times faster than the A, C can work five times faster than A. How many days will they take to do the work together ?

(a) 3 days
(b) 8/9 days
(c) 4 days
(d) can’t say
Ans. B
55. A car travels a certain distance taking 7 hrs in forward journey, during the return journey increased speed 12km/hr takes the times 5 hrs.What is the distance travelled

(a) 210 kms
(b) 30 kms
(c) 20 kms
(c) none of these
Ans. B
56. Instead of multiplying a number by 7, the number is divided by 7. What is the percentage of error obtained ?
57. Find (7x + 4y ) / (x-2y) if x/2y = 3/2 ?

(a) 6
(b) 8
(c) 7
(d) data insufficient
Ans. C
58. A man buys 12 lts of liquid which contains 20% of the liquid and the rest is water. He then mixes it with 10 lts of another mixture with 30% of liquid.What is the % of water in the new mixture?
59. If a man buys 1 lt of milk for Rs.12 and mixes it with 20% water and sells it for Rs.15, then what is the percentage of gain?
60. Pipe A can fill a tank in 30 mins and Pipe B can fill it in 28 mins.If 3/4th of the tank is filled by Pipe B alone and both are opened, how much time is required by both the pipes to fill the tank completely ?
61. If on an item a company gives 25% discount, they earn 25% profit. If they now give 10% discount then what is the profit percentage.
(a) 40%
(b) 55%
(c) 35%
(d) 30%
Ans. D
62. A certain number of men can finish a piece of work in 10 days. If however there were 10 men less it will take 10 days more for the work to be finished. How many men were there originally?

(a) 110 men
(b) 130 men
(c) 100 men
(d) none of these
Ans. A
63. In simple interest what sum amounts of Rs.1120/- in 4 years and Rs.1200/- in 5 years ?
(a) Rs. 500
(b) Rs. 600
(c) Rs. 800
(d) Rs. 900
Ans. C
64. If a sum of money compound annually amounts of thrice itself in 3 years. In how many years
will it become 9 times itself.

(a) 6
(b) 8
(c) 10
(d) 12
Ans A
65. Two trains move in the same direction at 50 kmph and 32 kmph respectively. A man in the slower train
observes the 15 seconds elapse before the faster train completely passes by him.
What is the length of faster train ?

(a) 100m
(b) 75m
(c) 120m
(d) 50m
Ans B
66. How many mashes are there in 1 squrare meter of wire gauge if each mesh
is 8mm long and 5mm wide ?

(a) 2500
(b) 25000
(c) 250
(d) 250000
Ans B
67. x% of y is y% of ?
(a) x/y
(b) 2y
(c) x
(d) can’t be determined
Ans. C
68. The price of sugar increases by 20%, by what % should a housewife reduce the consumption of sugar so that expenditure on sugar can be same as before ?
(a) 15%
(b) 16.66%
(c) 12%
(d) 9%
Ans B
69. A man spends half of his salary on household expenses, 1/4th for rent, 1/5th for travel expenses, the man deposits the rest in a bank. If his monthly deposits in the bank amount 50, what is his monthly salary ?
(a) Rs.500
(b) Rs.1500
(c) Rs.1000
(d) Rs. 900
Ans C
70. The population of a city increases @ 4% p.a. There is an additional annual increase of 4% of the population due to the influx of job seekers, find the % increase in population after 2 years ?
71. The ratio of the number of boys and girls in a school is 3:2 Out of these 10% the boys and 25% of girls are scholarship holders. % of students who are not scholarship holders.?
72. 15 men take 21 days of 8 hrs. each to do a piece of work. How many days of 6 hrs. each would it take for 21 women if 3 women do as much work as 2 men?
(a) 30
(b) 20
(c) 19
(d) 29
Ans. A
73. A cylinder is 6 cms in diameter and 6 cms in height. If spheres of the same size are made from the material obtained, what is the diameter of each sphere?
(a) 5 cms
(b) 2 cms
(c) 3 cms
(d) 4 cms
Ans C
74. A rectangular plank (2)1/2 meters wide can be placed so that it is on either side of the diagonal of a square shown below.(Figure is not available)What is the area of the plank?
Ans :7*(2)1/2
75. The difference b/w the compound interest payble half yearly and the simple interest on a
certain sum lent out at 10% p.a for 1 year is Rs 25. What is the sum?
(a) Rs. 15000
(b) Rs. 12000
(c) Rs. 10000
(d) none of these
Ans C
76. What is the smallest number by which 2880 must be divided in order to make it into a
perfect square ?

(a) 3
(b) 4
(c) 5
(d) 6
Ans. C
77. A father is 30 years older than his son however he will be only thrice as old as the son after 5 years
what is father’s present age ?

(a) 40 yrs
(b) 30 yrs
(c) 50 yrs
(d) none of these
Ans. A
78. An article sold at a profit of 20% if both the cost price and selling price would be Rs.20/- the profit would be 10% more. What is the cost price of that article?
29. If an item costs Rs.3 in ’99 and Rs.203 in ’00.What is the % increase in price?

(a) 200/3 %
(b) 200/6 %
(c) 100%
(d) none of these
Ans. A
80. 5 men or 8 women do equal amount of work in a day. a job requires 3 men and 5 women to finish the job in 10 days how many woman are required to finish the job in 14 days.

a) 10
b) 7
c) 6
d) 12
Ans 7
81. A simple interest amount of rs 5000 for six month is rs 200. what is the anual rate of interest?

a) 10%
b) 6%
c) 8%
d) 9%
Ans 8%
82. In objective test a correct ans score 4 marks and on a wrong ans 2 marks are —. a student score 480 marks from 150 question. how many ans were correct?
a) 120
b) 130
c) 110
d) 150
Ans130.
83. An artical sold at amount of 50% the net sale price is rs 425 .what is the list price of the artical?

a) 500
b) 488
c) 480
d) 510
Ans 500
84. A man leaves office daily at 7pm A driver with car comes from his home to pick him from office and bring back home
One day he gets free at 5:30 and instead of waiting for driver he starts walking towards home.
In the way he meets the car and returns home on car He reaches home 20 minutes earlier than usual.
In how much time does the man reach home usually??
Ans. 1hr 20min
85. A works thrice as much as B. If A takes 60 days less than B to do a work then find the number of days it would take to complete the work if both work together?
Ans. 22½days
86. How many 1’s are there in the binary form of 8*1024 + 3*64 + 3
Ans. 4
87. In a digital circuit which was to implement (A B) + (A)XOR(B), the designer implements (A B) (A)XOR(B)
What is the probability of error in it ?
88. A boy has Rs 2. He wins or loses Re 1 at a time If he wins he gets Re 1 and if he loses the game he loses Re 1.
He can loose only 5 times. He is out of the game if he earns Rs 5.
Find the number of ways in which this is possible?
Ans. 16
89. If there are 1024*1280 pixels on a screen and each pixel can have around 16 million colors
Find the memory required for this?
Ans. 4MB
90. On a particular day A and B decide that they would either speak the truth or will lie.
C asks A whether he is speaking truth or lying?
He answers and B listens to what he said. C then asks B what A has said B says “A says that he is a liar”
What is B speaking ?
(a) Truth
(b) Lie
(c) Truth when A lies
(d) Cannot be determined
Ans. (b)
91. What is the angle between the two hands of a clock when time is 8:30
Ans. 75(approx)
92. A student is ranked 13th from right and 8th from left. How many students are there in totality ?
93. A man walks east and turns right and then from there to his left and then 45degrees to
his right.In which direction did he go

Ans. North west
94. A student gets 70% in one subject, 80% in the other. To get an overall of 75% how much should get in third subject.
95. A man shows his friend a woman sitting in a park and says that she the daughter of my grandmother’s only son.
What is the relation between the two

Ans. Daughter

96. How many squares with sides 1/2 inch long are needed to cover a rectangle that is 4 ft long and 6 ft wide
(a) 24
(b) 96
(c) 3456
(d) 13824
(e) 14266
97. If a=2/3b , b=2/3c, and c=2/3d what part of d is b/
(a) 8/27
(b) 4/9
(c) 2/3
(d) 75%
(e) 4/3
Ans. (b)
2598Successive discounts of 20% and 15% are equal to a single discount of
(a) 30%
(b) 32%
(c) 34%
(d) 35%
(e) 36
Ans. (b)
99. The petrol tank of an automobile can hold g liters.If a liters was removed when the tank was full, what part of the full tank was removed?
(a)g-a
(b)g/a
(c) a/g
(d) (g-a)/a
(e) (g-a)/g
Ans. (c)
100. If x/y=4 and y is not ‘0’ what % of x is 2x-y

(a)150%
(b)175%
(c)200%
(d)250%

Ans. (b)
SET – 2
Aptitude Questions
1.If 2x-y=4 then 6x-3y=?
(a)15
(b)12
(c)18
(d)10

Ans. (b)
2.If x=y=2z and xyz=256 then what is the value of x?

(a)12
(b)8
(c)16
(d)6

Ans. (b)
3. (1/10)18 – (1/10)20 = ?
(a) 99/1020
(b) 99/10
(c) 0.9
(d) none of these
Ans. (a)
4.Pipe A can fill in 20 minutes and Pipe B in 30 mins and Pipe C can empty the same in 40 mins.If all of them work together, find the time taken to fill the tank
(a) 17 1/7 mins
(b) 20 mins
(c) 8 mins
(d) none of these
Ans. (a)
5. Thirty men take 20 days to complete a job working 9 hours a day.How many hour a day should 40 men work to complete the job?
(a) 8 hrs
(b) 7 1/2 hrs
(c) 7 hrs
(d) 9 hrs
Ans. (b)
6. Find the smallest number in a GP whose sum is 38 and product 1728
(a) 12
(b) 20
(c) 8
(d) none of these
Ans. (c)
7. A boat travels 20 kms upstream in 6 hrs and 18 kms downstream in 4 hrs.Find the speed of the boat in still water and the speed of the water current?
(a) 1/2 kmph
(b) 7/12 kmph
(c) 5 kmph
(d) none of these
Ans. (b)
8. A goat is tied to one corner of a square plot of side 12m by a rope 7m long.Find the area it can graze?
(a) 38.5 sq.m
(b) 155 sq.m
(c) 144 sq.m
(d) 19.25 sq.m
Ans. (a)
9. Mr. Shah decided to walk down the escalator of a tube station. He found that if he walks down 26 steps, he requires 30 seconds to reach the bottom. However, if he steps down 34 stairs he would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way in steps?
Ans.46 steps.
10. The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member ?
Ans.40 years.
11. Three containers A, B and C have volumes a, b, and c respectively; and container A is full of water while the other two are empty. If from container A water is poured into container B which becomes 1/3 full, and into container C which becomes 1/2 full, how much water is left in container A?
12. ABCE is an isosceles trapezoid and ACDE is a rectangle. AB = 10 and EC = 20. What is the length of AE?
Ans. AE = 10.
13. In the given figure, PA and PB are tangents to the circle at A and B respectively and the chord BC is parallel to tangent PA. If AC = 6 cm, and length of the tangent AP is 9 cm, then what is the length of the chord BC?
Ans. BC = 4 cm.
15 Three cards are drawn at random from an ordinary pack of cards. Find the probability that they will consist of a king, a queen and an ace.
Ans. 64/2210.
16. A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice. Each cat killed more mice than there were cats. How many cats do you think there were ?
Ans. 991.
17. If Log2 x – 5 Log x + 6 = 0, then what would the value / values of x be?
Ans. x = e2 or e3.
18. The square of a two digit number is divided by half the number. After 36 is added to the quotient, this sum is then divided by 2. The digits of the resulting number are the same as those in the original number, but they are in reverse order. The ten’s place of the original number is equal to twice the difference between its digits. What is the number?
Ans. 46
19.Can you tender a one rupee note in such a manner that there shall be total 50 coins but none of them would be 2 paise coins.?
Ans. 45 one paisa coins, 2 five paise coins, 2 ten paise coins, and 1 twenty-five paise coins.
20.A monkey starts climbing up a tree 20ft. tall. Each hour, it hops 3ft. and slips back 2ft. How much time would it take the monkey to reach the top?
Ans.18 hours.
21. What is the missing number in this series? 8 2 14 6 11 ? 14 6 18 12
Ans. 9
22. A certain type of mixture is prepared by mixing brand A at Rs.9 a kg. with brand B at Rs.4 a kg. If the mixture is worth Rs.7 a kg., how many kgs. of brand A are needed to make 40kgs. of the mixture?
Ans. Brand A needed is 24kgs.
23. A wizard named Nepo says “I am only three times my son’s age. My father is 40 years more than twice my age. Together the three of us are a mere 1240 years old.” How old is Nepo?
Ans. 360 years old.
24. One dog tells the other that there are two dogs in front of me. The other one also shouts that he too had two behind him. How many are they?
Ans. Three.
25. A man ate 100 bananas in five days, each day eating 6 more than the previous day. How many bananas did he eat on the first day?
Ans. Eight.
26. If it takes five minutes to boil one egg, how long will it take to boil four eggs?
Ans. Five minutes.
27. The minute hand of a clock overtakes the hour hand at intervals of 64 minutes of correct time. How much a day does the clock gain or lose?
Ans. 32 8/11 minutes.
28. Solve for x and y: 1/x – 1/y = 1/3, 1/x2 + 1/y2 = 5/9.
Ans. x = 3/2 or -3 and y = 3 or -3/2.
29. Daal is now being sold at Rs. 20 a kg. During last month its rate was Rs. 16 per kg. By how much percent should a family reduce its consumption so as to keep the expenditure fixed?
Ans. 20 %.
30. Find the least value of 3x + 4y if x2y3 = 6.
Ans. 10.
31. Can you find out what day of the week was January 12, 1979?
Ans. Friday.
32. A garrison of 3300 men has provisions for 32 days, when given at a rate of 850 grams per head. At the end of 7 days a reinforcement arrives and it was found that now the provisions will last 8 days less, when given at the rate of 825 grams per head. How, many more men can it feed?
Ans. 1700 men.
33. From 5 different green balls, four different blue balls and three different red balls, how many combinations of balls can be chosen taking at least one green and one blue ball?
Ans. 3720.
34. Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled?
Ans. 167 minutes.
35. A person walking 5/6 of his usual rate is 40 minutes late. What is his usual time? Ans. 3 hours 20 minutes.

36.For a motorist there are three ways going from City A to City C. By way of bridge the distance is 20 miles and toll is $0.75. A tunnel between the two cities is a distance of 10 miles and toll is $1.00 for the vehicle and driver and $0.10 for each passenger. A two-lane highway without toll goes east for 30 miles to city B and then 20 miles in a northwest direction to City C.

1. Which is the shortest route from B to C

(a) Directly on toll free highway to City C
(b) The bridge
(c) The Tunnel
(d) The bridge or the tunnel
(e) The bridge only if traffic is heavy on the toll free highway

Ans. (a)

2. The most economical way of going from City A to City B, in terms of toll and distance is to use the

(a) tunnel
(b) bridge
(c) bridge or tunnel
(d) toll free highway
(e) bridge and highway

Ans. (a)

3. Jim usually drives alone from City C to City A every working day. His firm deducts a percentage of employee pay for lateness. Which factor would most influence his choice of the bridge or the tunnel ?

(a) Whether his wife goes with him
(b) scenic beauty on the route
(c) Traffic conditions on the road, bridge and tunnel
(d) saving $0.25 in tolls
(e) price of gasoline consumed in covering additional 10 miles on the bridge

Ans. (a)

4. In choosing between the use of the bridge and the tunnel the chief factor(s) would be:
I. Traffic and road conditions
II. Number of passengers in the car
III. Location of one’s homes in the center or outskirts of one of the cities
IV. Desire to save $0.25

(a) I only
(b) II only
(c) II and III only
(d) III and IV only
(e) I and II only

Ans. (a)

37.The letters A, B, C, D, E, F and G, not necessarily in that order, stand for seven consecutive integers from 1 to 10
D is 3 less than A
B is the middle term
F is as much less than B as C is greater than D
G is greater than F

1. The fifth integer is
(a) A
(b) C
(c) D
(d) E
(e) F

Ans. (a)

2. A is as much greater than F as which integer is less than G
(a) A
(b) B
(c) C
(d) D
(e) E

Ans. (a)

3. If A = 7, the sum of E and G is
(a) 8
(b) 10
(c) 12
(d) 14
(e) 16

Ans. (a)

4. A – F = ?
(a) 1
(b) 2
(c) 3
(d) 4
(e) Cannot be determined

Ans. (a)

5. An integer T is as much greater than C as C is greater than E. T can be written as A + E. What is D?
(a) 2
(b) 3
(c) 4
(d) 5
(e) Cannot be determined

Ans. (a)

6. The greatest possible value of C is how much greater than the smallest possible value of D?
(a) 2
(b) 3
(c) 4
(d) 5
(e) 6

Ans. (a)

38.
1. All G’s are H’s
2. All G’s are J’s or K’s
3. All J’s and K’s are G’s
4. All L’s are K’s
5. All N’s are M’s
6. No M’s are G’s

1. If no P’s are K’s, which of the following must be true?

(a) All P’s are J’s
(b) No P is a G
(c) No P is an H
(d) If any P is an H it is a G
(e) If any P is a G it is a J

Ans. (a)

2. Which of the following can be logically deduced from the conditions stated?

(a) No M’s are H’s
(b) No M’s that are not N’s are H’s
(c) No H’s are M’s
(d) Some M’s are H’s
(e) All M’s are H’s

Ans. (a)

3. Which of the following is inconsistent with one or more of the conditions?

(a) All H’s are G’s
(b) All H’s that are not G’s are M’s
(c) Some H’s are both M’s and G’s
(d) No M’s are H’s
(e) All M’s are H’s

Ans. (a)

4. The statement “No L’s are J’s” is
I. Logically deducible from the conditions stated
II. Consistent with but not deducible from the conditions stated
III. Deducible from the stated conditions together with the additional statement “No J’s are K’s”

(a) I only
(b) II only
(c) III only
(d) II and III only
(e) Neither I, II nor III

Ans. (a)

39.In country X, democratic, conservative and justice parties have fought three civil wars in twenty years. TO restore stability an agreement is reached to rotate the top offices President, Prime Minister and Army Chief among the parties so that each party controls one and only one office at all times. The three top office holders must each have two deputies, one from each of the other parties. Each deputy must choose a staff composed of equally members of his or her chiefs party and member of the third party.

1. When Justice party holds one of the top offices, which of the following cannot be true

(a) Some of the staff members within that office are justice party members
(b) Some of the staff members within that office are democratic party members
(c) Two of the deputies within the other offices are justice party members
(d) Two of the deputies within the other offices are conservative party members
(e) Some of the staff members within the other offices are justice party members.

Ans. (a)

2. When the democratic party holds presidency, the staff of the prime minister’s deputies are composed
I. One-fourth of democratic party members
II. One-half of justice party members and one-fourth of conservative party members
III. One-half of conservative party members and one-fourth of justice party members.

(a) I only
(b) I and II only
(c) II or III but not both
(d) I and II or I and III
(e) None of these

Ans. (a)

3. Which of the following is allowable under the rules as stated:

(a) More than half of the staff within a given office belonging to a single party
(b) Half of the staff within a given office belonging to a single party
(c) Any person having a member of the same party as his or her immediate superior
(d) Half the total number of staff members in all three offices belonging to a single party
(e) Half the staff members in a given office belonging to parties different from the party of the top office holder in that office.

Ans. (a)

4. The office of the Army Chief passes from Conservative to Justice party. Which of the following must be fired.

(a) The democratic deputy and all staff members belonging to Justice party
(b) Justice party deputy and all his or hers staff members
(c) Justice party deputy and half of his Conservative staff members in the chief of staff office
(d) The Conservative deputy and all of his or her staff members belonging to Conservative party
(e) No deputies and all staff members belonging to conservative parties.

Ans. (a)

40.In recommendations to the board of trustees a tuition increase of $500 per year, the president of the university said “There were no student demonstrations over the previous increases of $300 last year and $200 the year before”. If the president’s statement is accurate then which of the following can be validly inferred from the information given:
I. Most students in previous years felt that the increases were justified because of increased operating costs.
II. Student apathy was responsible for the failure of students to protest the previous tuition increases.
III. Students are not likely to demonstrate over new tuition increases.

(a) I only
(b) II only
(c) I or II but not both
(d) I, II and III
(e) None

Ans. (a)

41. The office staff of XYZ corporation presently consists of three bookeepers–A, B, C and 5 secretaries D, E, F, G, H. The management is planning to open a new office in another city using 2 bookeepers and 3 secretaries of the present staff . To do so they plan to seperate certain individuals who don’t function well together. The following guidelines were established to set up the new office
I. Bookeepers A and C are constantly finding fault with one another and should not be sent together to the new office as a team
II. C and E function well alone but not as a team , they should be seperated
III. D and G have not been on speaking terms and shouldn’t go together
IV Since D and F have been competing for promotion they shouldn’t be a team
1.If A is to be moved as one of the bookeepers,which of the following cannot be a possible working unit.

A.ABDEH
B.ABDGH
C.ABEFH
D.ABEGH

Ans.B

2.If C and F are moved to the new office,how many combinations are possible

A.1
B.2
C.3
D.4

Ans.A

3.If C is sent to the new office,which member of the staff cannot go with C

A.B
B.D
C.F
D.G

Ans.B

4.Under the guidelines developed,which of the following must go to the new office

A.B
B.D
C.E
D.G

Ans.A

5.If D goes to the new office,which of the following is/are true

I.C cannot go
II.A cannot go
III.H must also go

A.I only
B.II only
C.I and II only
D.I and III only

Ans.D

42.After months of talent searching for an administrative assistant to the president of the college the field of applicants has been narrowed down to 5–A, B, C, D, E .It was announced that the finalist would be chosen after a series of all-day group personal interviews were held.The examining committee agreed upon the following procedure

I.The interviews will be held once a week
II.3 candidates will appear at any all-day interview session
III.Each candidate will appear at least once
IV.If it becomes necessary to call applicants for additonal interviews, no more 1 such applicant should be asked to appear the next week
V.Because of a detail in the written applications,it was agreed that whenever candidate B appears, A should also be present.
VI.Because of travel difficulties it was agreed that C will appear for only 1 interview.
1.At the first interview the following candidates appear A,B,D.Which of the follwing combinations can be called for the interview to be held next week.

A.BCD
B.CDE
C.ABE
D.ABC

Ans.B

2.Which of the following is a possible sequence of combinations for interviews in 2 successive weeks

A.ABC;BDE
B.ABD;ABE
C.ADE;ABC
D.BDE;ACD

Ans.C

3.If A ,B and D appear for the interview and D is called for additional interview the following week,which 2 candidates may be asked to appear with D?

I. A
II B
III.C
IV.E
A.I and II
B.I and III only
C.II and III only
D.III and IV only

Ans.D

4.Which of the following correctly state(s) the procedure followed by the search committee

I.After the second interview all applicants have appeared at least once
II.The committee sees each applicant a second time
III.If a third session,it is possible for all applicants to appear at least twice

A.I only
B.II only
C.III only
D.Both I and II

Ans.A

43. A certain city is served by subway lines A,B and C and numbers 1 2 and 3
When it snows , morning service on B is delayed
When it rains or snows , service on A, 2 and 3 are delayed both in the morning and afternoon
When temp. falls below 30 degrees farenheit afternoon service is cancelled in either the A line or the 3 line,
but not both.
When the temperature rises over 90 degrees farenheit, the afternoon service is cancelled in either the line C or the
3 line but not both.
When the service on the A line is delayed or cancelled, service on the C line which connects the A line, is delayed.
When service on the 3 line is cancelled, service on the B line which connects the 3 line is delayed.
Q1. On Jan 10th, with the temperature at 15 degree farenheit, it snows all day. On how many lines will service be
affected, including both morning and afternoon.
(A) 2
(B) 3
(C) 4
(D) 5
Ans. D

Q2. On Aug 15th with the temperature at 97 degrees farenheit it begins to rain at 1 PM. What is the minimum number
of lines on which service will be affected?
(A) 2
(B) 3
(C) 4
(D) 5
Ans. C

Q3. On which of the following occasions would service be on the greatest number of lines disrupted.
(A) A snowy afternoon with the temperature at 45 degree farenheit
(B) A snowy morning with the temperature at 45 degree farenheit
(C) A rainy afternoon with the temperature at 45 degree farenheit
(D) A rainy afternoon with the temperature at 95 degree farenheit
Ans. B

44. In a certain society, there are two marriage groups, red and brown. No marriage is permitted within a group. On marriage, males become part of their wives groups; women remain in their own group. Children belong to the same group as their parents. Widowers and divorced males revert to the group of their birth. Marriage to more than one person at the same time and marriage to a direct descendant are forbidden
Q1. A brown female could have had
I. A grandfather born Red
II. A grandmother born Red
III Two grandfathers born Brown
(A) I only
(B) III only
(C) I, II and III
(D) I and II only
Ans. D

Q2. A male born into the brown group may have
(A) An uncle in either group
(B) A brown daughter
(C) A brown son
(D) A son-in-law born into red group
Ans. A

Q3. Which of the following is not permitted under the rules as stated.
(A) A brown male marrying his father’s sister
(B) A red female marrying her mother’s brother
(C) A widower marrying his wife’s sister
(D) A widow marrying her divorced daughter’s ex-husband
Ans. B

Q4. If widowers and divorced males retained their group they had upon marrying which of the following would be permissible ( Assume that no previous marriage occurred)
(A) A woman marrying her dead sister’s husband
(B) A woman marrying her divorced daughter’s ex-husband
(C) A widower marrying his brother’s daughter
(D) A woman marrying her mother’s brother who is a widower.
Ans. D

Q5. I. All G’s are H’s
II. All G’s are J’s or K’s
III All J’s and K’s are G’s
IV All L’s are K’s
V All N’s are M’s
VI No M’s are G’s
45. There are six steps that lead from the first to the second floor. No two people can be on the same step
Mr. A is two steps below Mr. C
Mr. B is a step next to Mr. D
Only one step is vacant ( No one standing on that step )
Denote the first step by step 1 and second step by step 2 etc.
1. If Mr. A is on the first step, Which of the following is true?
(a) Mr. B is on the second step
(b) Mr. C is on the fourth step.
(c) A person Mr. E, could be on the third step
(d) Mr. D is on higher step than Mr. C.
Ans: (d)
2. If Mr. E was on the third step & Mr. B was on a higher step than Mr. E which step must be vacant
(a) step 1
(b) step 2
(c) step 4
(d) step 5
(e) step 6
Ans: (a)
3. If Mr. B was on step 1, which step could A be on?
(a) 2&e only
(b) 3&5 only
(c) 3&4 only
(d) 4&5 only
(e) 2&4 only
Ans: (c)
4. If there were two steps between the step that A was standing and the step that B was standing on, and A was on a higher step than D , A must be on step
(a) 2
(b) 3
(c) 4
(d) 5
(e) 6
Ans: (c)

5. Which of the following is false

i. B&D can be both on odd-numbered steps in one configuration
ii. In a particular configuration A and C must either both an odd numbered steps or both an even-numbered steps
iii. A person E can be on a step next to the vacant step.
(a) i only
(b) ii only
(c) iii only
(d) both i and iii
Ans: (c)

46. Six swimmers A, B, C, D, E, F compete in a race. The outcome is as follows.
i. B does not win.
ii. Only two swimmers separate E & D
iii. A is behind D & E
iv. B is ahead of E , with one swimmer intervening
v. F is a head of D
1. Who stood fifth in the race ?
(a) A
(b) B
(c) C
(d) D
(e) E
Ans: (e)
2. How many swimmers seperate A and F ?
(a) 1
(b) 2
(c) 3
(d) 4
(e) cannot be determined
Ans: (d)
3. The swimmer between C & E is
(a) none
(b) F
(c) D
(d) B
(e) A
Ans: (a)

4. If the end of the race, swimmer D is disqualified by the Judges then swimmer B finishes in which place
(a) 1
(b) 2
(c) 3
(d) 4
(e) 5
Ans: (b)
47. Five houses lettered A,B,C,D, & E are built in a row next to each other. The houses are lined up in the order A,B,C,D, & E. Each of the five houses has a colored chimney. The roof and chimney of each housemust be painted as follows.
i. The roof must be painted either green,red ,or yellow.
ii. The chimney must be painted either white, black, or red.
iii. No house may have the same color chimney as the color of roof.
iv. No house may use any of the same colors that the every next house uses.
v. House E has a green roof.
vi. House B has a red roof and a black chimney
1. Which of the following is true ?
(a) At least two houses have black chimney.
(b) At least two houses have red roofs.
(c) At least two houses have white chimneys
(d) At least two houses have green roofs
(e) At least two houses have yellow roofs
Ans: (c)
2. Which must be false ?
(a) House A has a yellow roof
(b) House A & C have different color chimney
(c) House D has a black chimney
(d) House E has a white chimney
(e) House B&D have the same color roof.
Ans: (b)
3. If house C has a yellow roof. Which must be true.
(a) House E has a white chimney
(b) House E has a black chimney
(c) House E has a red chimney
(d) House D has a red chimney
(e) House C has a black chimney
Ans: (a)
4. Which possible combinations of roof & chimney can house
I. A red roof 7 a black chimney
II. A yellow roof & a red chimney
III. A yellow roof & a black chimney

(a) I only
(b) II only
(c) III only
(d) I & II only
(e) I&II&III
Ans: (e)
48. Find x+2y
(i). x+y=10
(ii). 2x+4y=20
Ans: (b)

49. Is angle BAC is a right angle
(i) AB=2BC
(2) BC=1.5AC
Ans: (e)
50. Is x greater than y
(i) x=2k
(ii) k=2y
Ans: (e)

Aptitude Questions
Solve the following and check with the answers given at the end.

1. It was calculated that 75 men could complete a piece of work in 20 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?

2. A student divided a number by 2/3 when he required to multiply by 3/2. Calculate the percentage of error in his result.

3. A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 950gm. for a kg. His gain is …%.

4. A software engineer has the capability of thinking 100 lines of code in five minutes and can type 100 lines of code in 10 minutes. He takes a break for five minutes after every ten minutes. How many lines of codes will he complete typing after an hour?

5. A man was engaged on a job for 30 days on the condition that he would get a wage of Rs. 10 for the day he works, but he have to pay a fine of Rs. 2 for each day of his absence. If he gets Rs. 216 at the end, he was absent for work for … days.

6. A contractor agreeing to finish a work in 150 days, employed 75 men each working 8 hours daily. After 90 days, only 2/7 of the work was completed. Increasing the number of men by ________ each working now for 10 hours daily, the work can be completed in time.

7. what is a percent of b divided by b percent of a?
(a) a (b) b (c) 1 (d) 10 (d) 100

8. A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him was Rs._______ for the horse and Rs.________ for the cart.

9. A tennis marker is trying to put together a team of four players for a tennis tournament out of seven available. males – a, b and c; females – m, n, o and p. All players are of equal ability and there must be at least two males in the team. For a team of four, all players must be able to play with each other under the following restrictions:
b should not play with m,
c should not play with p, and
a should not play with o.
Which of the following statements must be false?
1. b and p cannot be selected together
2. c and o cannot be selected together
3. c and n cannot be selected together.

10-12. The following figure depicts three views of a cube. Based on this, answer questions 10-12.
10. The number on the face opposite to the face carrying 1 is _______ .

11. The number on the faces adjacent to the face marked 5 are _______ .

12. Which of the following pairs does not correctly give the numbers on the opposite faces.
(1) 6,5 (2) 4,1 (3) 1,3 (4) 4,2

13. Five farmers have 7, 9, 11, 13 & 14 apple trees, respectively in their orchards. Last year, each of them discovered that every tree in their own orchard bore exactly the same number of apples. Further, if the third farmer gives one apple to the first, and the fifth gives three to each of the second and the fourth, they would all have exactly the same number of apples. What were the yields per tree in the orchards of the third and fourth farmers?

14. Five boys were climbing a hill. J was following H. R was just ahead of G. K was between G & H. They were climbing up in a column. Who was the second?

15-18 John is undecided which of the four novels to buy. He is considering a spy
thriller, a Murder mystery, a Gothic romance and a science fiction novel. The books are written by Rothko, Gorky, Burchfield and Hopper, not necessary in that order, and published by Heron, Piegon, Blueja and sparrow, not necessary in that order.
(1) The book by Rothko is published by Sparrow.
(2) The Spy thriller is published by Heron.
(3) The science fiction novel is by Burchfield and is not published by Blueja.
(4)The Gothic romance is by Hopper.

15. Pigeon publishes ____________.

16. The novel by Gorky ________________.

17. John purchases books by the authors whose names come first and third in alphabetical order. He does not buy the books ______.

18. On the basis of the first paragraph and statement (2), (3) and (4) only, it is possible to deduce that
1. Rothko wrote the murder mystery or the spy thriller
2. Sparrow published the murder mystery or the spy thriller
3. The book by Burchfield is published by Sparrow.

19. If a light flashes every 6 seconds, how many times will it flash in ¾ of an hour?

20. If point P is on line segment AB, then which of the following is always true?
(1) AP = PB (2) AP > PB (3) PB > AP (4) AB > AP (5) AB > AP + PB

21. All men are vertebrates. Some mammals are vertebrates. Which of the following conclusions drawn from the above statement is correct.
All men are mammals
All mammals are men
Some vertebrates are mammals.
None

22. Which of the following statements drawn from the given statements are correct?
Given:
All watches sold in that shop are of high standard. Some of the HMT watches are sold in that shop.
a) All watches of high standard were manufactured by HMT.
b) Some of the HMT watches are of high standard.
c) None of the HMT watches is of high standard.
d) Some of the HMT watches of high standard are sold in that shop.

23-27.
1. Ashland is north of East Liverpool and west of Coshocton.
2. Bowling green is north of Ashland and west of Fredericktown.
3. Dover is south and east of Ashland.
4. East Liverpool is north of Fredericktown and east of Dover.
5. Fredericktown is north of Dover and west of Ashland.
6. Coshocton is south of Fredericktown and west of Dover.

23. Which of the towns mentioned is furthest of the north – west
(a) Ashland (b) Bowling green (c) Coshocton
(d) East Liverpool (e) Fredericktown

24. Which of the following must be both north and east of Fredericktown?
(a) Ashland (b) Coshocton (c) East Liverpool
I a only II b only III c only IV a & b V a & c

25. Which of the following towns must be situated both south and west of at least one other town?
A. Ashland only
B. Ashland and Fredericktown
C. Dover and Fredericktown
D. Dover, Coshocton and Fredericktown
E. Coshocton, Dover and East Liverpool.

26. Which of the following statements, if true, would make the information in the numbered statements more specific?
(a) Coshocton is north of Dover.
(b) East Liverpool is north of Dover
(c) Ashland is east of Bowling green.
(d) Coshocton is east of Fredericktown
(e) Bowling green is north of Fredericktown

27. Which of the numbered statements gives information that can be deduced from one or more of the other statements?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 6

28. Eight friends Harsha, Fakis, Balaji, Eswar, Dhinesh, Chandra, Geetha, and Ahmed are sitting in a circle facing the center. Balaji is sitting between Geetha and Dhinesh. Harsha is third to the left of Balaji and second to the right of Ahmed. Chandra is sitting between Ahmed and Geetha and Balaji and Eshwar are not sitting opposite to each other. Who is third to the left of Dhinesh?

29. If every alternative letter starting from B of the English alphabet is written in small letter, rest all are written in capital letters, how the month “ September” be written.
(1) SeptEMbEr (2) SEpTeMBEr (3) SeptembeR
(4) SepteMber (5) None of the above.

30. The length of the side of a square is represented by x+2. The length of the side of an equilateral triangle is 2x. If the square and the equilateral triangle have equal perimeter, then the value of x is _______.

31. It takes Mr. Karthik y hours to complete typing a manuscript. After 2 hours, he was called away. What fractional part of the assignment was left incomplete?

32. Which of the following is larger than 3/5?
(1) ½ (2) 39/50 (3) 7/25 (4) 3/10 (5) 59/100

33. The number that does not have a reciprocal is ____________.

34. There are 3 persons Sudhir, Arvind, and Gauri. Sudhir lent cars to Arvind and Gauri as many as they had already. After some time Arvind gave as many cars to Sudhir and Gauri as many as they have. After sometime Gauri did the same thing. At the end of this transaction each one of them had 24. Find the cars each originally had.

35. A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him was Rs._______ for the horse and Rs.________ for the cart.

Answers:

1. Answer:
30 days.
Explanation:
Before:
One day work = 1 / 20
One man’s one day work = 1 / ( 20 * 75)
Now:
No. Of workers = 50
One day work = 50 * 1 / ( 20 * 75)

The total no. of days required to complete the work = (75 * 20) / 50 = 30

2. Answer:
0 %
Explanation:
Since 3x / 2 = x / (2 / 3)

3. Answer:
5.3 %
Explanation:
He sells 950 grams of pulses and gains 50 grams.
If he sells 100 grams of pulses then he will gain (50 / 950) *100 = 5.26

4. Answer:
250 lines of codes

5. Answer:
7 days
Explanation:
The equation portraying the given problem is:
10 * x – 2 * (30 – x) = 216 where x is the number of working days.
Solving this we get x = 23
Number of days he was absent was 7 (30-23) days.

6. Answer:
150 men.
Explanation:
One day’s work = 2 / (7 * 90)
One hour’s work = 2 / (7 * 90 * 8)
One man’s work = 2 / (7 * 90 * 8 * 75)

The remaining work (5/7) has to be completed within 60 days, because the total number of days allotted for the project is 150 days.

So we get the equation

(2 * 10 * x * 60) / (7 * 90 * 8 * 75) = 5/7 where x is the number of men working after the 90th day.

We get x = 225
Since we have 75 men already, it is enough to add only 150 men.

7. Answer:
(c) 1
Explanation:
a percent of b : (a/100) * b
b percent of a : (b/100) * a
a percent of b divided by b percent of a : ((a / 100 )*b) / (b/100) * a )) = 1

8. Answer:
Cost price of horse = Rs. 400 & the cost price of cart = 200.
Explanation:-
Let x be the cost price of the horse and y be the cost price of the cart.
In the first sale there is no loss or profit. (i.e.) The loss obtained is equal to the gain.

Therefore (10/100) * x = (20/100) * y

X = 2 * y —————–(1)
In the second sale, he lost Rs. 10. (i.e.) The loss is greater than the profit by Rs. 10.

Therefore (5 / 100) * x = (5 / 100) * y + 10 ——-(2)
Substituting (1) in (2) we get
(10 / 100) * y = (5 / 100) * y + 10
(5 / 100) * y = 10
y = 200
From (1) 2 * 200 = x = 400

9. Answer:
3.
Explanation:
Since inclusion of any male player will reject a female from the team. Since there should be four member in the team and only three males are available, the girl, n should included in the team always irrespective of others selection.

10. Answer:
5

11. Answer:
1,2,3 & 4

12. Answer:
B

13. Answer:
11 & 9 apples per tree.
Explanation:
Let a, b, c, d & e be the total number of apples bored per year in A, B, C, D & E ‘s orchard. Given that a + 1 = b + 3 = c – 1 = d + 3 = e – 6
But the question is to find the number of apples bored per tree in C and D ‘s orchard. If is enough to consider c – 1 = d + 3.
Since the number of trees in C’s orchard is 11 and that of D’s orchard is 13. Let x and y be the number of apples bored per tree in C & d ‘s orchard respectively.
Therefore 11 x – 1 = 13 y + 3
By trial and error method, we get the value for x and y as 11 and 9

14. Answer:
G.
Explanation:
The order in which they are climbing is R – G – K – H – J

15 – 18
Answer:
Novel Name Author Publisher
Spy thriller Rathko Heron
Murder mystery Gorky Piegon
Gothic romance Burchfield Blueja
Science fiction Hopper Sparrow

Explanation:
Given
Novel Name Author Publisher
Spy thriller Rathko Heron
Murder mystery Gorky Piegon
Gothic romance Burchfield Blueja
Science fiction Hopper Sparrow

Since Blueja doesn’t publish the novel by Burchfield and Heron publishes the novel spy thriller, Piegon publishes the novel by Burchfield.
Since Hopper writes Gothic romance and Heron publishes the novel spy thriller, Blueja publishes the novel by Hopper.
Since Heron publishes the novel spy thriller and Heron publishes the novel by Gorky, Gorky writes Spy thriller and Rathko writes Murder mystery.

19. Answer:
451 times.
Explanation:
There are 60 minutes in an hour.
In ¾ of an hour there are (60 * ¾) minutes = 45 minutes.
In ¾ of an hour there are (60 * 45) seconds = 2700 seconds.
Light flashed for every 6 seconds.
In 2700 seconds 2700/6 = 450 times.
The count start after the first flash, the light will flashes 451 times in ¾ of an hour.
20. Answer:
(4)
Explanation:
P
A B
Since p is a point on the line segment AB, AB > AP

21. Answer: (c)

22. Answer: (b) & (d).
Ahmed
23 – 27.Answer:
Fakis Chandra
28. Answer: Fakis
Explanation: Harsha Geetha

Eswar Balaji

Dhinesh

29. Answer:
(5).
Explanation:
Since every alternative letter starting from B of the English alphabet is written in small letter, the letters written in small letter are b, d, f…
In the first two answers the letter E is written in both small & capital letters, so they are not the correct answers. But in third and fourth answers the letter is written in small letter instead capital letter, so they are not the answers.

30. Answer:
x = 4
Explanation:
Since the side of the square is x + 2, its perimeter = 4 (x + 2) = 4x + 8
Since the side of the equilateral triangle is 2x, its perimeter = 3 * 2x = 6x
Also, the perimeters of both are equal.
(i.e.) 4x + 8 = 6x
(i.e.) 2x = 8  x = 4.

31. Answer:
(y – 2) / y.
Explanation:
To type a manuscript karthik took y hours.
Therefore his speed in typing = 1/y.
He was called away after 2 hours of typing.
Therefore the work completed = 1/y * 2.
Therefore the remaining work to be completed = 1 – 2/y.
(i.e.) work to be completed = (y-2)/y

32. Answer:
(2)

33. Answer:
1
Explanation:
One is the only number exists without reciprocal because the reciprocal of one is one itself.

34. Answer:
Sudhir had 39 cars, Arvind had 21 cars and Gauri had 12 cars.
Explanation:
Sudhir Arvind Gauri

Finally 24 24 24
Before Gauri’s transaction 12 12 48
Before Arvind’s transaction 6 42 24
Before Sudhir’ s transaction 39 21 12

35. Answer:
Cost price of horse: Rs. 400 &
Cost price of cart: Rs. 200
Explanation:
Let x be the cost of horse & y be the cost of the cart.
10 % of loss in selling horse = 20 % of gain in selling the cart
Therefore (10 / 100) * x = (20 * 100) * y
 x = 2y ———–(1)
5 % of loss in selling the horse is 10 more than the 5 % gain in selling the cart.
Therefore (5 / 100) * x – 10 = (5 / 100) * y
 5x – 1000 = 5y
Substituting (1)
10y – 1000 = 5y
5y = 1000
y = 200
x = 400 from (1)

Exercise 2.1
For the following, find the next term in the series

1. 6, 24, 60,120, 210

a) 336 b) 366 c) 330 d) 660

Answer : a) 336
Explanation : The series is 1.2.3, 2.3.4, 3.4.5, 4.5.6, 5.6.7, ….. ( ‘.’ means product)

2. 1, 5, 13, 25

Answer : 41
Explanation : The series is of the form 0^2+1^2, 1^2+2^2,…

3. 0, 5, 8, 17

Answer : 24
Explanation : 1^2-1, 2^2+1, 3^2-1, 4^2+1, 5^2-1

4. 1, 8, 9, 64, 25 (Hint : Every successive terms are related)

Answer : 216
Explanation : 1^2, 2^3, 3^2, 4^3, 5^2, 6^3

5. 8,24,12,36,18,54

Answer : 27

6. 71,76,69,74,67,72
Answer : 67

7. 5,9,16,29,54
Answer : 103
Explanation : 5*2-1=9; 9*2-2=16; 16*2-3=29; 29*2-4=54; 54*2-5=103

8. 1,2,4,10,16,40,64 (Successive terms are related)
Answer : 200
Explanation : The series is powers of 2 (2^0,2^1,..).
All digits are less than 8. Every second number is in octal number system.
128 should follow 64. 128 base 10 = 200 base 8.

Exercise 2.2

Find the odd man out.

1. 3,5,7,12,13,17,19
Answer : 12
Explanation : All but 12 are odd numbers

2. 2,5,10,17,26,37,50,64
Answer : 64
Explanation : 2+3=5; 5+5=10; 10+7=17; 17+9=26; 26+11=37; 37+13=50; 50+15=65;

3. 105,85,60,30,0,-45,-90
Answer : 0
Explanation : 105-20=85; 85-25=60; 60-30=30; 30-35=-5; -5-40=-45; -45-45=-90;

Exercise 3
Solve the following.

1. What is the number of zeros at the end of the product of the numbers from 1 to 100?
Answer : 127
2. A fast typist can type some matter in 2 hours and a slow typist can type the same in 3 hours. If both type combinely, in how much time will they finish?
Answer : 1 hr 12 min
Explanation : The fast typist’s work done in 1 hr = 1/2
The slow typist’s work done in 1 hr = 1/3
If they work combinely, work done in 1 hr = 1/2+1/3 = 5/6
So, the work will be completed in 6/5 hours. i.e., 1+1/5 hours = 1hr 12 min

3. Gavaskar’s average in his first 50 innings was 50. After the 51st innings, his average was 51. How many runs did he score in his 51st innings. (supposing that he lost his wicket in his 51st innings)
Answer : 101
Explanation : Total score after 50 innings = 50*50 = 2500
Total score after 51 innings = 51*51 = 2601
So, runs made in the 51st innings = 2601-2500 = 101
If he had not lost his wicket in his 51st innings, he would have scored an unbeaten 50 in his 51st innings.

4. Out of 80 coins, one is counterfeit. What is the minimum number of weighings needed to find out the counterfeit coin?
Answer : 4

5. What can you conclude from the statement : All green are blue, all blue are red. ?
(i) some blue are green
(ii) some red are green
(iii) some green are not red
(iv) all red are blue
(a) i or ii but not both
(b) i & ii only
(c) iii or iv but not both
(d) iii & iv

Answer : (b)

6. A rectangular plate with length 8 inches, breadth 11 inches and thickness 2 inches is available. What is the length of the circular rod with diameter 8 inches and equal to the volume of the rectangular plate?
Answer : 3.5 inches
Explanation : Volume of the circular rod (cylinder) = Volume of the rectangular plate
(22/7)*4*4*h = 8*11*2
h = 7/2 = 3.5

7. What is the sum of all numbers between 100 and 1000 which are divisible by 14 ?
Answer : 35392
Explanation : The number closest to 100 which is greater than 100 and divisible by 14 is 112, which is the first term of the series which has to be summed.
The number closest to 1000 which is less than 1000 and divisible by 14 is 994, which is the last term of the series.
112 + 126 + …. + 994 = 14(8+9+ … + 71) = 35392

8. If s(a) denotes square root of a, find the value of s(12+s(12+s(12+ …… upto infinity.
Answer : 4
Explanation : Let x = s(12+s(12+s(12+…..
We can write x = s(12+x). i.e., x^2 = 12 + x. Solving this quadratic equation, we get x = -3 or x=4. Sum cannot be -ve and hence sum = 4.

9. A cylindrical container has a radius of eight inches with a height of three inches. Compute how many inches should be added to either the radius or height to give the same increase in volume?
Answer : 16/3 inches
Explanation : Let x be the amount of increase. The volume will increase by the same amount if the radius increased or the height is increased.
So, the effect on increasing height is equal to the effect on increasing the radius.
i.e., (22/7)*8*8*(3+x) = (22/7)*(8+x)*(8+x)*3
Solving the quadratic equation we get the x = 0 or 16/3. The possible increase would be by 16/3 inches.

10. With just six weights and a balance scale, you can weigh any unit number of kgs from 1 to 364. What could be the six weights?
Answer : 1, 3, 9, 27, 81, 243 (All powers of 3)

11. Diophantus passed one sixth of his life in childhood, one twelfth in youth, and one seventh more as a bachelor; five years after his marriage a son was born who died four years before his father at half his final age. How old is Diophantus?
Answer : 84 years
Explanation : x/6 + x/12 + x/7 + 5 + x/2 + 4 = x

12 . If time at this moment is 9 P.M., what will be the time 23999999992 hours later?
Answer : 1 P.M.
Explanation : 24 billion hours later, it would be 9 P.M. and 8 hours before that it would be 1 P.M.

13. How big will an angle of one and a half degree look through a glass that magnifies things three times?
Answer : 1 1/2 degrees
Explanation : The magnifying glass cannot increase the magnitude of an angle.

14. Divide 45 into four parts such that when 2 is added to the first part, 2 is subtracted from the second part, 2 is multiplied by the third part and the fourth part is divided by two, all result in the same number.
Answer: 8, 12, 5, 20
Explanation: a + b + c + d =45; a+2 = b-2 = 2c = d/2; a=b-4; c = (b-2)/2; d = 2(b-2); b-4 + b + (b-2)/2 + 2(b-2) = 45;

15. I drove 60 km at 30 kmph and then an additional 60 km at 50 kmph. Compute my average speed over my 120 km.
Answer : 37 1/2
Explanation : Time reqd for the first 60 km = 120 min.; Time reqd for the second 60 km = 72 min.; Total time reqd = 192 min
Avg speed = (60*120)/192 = 37 1/2

Questions 16 and 17 are based on the following :
Five executives of European Corporation hold a Conference in Rome
Mr. A converses in Spanish & Italian
Mr. B, a spaniard, knows English also
Mr. C knows English and belongs to Italy
Mr. D converses in French and Spanish
Mr. E , a native of Italy knows French

16. Which of the following can act as interpreter if Mr. C & Mr. D wish to converse
a) only Mr. A b) Only Mr. B c) Mr. A & Mr. B d) Any of the other three

Answer : d) Any of the other three.
Explanation : From the data given, we can infer the following.
A knows Spanish, Italian
B knows Spanish, English
C knows Italian, English
D knows Spanish, French
E knows Italian, French
To act as an interpreter between C and D, a person has to know one of the combinations Italian&Spanish, Italian&French, English&Spanish, English&French
A, B, and E know atleast one of the combinations.

17. If a 6th executive is brought in, to be understood by maximum number of original five he should be fluent in
a) English & French b) Italian & Spanish c) English & French d) French & Italian
Answer : b) Italian & Spanish
Explanation : No of executives who know
i) English is 2
ii) Spanish is 3
iii) Italian is 3
iv) French is 2
Italian & Spanish are spoken by the maximum no of executives. So, if the 6th executive is fluent in Italian & Spanish, he can communicate with all the original five because everybody knows either Spanish or Italian.

18. What is the sum of the first 25 natural odd numbers?
Answer : 625
Explanation : The sum of the first n natural odd nos is square(n).
1+3 = 4 = square(2) 1+3+5 = 9 = square(3)

19. The sum of any seven consecutive numbers is divisible by
a) 2 b) 7 c) 3 d) 11

Exercise 3
Try the following.

1. There are seventy clerks working in a company, of which 30 are females. Also, 30 clerks are married; 24 clerks are above 25 years of age; 19 married clerks are above 25 years, of which 7 are males; 12 males are above 25 years of age; and 15 males are married. How many bachelor girls are there and how many of these are above 25?

2. A man sailed off from the North Pole. After covering 2,000 miles in one direction he turned West, sailed 2,000 miles, turned North and sailed ahead another 2,000 miles till he met his friend. How far was he from the North Pole and in what direction?

3. Here is a series of comments on the ages of three persons J, R, S by themselves.
S : The difference between R’s age and mine is three years.
J : R is the youngest.
R : Either I am 24 years old or J 25 or S 26.
J : All are above 24 years of age.
S : I am the eldest if and only if R is not the youngest.
R : S is elder to me.
J : I am the eldest.
R : S is not 27 years old.
S : The sum of my age and J’s is two more than twice R’s age.
One of the three had been telling a lie throughout whereas others had spoken the truth. Determine the ages of S,J,R.

4. In a group of five people, what is the probability of finding two persons with the same month of birth?

5. A father and his son go out for a ‘walk-and-run’ every morning around a track formed by an equilateral triangle. The father’s walking speed is 2 mph and his running speed is 5 mph. The son’s walking and running speeds are twice that of his father. Both start together from one apex of the triangle, the son going clockwise and the father anti-clockwise. Initially the father runs and the son walks for a certain period of time. Thereafter, as soon as the father starts walking, the son starts running. Both complete the course in 45 minutes. For how long does the father run? Where do the two cross each other?

6. The Director of Medical Services was on his annual visit to the ENT Hospital. While going through the out patients’ records he came across the following data for a particular day : ” Ear consultations 45; Nose 50; Throat 70; Ear and Nose 30; Nose and Throat 20; Ear and Throat 30; Ear, Nose and Throat 10; Total patients 100.” Then he came to the conclusion that the records were bogus. Was he right?

7. Amongst Ram, Sham and Gobind are a doctor, a lawyer and a police officer. They are married to Radha, Gita and Sita (not in order). Each of the wives have a profession. Gobind’s wife is an artist. Ram is not married to Gita. The lawyer’s wife is a teacher. Radha is married to the police officer. Sita is an expert cook. Who’s who?

8. What should come next?
1, 2, 4, 10, 16, 40, 64,

Questions 9-12 are based on the following :
Three adults – Roberto, Sarah and Vicky – will be traveling in a van with five children – Freddy, Hillary, Jonathan, Lupe, and Marta. The van has a driver’s seat and one passenger seat in the front, and two benches behind the front seats, one beach behind the other. Each bench has room for exactly three people. Everyone must sit in a seat or on a bench, and seating is subject to the following restrictions: An adult must sit on each bench.
Either Roberto or Sarah must sit in the driver’s seat.
Jonathan must sit immediately beside Marta.

9. Of the following, who can sit in the front passenger seat ?
(a) Jonathan (b) Lupe (c) Roberto (d) Sarah (e) Vicky

10. Which of the following groups of three can sit together on a bench?
(a) Freddy, Jonathan and Marta (b) Freddy, Jonathan and Vicky
(c) Freddy, Sarah and Vicky (d) Hillary, Lupe and Sarah
(e) Lupe, Marta and Roberto

11. If Freddy sits immediately beside Vicky, which of the following cannot be true ?
a. Jonathan sits immediately beside Sarah
b. Lupe sits immediately beside Vicky
c. Hillary sits in the front passenger seat
d. Freddy sits on the same bench as Hillary
e. Hillary sits on the same bench as Roberto

12. If Sarah sits on a bench that is behind where Jonathan is sitting, which of the following must be true ?
a. Hillary sits in a seat or on a bench that is in front of where Marta is sitting
b. Lupe sits in a seat or on a bench that is in front of where Freddy is sitting
c. Freddy sits on the same bench as Hillary
d. Lupe sits on the same bench as Sarah
e. Marta sits on the same bench as Vicky

13. Make six squares of the same size using twelve match-sticks. (Hint : You will need an adhesive to arrange the required figure)

14. A farmer has two rectangular fields. The larger field has twice the length and 4 times the width of the smaller field. If the smaller field has area K, then the are of the larger field is greater than the area of the smaller field by what amount?
(a) 6K (b) 8K (c) 12K (d) 7K

15. Nine equal circles are enclosed in a square whose area is 36sq units. Find the area of each circle.

16. There are 9 cards. Arrange them in a 3*3 matrix. Cards are of 4 colors. They are red, yellow, blue, green. Conditions for arrangement: one red card must be in first row or second row. 2 green cards should be in 3rd column. Yellow cards must be in the 3 corners only. Two blue cards must be in the 2nd row. At least one green card in each row.

17. Is z less than w? z and w are real numbers.
(I) z2 = 25
(II) w = 9
To answer the question,
a) Either I or II is sufficient
b) Both I and II are sufficient but neither of them is alone sufficient
c) I & II are sufficient
d) Both are not sufficient

18. A speaks truth 70% of the time; B speaks truth 80% of the time. What is the probability that both are contradicting each other?

19. In a family 7 children don’t eat spinach, 6 don’t eat carrot, 5 don’t eat beans, 4 don’t eat spinach & carrots, 3 don’t eat carrot & beans, 2 don’t eat beans & spinach. One doesn’t eat all 3. Find the no. of children.

20. Anna, Bena, Catherina and Diana are at their monthly business meeting. Their occupations are author, biologist, chemist and doctor, but not necessarily in that order. Diana just told the neighbour, who is a biologist that Catherina was on her way with doughnuts. Anna is sitting across from the doctor and next to the chemist. The doctor was thinking that Bena was a good name for parent’s to choose, but didn’t say anything. What is each person’s occupation?

Posted by: SATYASRINIVAS | May 26, 2007

MCA, nitc 1999

CALICUT REGIONAL ENGINEERING COLLEGE
MCA ENTRANCE EXAMINATION, 1999
QUESTIONS

1. The number of divisors of 600 is
(A) 30 (B) 24 (C) 20 (D) 28
2. What is Hot Java
(A) a protocol (B) a compiler
(C) a version of Java (D) a browser
3. If by doubling the radius of a sphere, the ratio of the surface area
to the volume changes by _ times.
(A) 1 (B) 1/2 (C) 2 (D) 4
*4. The expression |~|_9.1_| / 2.1~| – |_|~8.5~| / 3.5_| evaluates to
(A) 3 (B) 2.1 (C) 2 (D) none of the above
5. The least positive integer ( mode 11) to which 282 is congruent
(A) 10 (B) 2 (C) 7 (D) 3
6. For which of the following applications is real time processing not
essential ?
(A) Guided missile control (B) intensive care monitoring
(C) traffic control (D) patient record
7. Let f(x) = x(x-1) + 1, 0 B is given by
(A) n! (B) n^m (C) m^n (D) nm
10. What is the name of the technique in which the operating system of a
computer executes several programs concurrently by switching back and
forth between them ?
(A) Partitioning (B) Multitasking (C) Windowing (D) Paging
11. Nine hundred n-digit numbers are to be formed using only the three digits
2, 5 and 7. The smallest value of n for which this is possible is
(A) 6 (B) 7 (C) 8 (D) 9
12. The binary representation of the hexadecimal number 3B7F is
(A) 0110100111101101 (B) 0011101101111111
(C) 01110111111111 (D) 001110011111111
13. If A is an n * n upper triangular matrix with diagonal entries 1, 2 … n,
then the sum of the eigen values of A is
(A) n(n+1)/2 (B) n (C) 2n (D) n!
14. Which of the following is an example of a problem-oriented language ?
(A) BASIC (B) PL/I (C) FORTRAN (D) none of the above
15. Which of the following is not a perfect number ?
(A) 28 (B) 496 (C) 1024 (D) 8128
16. For electronic mail service, TCP/IP provides
(A) SMTP (B) Telnet (C) HTTP (D) FTP
17. The highest power of 3 in 100! is
(A) 48 (B) 64 (C) 40 (D) 28
18. Data encryption techniques are particularly useful for
(A) reducing storage space requirements
(B) improving dat integrity
(C) protecting data in data communication systems
(D) all of the above
19. What set-theoretic expression is equal to A – ( B ^ C ) ?
( ^ = Intersection )
(A) ( A – B ) U ( A – C ) (B) ( A – B ) ^ ( A – C )
(C) ( A ^ B ) – ( A ^ C ) (D) ( A U B ) – ( A U C )
20. Which of the following might prevent a successful program being modified
in the future ?
(A) logic errors (B) semantic errors
(C) lack of program documentation (D) syntax errors

21. “Mathematics is the queen of sciences and number theory is the queen of
mathematics”. The above statement is due to
(A) George Boole (B) Pierre de Fermat
(C) Karl F. Gauss (D) Giuseppe Peano
22. The compiler produce diagnostic messages identifying
(A) syntactic errors (B) logic errors
(C) both syntactic and logic errors (D) none of the above
23. Let x > y > z. Then
(A) ( x + z ) / ( y + z ) 1
(C) y + z > x (D) none of the above
24. A computer with a 32-bit word size uses 2’s complement to represent
numbers. The range of integers that can be represented by this
computer is
(A) -2^32 to 2^32-1 (B) -2^31 to 2^32
(C) -2^31 to 2^31-1 (D) -2^32 to 2^31
25. Sum of the internal angles of a 10 polygon is
(A) 8 pi (B) 9 pi (C) 10 pi (D) 5 pi
26. The correct hierarchical relationships among context-free, right-linear,
and context-sensitive languages is given by ( C = subset )
(A) context-free C context-sensitive C right-linear
(B) context-sensitive C context-free C right-linear
(C) context-sensitive C right-linear C context-free
(D) right-linear C context-free C context-sensitive
27. The number of circles passing through three points in a plane if they
are not collinear is
(A) 1 (B) 3 (C) infinitely many (D) none of the above
28. To see whether a remote computer is responding, which should we use ?
(A) cat (B) who (C) ping (D) pwd
29. If y = x^y, then dy/dx is equal to
(A) y^2/x + y*log x (B) y^2 / ( 1-log y)x
(C) y x^(y-1) (D) none of the above
30. Which of the following is not output device of a computer ?
(A) printer (B) keyword (C) VDU (D) CRT screen
31. When a language has the capability to produce new data types, it is
said to be
(A) reprehensible (B) encapsulated
(B) overloaded (D) extensible
32. Two oranges, three bananas and four apples cost Rs.30/-, and four oranges,
three bananas and two apples also cost Rs.30/-. Then how much two oranges,
two bananas and two apples
(A) Rs.10/- (B) Rs.20/- (C) Rs.30/- (D) Rs.40/-
33. If the third term of a GP is x, then the product of the first 5 terms is
(A) x^5 (B) 5x (C) x^4 (D) none of the above
34. Four 256 * 8 PROM chips are used to produce a total capacity of 1024 * 8.
What is the address bus width required ?
(A) 4 (B) 8 (C) 10 (D) 16
35. If ( x + 1/x)^2 = 3, then x^3 + 1/x^3 =
(A) 3 * sqrt(2) (B) 0 (C) 4^3 (D) none of the above
36. How many boolean functions of 3 variables are there ?
(A) 16 (B) 64 (C) 256 (D) 512
37. If x satisfies e^(-x) = -1 and x is real, then
(A) x > 0 (B) x y
(C) x = y (D) Need to know the initial amount of petrol and diesel
67. A cube is coloured in red except one face. Then the cube is cut into 27
small cubes of equal size. Then the number of cubes without red colour on
any of its faces is
(A) 1 (B) 2 (C) 3 (D) none of the above
68. The compressibility factor of an ideal gas is
(A) 1.5 (B) 1.0 (C) 2.0 (D) Infintiy
69. Complete the title of the play “….. of Windsor”( by William Shakespeare)
(A) Nights (B) Castle (C) The Merry Wives (D) Dreams
70. Consider the four vertices and the meeting point of the diagonals of a
square. What is the maximum number of triangles that can be formed using
these points.
(A) 8 (B) 6 (C) 4 (D) none of the above
71. World’s deepest lake is
(A) Caspian Sea (B) Dead Sea (C) Lake Superior (D) Lake Baikal
72. p-chloraniline and anilinium hydrochloride can be distinguished by
(A) AgN(O)3 (B) Sandmeyer reaction
(C) NaHC(O)3 (D) carbylamine test
73. What is the currency of Brazil ?
(A) Peseta (B) Escudos (C) Real (D) Shilling
74. Find the Nobel laurete who bagged Nobel Prize in a discipline different
from others
(A) Emest Rutherford (B) William Shockley
(C) Ervin Schrodinger (D) Niels Bohr
75. The green coloured powder blown in the air in ammonium dichromate based
fire works is
(A) Cr(O)3 (B) (Cr)2(O)3 (C) Cr (D) CrO(O)2
76. Who discovered planet Pluto
(A) Tombaugh (B) George Gammo
(C) Reiph Athfer (D) Galileo
77. In which city, Indian Standard Time (IST) is recorded ?
(A) New Delhi (B) Nagpur (C) Calcutta (D) Allahabad
78. The work function of a substance is 4 eV. The longest wavelength of light
that can cause photoelectric emission from this substance is approximately
(A) 310nm (B) 540nm (C) 400nm (D) 220nm
79. The headquarters of Amnesty International is at
(A) New York (B) Montreal (C) London (D) Geneva
80. A cylindrical can filled with water to a height of 40 cm has on its side
two small holes of equal area, one at a height of 10 cm and the other at
a height of 30 cm. At the initial time, what is the ratio of the mass of
water flowing per second through the lower hole to that flowing through
the upper hole ?
(A) sqrt(3) (B) sqrt(2) (C) 1/3 (D) none of the above
81. The list of The Wonders of the World was revised in 1931. Which of the
following is not included in this revised list of The Seven Wonders of
the Modern Period ?
(A) Eiffel Tower (B) Taj Mahal
(C) Great Wall of China (D) Hagea Sophia
82. How much energy (in joules) would be released if a meteor of 1 kg of
antimatter were to hit the earth ?
(A) 3 x 10^8 (B) 3 x 10^16 (C) 9 x 10^64 (D) 1.8 x 10^17
83. With what sports the “Irani Cup” associated
(A) Hockey (B) Lawn Tennis (C) Foot Ball (D) Cricket
84. A person aims a gun at a bird on the ground from a horizontal distance
of 100m. If the gun can impart a velocity of 500 m/s to the bullet, at
what height above the ground must he aim his gun to hit the bird ?
(A) 10 cm (B) 20 cm (C) 50 cm (D) 100 cm
85. The Latin phrase “Anno Domini” stands for
(A) After Christ (B) In the year of our Lord
(C) After Domini (D) Roman Calendar
86. The intensity of radiation emitted by the Sun has its maximum value at
a wavelength of 510 nm and that emitted by the North Star has the maximum
value at 350 nm. If these stars behave like black bodies, then the ratio
of the surface temperature of the Sun and North Star is
(A) 1.46 (B) 0.69 (C) 1.21 (D) 0.83
87. Which of the following will react with water ?
(A) CH(Cl)3 (B) (Cl)3CCHO (C) C(Cl)4 (D) ClC(H)2C(H)2Cl
88. A blackbody is at a temperature of 2880 K. The energy of radiation emitted
by this object with wavelength between 499 nm and 500 nm is U1, between
999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien
constant b = 2.88 x 10^6 nmK. Then
(A) U1 = 0 (B) U3 = 0 (C) U1 > U2 (D) U2 > U1
89. Of the following cycloalkanes, which one is expected to have the largest
negative value of enthalpy of combustion ?
(A) cyclohexane (B) cyclobutane
(C) cyclopropane (D) cyclopentane
90. The two rails of a railway track are insulated from each other and from
ground and are connected by a millivoltmeter. What is the reading when
a train travels 180 km/hr down the track, assuming that the vertical
component of the earth’s field is 0.2 gauss and that the tracks are
separated by one metre ?
(A) 3.6 * 10^(-3) V (B) 10^(-3) V
(C) 9 * 10^(-3) V (D) none of the above
91. Of the following elements, which has the minimum value of first
ionization enthalpy ?
(A) B (B) Be (C) C (D) N
92. A travelling wave in a stretched string is described by the equation
y = A sin( kx – wt). The maximum particle velocity is
(A) x/t (B) w/x (C) Aw (D) none of the above

93. Which is the oldest Veda ?
(A) Yajurveda (B) Rigveda (C) Samaveda (D) Atharvaveda
94. What would be the approximate length of one day if the earth spun so fast
that bodies floated at the equator( the radius of the earth is 6.4*10^6 m)
(A) 3 hours (B) 2 hours (C) 1.5 hours (D) 0.5 hours
95. The Xe atom in Xe(F)2 is
(A) sp hybridised (B) sp^2 hybridised
(C) sp^2d hybridised (D) sp^3 hybridised
96. Which city is known as “The City of Golden Gate” ?
(A) Johannesburg (B) Los Angeles (C) Sao Paulo (D) San Francisco
97. Which of the following is an organometallic compound?
(A) lithium methoxide (B) lithium acetate
(C) lithium dimethylamide (D) methyl lithium
98. An artificial satellite moving in a circular orbit around earth has a
total ( kinetic + potential ) energy Eo. Its potential energy is
(A) 2Eo (B) 1.5Eo (C) Eo (D) -Eo
99. Of the following molecules, which one has minimum vibrational degree
of freedom ?
(A) HCN (B) (N)2O (C) N(O)2 (D) C(O)2
100. Pyrophosphoric acid is a
(A) monobasic acid (B) dibasic acid
(C) tribasic acid (D) tetrabasic acid

********* ANSWERS ***********

1. B 21. C 41. C 61. C 81. C
2. D 22. A 42. B 62. B 82. D
3. B 23. D 43. D 63. B 83. D
4. A 24. C 44. B 64. A 84. B
5. C 25. A 45. C 65. A 85. B
6. D 26. D 46. B 66. C 86. B
7. B 27. A 47. D 67. B 87. B
8. A 28. C 48. B 68. B 88. D
9. B 29. B 49. B 69. C 89. A
10. B 30. B 50. B 70. A 90. B
11. B 31. D 51. A 71. D 91. A
12. B 32. B 52. D 72. A 92. C
13. A 33. A 53. A 73. C 93. A
14. D 34. C 54. D 74. A 94. C
15. C 35. B 55. D 75. B 95. D
16. A 36. C 56. C 76. A 96. D
17. A 37. D 57. A 77. D 97. D
18. C 38. B 58. A 78. A 98. A
19. A 39. A 59. C 79. C 99. C
20. C 40. A 60. C 80. A 100. D

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Posted by: SATYASRINIVAS | May 26, 2007

MCA 2000

CALICUT REGIONAL ENGINEERING COLLEGE

MCA ENTRANCE EXAMINATION,2000
QUESTIONS
1 OCT 2000.

1. The maximum degree of any node in a simple graph with n vertices is
(A) n-1 (B) n (C) n/2 (D)n-2

2. The function f(x) = 1/x in (0,1) is
(A) continuous and bounded (B) bounded but not continuous
(C) continuous but not bounded (D) neither bounded nor continuous

3. The parity bit is added to a message for
(A) encryption (B) indexing (C) error detection (D) route control

4. The function f(x) = { x, x>=1 at x=1 is
{ x^2, xINF [ 1^k + 2^k +… +n^k] / n^(k+1) for positive rational k is
(A) 1 / (1+k^2) (B) 1 / (1+k) (C) k / (1+k^2) (D) k / (1+k)

28. Let A be a sorted array with n = 10 elements. Which of the following
denotes the average successful time for finding an arbitrary elements
x in A using a binary search? Assume that only one comparision is
required to determine whether the target is equal to, less than,
or greater than A[i].
(A) 1.6 (B) 2.9 (C) 5.5 (D) 10

29. The interval of convergence of summation (1 to infinite) of x^n /n is
(A) [1,-1] (B) [-1,1) (C) (-1,1] (D) (-1,1)

30. A decimal number has 30 digits. Approximatly, how many bits would
its binary representation have?
(A) 60 (B) 90 (C) 120 (D) 150

31. For a series, Summation An to converge, Lim ( n -> INF ) An = 0 is
(A) necessary and sufficient (B) necessary but not sufficient
(C) sufficient but not necessary (D) neither necessary nor sufficient

32. The average time required to perform a successful sequential search
for an element in an array A(1:n) is given by
(A) (n+1)/2 (B) n(n+1)/2 (C) log(2)n (D) n^2

33. Let a > 0, X1 > 0. The sequence is defined by
X(n+1) =(Xn + a/Xn)/2. Then Lim( n -> INF ) Xn =
(A) – sqrt(a) (B) sqrt(a) (C) a (D) -a

34. Let B be an invertible linear transformation in R^3. Then the rank of
the matrix of B is
(A) 0 (B) 1 (C) 2 (D) 3

35. Classes are useful because they
(A) permit data to be hidden from other classes
(B) bring together all aspects of an entity in one place
(C) can closely model objects in the real world
(D) all of the above

36. If x, y, z are vectors in a vector space with x + y + z = 0, then
the subspace spanned by x, y and z is at most
(A) 0 (B) 1 (C) 2 (D) 3

37. The language used in application programs to request data from the
DBMS is referred to as the
(A) DML (B) DDL (C) HDL (D) all of the above

38. Which of the following is not a characteristic of a relational
database model?
(A) tables (B) treelike structure (C) records (D) fields

39. Sand falls into a conical pile at the rate of 10 * 3.14 m^3 / min.
The radius of the base of the pile is always equal to one half of
its altitude. When the height of the pile is 5m the rate of increase
of height of the pile is
(A) 2/5 m/min (B) 4/5 m/min (C) 6/5 m/min (D) 8/5 m/min

40. The operating system of a computer serves as a software interface
between the user and
(A) peripheral (B) hardware (C) memory (D) screen

41. Identify from the following, the average which is greatly affected by
extreme values:
(A) median (B) geometric mean (C) arithmetic mean (D) mode

42. A distribution with the quartiles Q1 = 25.8, Q2 = 49.0 and Q3 = 64.2 is
(A) positively skewed (B) negatively skewed
(C) symmetric (D) none of the above

43. A distribution with M2 = 1.4, M3 = -0.2 and M4 = 8.5 is ( M = mue )
(A) leptokurtic (B) platykurtic (C) mesokurtic (D) none of the above

44. X and Y are events with P(X) = 1/3, P(Y) = 1/4 and P(X U Y) = 1/2.
P( X/(Y^C) ) equals
(A) 1/6 (B) 1/5 (C) 1/4 (D) 1/3

45. A committee of 6 is to be formed from 5 students and 3 teachers. If
the members of the committee are chosen at random, the probability that
there will be a majority of students on the committee is
(A) 5/14 (B) 7/14 (C) 9/14 (D) 11/14

46. There are two bags one of which contains 5 red and 6 green balls and
the other 8 red and 4 green balls. If a ball is drawn at random from
one of these bags, the probability that it is green is
(A) 29/66 (B) 29/33 (C) 3/11 (D) 1/6

47. During a war, 1 ship in 10 would be sunk on the average in making a
certain voyage. The probability that exactly 3 out of a convoy of 6
ships making that voyage would arrive safely is
(A) 0.01234 (B) 0.01364 (C) 0.01458 (D) 0.01642

48. A die is loaded in such a way that each odd number is twice likely to
occur as an even number. What is the probability that in a throw of
the die, a number greater than 3 appears?
(A) 4/9 (B) 3/5 (C) 1/2 (D) 3/10

49. The value of k for which the function f(x,y) = kxy for x = 1,2 and
y = 1,2 can serve as a joint probability density function is
(A) 4/9 (B) 4/10 (C) 2/3 (D) 1/9

50. A bin with 100 balls contains 25 red balls. If 20 balls are chosen at
random, what is the expected number of red balls?
(A) 4 (B) 5 (C) 10 (D) 12

51. Tom flips one fair coin. Jerry flips two fair coins. What is the
probability that Jerry gets more heads than Tom?
(A) 1/2 (B) 1/3 (C) 3/4 (D) 1/4

52. A particle executing simple harmonic motion has an acceleration of
1.92 m/s^2 when its displacement is 0.12 m. Its time period is (# = 3.14)
(A) #/4 sec (B) #/2 (C) # sec (D) 2#sec

53. The number of positive integers not exceeding 100 which are relatively
prime to 100 is
(A) 10 (B) 20 (C) 30 (D) 40

54. A thin transparent sheet of thickness 2 * 10^(-6) m and refractive index
1.6 is introduced in the path of one of the interfering beams. The wave
length of light used is 6000 A(o). The central bright maximum will shift
through a distance equal to the width of
(A) 10 fringes (B) 5 fringes (C) 2 fringes (D) 20 fringes

55. The sum 2^n + 2^(n+1) + … + 2^(2n) is equal to
(A) 2^(n+1) – 2^n (B) 2^(2n+1) – 1
(C) 2^(2n+2) – 2 (D) 2^(2n+1) – 2^n

56. Two plates of the same area and same thickness form a composite insulating
plate, the temperature on one side of which is zero degree C and that on
the other side is 60 degree C. If ratio of thermal conductivities is 3:1
and the more conducting plate faces zero degree C, the temperature of the
interface is
(A) 45 d C (B) 40 d C (C) 20 d C (D) 15 d C

57. The coefficient of (x^3)y(z^2) in the expansion of (x+y+z)^6 is
(A) 20 (B) 36 (C) 60 (D) 72

58. The activity of a radio active sample goes down to about 3% in a time of
3 hours. The half life of the sample in minutes is about
(A) 36 (B) 18 (C) 72 (D) 144

59. How many different permutations can be formed with letters of the word
‘hello’ ?
(A) 24 (B) 60 (C) 72 (D) 120

60. The rest mass of an electron is Mo. If it is moving with a velocity
v = 0.6c where c is the velocity of light, its mass becomes
(A) (0.8)Mo (B) (0.6)Mo (C) Mo/(0.8) (D) Mo/(0.6)

61. Who founded the Asiatic Society of Calcutta ?
(A) Lord Wavel (B) William Jones
(C) Max Muller (D) Robert Clive

62. The amplification factor of a triode is 10 and its mutual conductance is
2 * 10^(-3) A/V. The plate resistance of the triode is
(A) 5 * 10^3 Ohm (B) 20 * 10^3 Ohm
(C) 2.5 * 10^3 Ohm (D) 25 * 10^3 Ohm

63. ‘Caesar and Cleopatra’ is a play written by
(A) Christopher Marlowe (B) William Shakespeare
(C) Bernard Shaw (D) John Galsworthy

64. The intrinsic conductivity of Ge at room temperature is 2.12/Ohm/m and
the mobilities of electrons and holes are 0.36m^2/V/s and 0.17m^2/V/s
respectively. The density of carriers is
(A) 2.5 * 10^19 m^(-3) (B) 3.75 * 10^19 m^(-3)
(C) 1.8 * 10^19 m^(-3) (D) 5.0 * 10^19 m^(-3)

65. The highest mountain peak in the Western Hemisphere is
(A) Mt. Kilimanjaro (B) Mt. McKinley
(C) Mt.Aconcagua (D) Mt.Blanc

66. When the cold junction of a thermocouple is kept at 0 degree C, the
neutral temperature is 90 degree C and the temperature of inversion
is 180 degr C. When the temperature of the cold junction is increased
to 30 deg C, the neutral temperature and the temperature of inversion
of the thermocouple will be respectively
(A) 90 deg C and 150 deg C (B) 90 deg C and 180 deg C
(C) 120 deg C and 210 deg C (D) 120 deg C and 180 deg C

67. What is the distance of Marathone track ?
(A) 22.195km (B) 26.2km (C) 38.3km (D) 42.2km

68. The inductance of a coil in which a current of 0.2 A yields and energy
storage of 0.2J is
(A) 1 H (B) 10 H (C) 4 H (D) 20 H

69. Which is the longest National Highway in India ?
(A) NH-2 (B) NH-5 (C) NH-7 (D) NH-17

70. A 1000 W heating unit is designed to operate on a 120 V line. The line
voltage drops to 110 V. The percentage of heat output drop by about
(A) 9% (B) 27% (C) 16% (D) 30%

71. Suez Canal was opened in which year ?
(A) 1956 (B) 1889 (C) 1869 (D) 1909

72. If a bulb is placed between two plane mirrors inclined at 60 deg C, the
number of images formed will be
(A) 2 (B) 4 (C) 5 (D) 6

73. Which one of the following is known as ‘Sorrow of Bihar’ ?
(A) Damodar (B) Gandak (C) Kosi (D) Sone

74. Two bodies A and B having masses m and M respectively possess the same
kinetic energy, given the M > m. If Pa and Pb be their momenta, then
which of the following statements is true ?
(A) Pa = Pb (B) Pa > Pb
(C) Pa/Pb = sqrt(m/M) (D) m * Pa = M * Pb

75. The tape of tape recorder is coated with
(A) copper sulphate (B) ferro magnetic powder
(C) silica (D) zinc sulphide

76. A note produces 4 beats/sec with a tuning fork of frequency 512 Hz and
6 beats/sec with a fork of frequency 514 Hz. The frequency of the note is
(A) 516 Hz (B) 520 Hz (C) 524 Hz (D) 508 Hz

77. A bang occurs in an electric bulb when it breaks
(A) due to high pressure within
(B) due to the rushing of air to fill up the vaccum
(C) due to the combining of two gases
(D) none of the above

78. A sphere of brass released in a long liquid column attains a terminal
speed Vo. If the terminal speed attained by a sphere of marble of the same
radius and released in the same liquid is nVo, then the value of n will
be ( relative densities of brass, marble and the liquid are 8.5, 2.5
and 0.8 respectively )
(A) 5 /17 (B) 11/31 (C) 17/77 (D) 17/5

79. ‘Tripitakas’ are the sacred books of the
(A) Hindus (B) Parsis (C) Jains (D) Buddhists

80. Two capacitors ( 2 micro F and 4 micro F) are connected in parallel
across a 300 V potential difference. The total energy stored in the
system is
(A) 0.27 J (B) 2.7 J (C) 27 J (D) 270 J

81. Which of the following numbers belong to the series 9, 22, 35, 48 … ?
(A) 189 (B) 511 (C) 3259 (D) 433

82. The solubility of a gas in a liquid is proportional to the partial
pressure of the gas. This law is known as
(A) Avagadro’s law (B) Dalton’s law
(C) Henry’s law (D) vant Hoff’s law

83. If AIRCRAFT is coded as YZXPXYSU and CAKE as PYNV, how is CRICKET to be
coded in that code ?
(A) PXZPNVU (B) PXZNPUV (C) PXZNVUP (D) PXZPUNV

84. An increase in entropy of the universe occurs when the free energy
(A) increases (B) decreases
(C) increases initially and then decreases (D) does not change

85. Pointing to a man, a woman said, “His mother is the only daughter-in-law
of my mother-in-law”. How was the man related to the woman ?
(A) father (B) sister’s husband (C) son (D) brother

86. If the signs + and / and numbers 8 and 4 are interchanged, which one of
the four equations will be correct ?
(A) 8 + 4 / 3 = 4 (B) 4 / 8 + 4 = 8.5
(C) 8 / 4 + 4 = 6 (D) 4 + 8 / 1 = 4

87. Ni ion in solution can be tested with the help of
(A) methylene blue (B) rhodamine – B
(C) dimethylamide (D) dimethyl glyoxime

88. Ramesh was born on May 17, 1984. Suresh was born 6 days earlier. If the
Republic day of India that year was on a Wednesday, on what day was Suresh
born ?
(A) Thursday (B) Tuesday (C) Sunday (D) Saturday

89. The knocking property of a sample of petrol can be reduced by the
addition of
(A) diethyl lead (B) tetra ethyl lead
(C) ethyl bromide (D) ethylene dibromide

90. Vivek is taller than Rahul who is shorter than Rajeev. Varun is taller
than Anand but shorter than Rahul. Rajeev is taller than than Vivek.
Who is the shortest of all ?
(A) Anand (B) Rajeev (C) Rahul (D) Varun

91. The degree of freedom, F of the dehydration of hydrated copper sulphate is
(A) 0 (B) 1 (C) 2 (D) 3

92. A lady is now 5 times as old as her son and 10 years younger than her
husband. If her son will be 15, eight years hence, the present age of
her husband is
(A) 45 (B) 35 (C) 55 (D) 50

93. When the partial molar enthalpy of solution of a substance is positive,
the solubility of the substance
(A) increases with increasing temperature
(B) increases with decreasing temperature
(C) decreases with increasing temperature
(D) remains the same.

94. ‘P x Q’ means ‘P is the wife of Q’, ‘P * Q’ means ‘P is the brother of Q’,
‘P + Q’ means ‘P is the father of Q’, and ‘P / Q’ means ‘P is the sister
of Q’. Which of the following codes means, “R is the maternal uncle of P” ?
(A) N x R + P / Q (B) R * Q + P / S
(C) R + A x N / P (D) R * N x Q + P

95. A crystalline form X of a mineral of ( SiO)2 on heating below 870 deg C
temperature gives another crystalline form Y, which is a three dimensional
network of ( SiO)4 tetrahedra. The form Y is
(A) quartz (B) tridynamite (C) wurtzite (D) cristobalite

96. One of the days of the week is coded as VDCMDRCZX. In the same system,
how will the month “AUGUST” be coded ?
(A) ZVHVTU (B) ZVHVRS (C) ZTFTRS (D) ZTFRST

97. The main ingredient of Benedicts solution is
(A) sodium citrate (B) sodium tartrate
(C) copper sulphate (D) chromium sulphate

98. The stability of a conjugated cyclic organic molecule is attributed to
(A) delocalisation of pi electrons (B) localisation of pi electrons
(C) high resonance energy (D) presence of multiple bonds

99. To avoid paying toll tax on a direct, straight line road AB, a man starts
from A and drives 10 km south, then 8 km west, then 10 km south, then
48 km east and then 50 km north and reaches B. What is the length of
the direct road AB ?
(A) 126 km (B) 50 km (C) 40 km (D) 28 km

100. The antibiotic drug penicillin contains the following elements in its
cylic structure
(A) Mg and N (B) Mg and S (C) S and N (D) S and Fe

******* ANSWERS *******

1. A 21. B 41. C 61. B 81. C
2. C 22. A 42. B 62. A 82. C
3. C 23. D 43. A 63. C 83. A
4. B 24. C 44. D 64. A 84. B
5. A 25. A 45. C 65. C 85. C
6. C 26. B 46. A 66. A 86. B
7. D 27. B 47. C 67. D 87. D
8. C 28. B 48. A 68. B 88. A
9. C 29. B 49. D 69. C 89. B
10. A 30. B 50. B 70. C 90. A
11. D 31. B 51. A 71. C 91. B
12. B 32. A 52. B 72. C 92. A
13. D 33. B 53. D 73. C 93. A
14. C 34. D 54. C 74. C 94. D
15. C 35. D 55. D 75. B 95. A
16. C 36. C 56. D 76. D 96. A
17. B 37. A 57. C 77. B 97. C
18. A 38. B 58. A 78. C 98. A
19. A 39. D 59. B 79. D 99. B
20. D 40. B 60. C 80. A 100. C

Posted by: SATYASRINIVAS | May 26, 2007

FUNNY ONLINERS

100,000 sperm and you were the fastest?
42.7 percent of all statistics are made up on the spot.
99 percent of lawyers give the rest a bad name.
A bartender is just a pharmacist with a limited inventory.
A clean desk is a sign of a cluttered desk drawer.
A clear conscience is usually the sign of a bad memory.
A closed mouth gathers no foot.
A conclusion is the place where you got tired of thinking.
A day without sunshine is like, night.
A diplomat is someone who can tell you to go to hell in such a way that you will look forward to the trip.
A flashlight is a case for holding dead batteries.
All generalizations are false, including this one.
All men are idiots, and I married their King.
Always remember you’re unique, just like everyone else.
Always try to be modest and be proud of it!
Anything worth taking seriously is worth making fun of.
Artificial Intelligence usually beats real stupidity.
Assassins do it from behind.
Atheism is a non-prophet organization.
Auntie Em, Hate you, hate Kansas, taking the dog. Dorothy.
Be nice to your kids. They’ll choose your nursing home.
Beauty is in the eye of the beer holder.
Beer: It’s not just for breakfast anymore.
Before you criticize someone, you should walk a mile in their shoes. That way, when you criticize them, you’re a mile away and you have their shoes.
Better to understand a little than to misunderstand a lot.
Bills travel through the mail at twice the speed of checks
Borrow money from a pessimist, they don’t expect it back.
Boycott shampoo! Demand the REAL poo!
C program run. C program crash. C programmer quit.
Change is inevitable, except from a vending machine.
Chocolate: the OTHER major food group.
Consciousness: That annoying time between naps.
Corduroy pillows: They’re making headlines!
Could you drive any better if I shoved that cell phone up your ass?
Criminal Lawyer is a redundancy.
Daddy, why doesn’t this magnet pick up this floppy disk?
Death is hereditary.
Despite the cost of living, have you noticed how popular it remains?
Did anyone see my lost carrier?
Diplomacy is the art of saying good doggie while looking for a bigger stick.
Do not walk behind me, for I may not lead. Do not walk ahead of me, for I may not follow. Do not walk beside me, either. Just leave me alone.
Don’t be irreplaceable; if you can’t be replaced, you can’t be promoted.
Don’t drink and drive. You might hit a bump and spill your drink.
Don’t piss me off! I’m running out of places to hide the bodies.
Don’t take life too seriously, you won’t get out alive.
Double your drive space. Delete Windows!
Duct tape is like the force, it has a light side and a dark side and it holds the universe together.
Eagles may soar, but weasels don’t get sucked into jet engines.
Energizer Bunny arrested and charged with battery.
Error, no keyboard. Press F1 to continue.
Ever notice how fast Windows runs? Neither did I.
Ever stop to think, and forget to start again?
Everyone has a photographic memory. Some don’t have film.
Experience is something you don’t get until just after you need it.
Experience is what you get when you didn’t get what you wanted.
Few women admit their age. Few men act theirs.
For every action there is an equal and opposite criticism.
For Sale: Parachute. Only used once, never opened, small stain.
Forget world peace. Visualize using your turn signal.
Friends help you move. Real friends help you move bodies.
Friends may come and go, but enemies tend to accumulate.
Generally speaking, you aren’t learning much when your mouth is moving.
Genius does what it must, talent does what it can, and you had best do what you’re told.
Get a new car for your spouse; it’ll be a great trade!
Give a man a fish and he will eat for a day. Teach him how to fish, and he will sit in a boat and drink beer all day.
Give me ambiguity or give me something else.
Good judgment comes from bad experience and a lot of that comes from bad judgment.
Hard work has a future payoff. Laziness pays off now.
He who laughs last thinks slowest.
Honk if you love peace and quiet.
Honk if you want to see my finger.
How do you tell when you run out of invisible ink?
How does Teflon stick to the pan?
How many of you believe in telekinesis? Raise my hand.
I am not a vegetarian because I love animals. I am a vegetarian because I hate plants.
I couldn’t repair your brakes, so I made your horn louder.
I didn’t say it was your fault. I said I was going to blame you.
I don’t suffer from insanity. I enjoy every minute of it.
I feel like I’m diagonally parked in a parallel universe.
I get enough exercise just pushing my luck.
I just got lost in thought. It was unfamiliar territory.
I need someone really bad. Are you really bad?
I poured Spot remover on my dog. Now he’s gone.
I took an IQ test and the results were negative.
I tried sniffing Coke once, but the ice cubes got stuck in my nose.
I used to be indecisive. Now I’m not sure.
I used to have a handle on life, and then it broke.
I used to have an open mind but my brains kept falling out.
I won’t rise to the occasion, but I’ll slide over to it.
I wouldn’t be caught dead with a necrophiliac.
I’m as confused as a baby in a topless bar.
I’m not a complete idiot, some parts are missing!
I’m writing a book. I’ve got the page numbers done.
If at first you don’t succeed, destroy all evidence that you tried.
If at first you don’t succeed, skydiving is not for you.
If Barbie is so popular, why do you have to buy her friends?
If ignorance is bliss, you must be orgasmic.
If you can read this, I can slam on my brakes and sue you!
If you can’t convince them, confuse them.
If you choke a smurf, what color does it turn?
If you get to it and you can’t do it, well there you jolly well are, aren’t you.
If you haven’t much education you must use your brain.
If you lend someone $20, and never see that person again; it was probably worth it.
If you tell the truth you don’t have to remember anything.
If you think nobody cares if you’re alive, try missing a couple of car payments.
IRS: We’ve got what it takes to take what you’ve got.
It IS as bad as you think, and they ARE out to get you.
It is far more impressive when others discover your good qualities without your help.
It may be that your sole purpose in life is simply to serve as a warning to others.
It’s always darkest before dawn. So if you’re going to steal the neighbor’s newspaper, that’s the time to do it.
It’s lonely at the top, but you eat better.
Jack Kevorkian for White House Physician.
Jesus loves you, but everyone else thinks you’re an asshole.
Join the Army, meet interesting people, and kill them.
Keep honking. I’m reloading.
Laughing stock: cattle with a sense of humor.
Learn from your parents’ mistakes: use birth control.
Lottery: A tax on people who are bad at math.
Love may be blind but marriage is a real eye-opener.
Make it idiot proof and someone will make a better idiot.
Monday is an awful way to spend 1/7th of your life.
Montana: At least our cows are sane!
More hay, Trigger? No thanks, Roy, I’m stuffed!
Multitasking means screwing up several things at once.
My hockey mom can beat up your soccer mom.
My mind is like a steel trap, rusty and illegal in 37 states.
Never ask a barber if he thinks you need a haircut.
Never do card tricks for the group you play poker with.
Never mess up an apology with an excuse.
Never miss a good chance to shut up.
Never test the depth of the water with both feet.
Never underestimate the power of stupid people in large groups.
No one is listening until you make a mistake.
Oh Lord, give me patience, and GIVE IT TO ME NOW!
Okay, who put a stop payment on my reality check?
On the other hand, you have different fingers.
Oops. My brain just hit a bad sector.
Out of my mind. Back in five minutes.
Pentiums melt in your PC, not in your hand.
Plan to be spontaneous, tomorrow.
Pride is what we have. Vanity is what others have.
Puritanism: The haunting fear that someone, somewhere may be happy.
Quantum mechanics: The dreams stuff is made of.
Quickly, I must hurry, for there go my people and I am their leader.
Reality is a crutch for people who can’t handle drugs.
Remember half the people you know are below average.
Save the whales. Collect the whole set
Save your breath. You’ll need it to blow up your date!
Sex is like air; it’s not important unless you aren’t getting any.
Shin: a device for finding furniture in the dark.
Smile, it’s the second best thing you can do with your lips.
Smith & Wesson: The original point and click interface.
Some days you are the bug, some days you are the windshield.
Some drink at the fountain of knowledge. Others just gargle.
Some people are only alive because it is illegal to shoot them.
Success always occurs in private and failure in full view.
Suicidal twin kills sister by mistake!
Support bacteria, they’re the only culture some people have.
The Bermuda Triangle got tired of warm weather. It moved to Finland. Now Santa Claus is missing.
The colder the x-ray table, the more of your body is required on it.
The early bird may get the worm, but the second mouse gets the cheese.
The hardness of butter is directly proportional to the softness of the bread.
The journey of a thousand miles begins with a broken fan belt and a flat tire.
The more you complain, the longer God makes you live.
The only substitute for good manners is fast reflexes.
The problem with the gene pool is that there is no lifeguard.
The quickest way to double your money is to fold it in half and put it back in your pocket.
The secret of the universe is @*&^^^ NO CARRIER
The severity of the itch is inversely proportional to the ability to reach it.
The sex was so good that even the neighbors had a cigarette.
The shortest distance between two points is under construction.
The sooner you fall behind the more time you’ll have to catch up.
The universe is a figment of its own imagination. There’s no future in time travel.
There are 3 kinds of people: those who can count & those who can’t.
There are two theories to arguing with women. Neither one works.
There’s too much blood in my caffeine system.
Things are more like they are now than they ever were before.
Time is the best teacher; unfortunately it kills all of its students.
Time is what keeps everything from happening at once.
Timing has an awful lot to do with the outcome of a rain dance.
To steal ideas from one person is plagiarism; to steal from many is research.
To succeed in politics, it is often necessary to rise above your principles.
Very funny Scotty, now beam down my clothes.
Wanted: Meaningful overnight relationship.
Warning: Dates in calendar are closer than they appear.
We have enough youth, how about a fountain of smart?
We were born naked, wet and hungry. Then things got worse.
Wear short sleeves! Support your right to bare arms!
What happens if you get scared half to death twice?
What is a free gift? Aren’t all gifts free?
What’s the speed of dark?
When everything’s coming your way, you’re in the wrong lane and going the wrong way.
When there’s a will, I want to be in it.
When you don’t know what you are doing, do it neatly.
Who is General Failure and why is he reading my hard disk?
Who stopped payment on my reality check?
Why do psychics have to ask you for your name?
Why is abbreviation such a long word?
Why isn’t phonetic spelled the way it sounds?
Women who seek to be equal to men lack ambition.
You are depriving some poor village of its idiot.
You can do more with a kind word and a gun than with just a kind word.
You have the right to remain silent. Anything you say will be misquoted then used against you.
You’re just jealous because the voices are talking to me and not you!
Your gene pool could use a little chlorine.
Your kid may be an honors student, but you’re still an idiot.

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