Posted by: SATYASRINIVAS | May 26, 2007

good problems assorted with solution

haripi2 wrote:
1) 11^(2x^2) -(2*11^(x^2 + 2x+8 )) +11^(4*x + 16) = 0

Given equation is basically expansion of :
{ 11^(x^2) – 11^(2x+8 ) }^2 = 0

Since if A^2 = 0 implies that A = 0, we have 11^(x^2) – 11^(2x+8 ) = 0.

Divide the expression by 11^(2x+8 ), we have 11^(x^2 – 2x -8 ) = 1.

This is possible only when x=4 and x = -2!

Quote:
4)there are 21 slips labelled 1 to 21.what is the prob that 6 slips drawn in random are in AP??

Since we need 6 terms in the AP, we need to take it as 21 – (d*5) instead of 6

so no. of sets will be :

for d = 1, 21 – (1*5) = 16 {consider all APs with 1st term 1,2,…,16}
for d = 2, 21 – (2*5) = 11 {APs with d = 2, 1st term going from 1 upto 11}
for d = 3, 21 – (3*5) = 6
for d = 4, 21 – (4*5) = 1

So prob = 34/(21C6)

3) when doin a * of two diff: 2 digit numbers,ab reversed the digits of one of teh numbers and found the product increased by 1224.if the other number is less than 20 ,whatis new product??

hey
i think the answer is 1477
if you reverse the digits of a no., then you get a no. bigger (in this case , as the product has increased) but it is bigger by an integer as both the no.s are integers and their diff. will also be an integer.
so now this diff. multiplied by the second(unreversed no.) is the reason for the product to be greater by 1224.
so now find factors of 1224 from 10-20….these will come out to be 12,17,18…

so by dividing 1224 by the unreversed no. , we will get the diff. between the first no. and its reversed no.

now the diff. between a 2-digit no. and the no. formed by reversing its digits is always divisible by 9 because
ab=10a + b
ba= 10b+a
so ab-ba=9(a-b)

so assuming the unreversed no. is 12 , we get the diff. between the changed no. and unchanged no. as 204 which cannot be as these are 2 digit no.s

assuming it to be 18 , we get the diff. as 68 which also cannot be as the diff. should be divisible by 9.

so we get 17 as the second no. and the diff. as 81
now ab-ba=9(a-b)
9(a-b) = 72
so a-b = 8
so a = 8 +b
so as b=0 gives 08 which is not a 2 digit no.
so a = 9 and b =1 as for greater than 1 a will cease to be a digit.
so the new no. is 91
and the new product is 1477.
hope you got it

1) > > A Candle Burns in 6 Hrs..Another Candle of the
> same height and width
> > burns
> > in 8 Hrs…After How Many Hours the height of the
> first candle will
> > be
> > half of the second Candle….

height of candle1 after x hrs=(6-x)/6
height of candle2 after x hrs=(8-x)/8
2*(6-x)6=(8-x)/8
x=4.8
Quote:
2) What is the number of scores possible in a 150 bit CAT paper, where 1/3
mark is deducted for every wrong answer and 1 mark is awarded for every
correct answer?

maximum possible score = 150
min possible score = -50
total possible scores = 200 * 3 = 600 – 3 + 1 ( for Zero )= 598
Quote:
3) What does 100 stand for if 5 X 6 = 33
90 81 100 110

we know that 5*6 = 30 is represented as 33 in a particular no sys, say the base is ‘n’

33 = 3(n+1) = 30 => n = 9
now, 100 is nothing but n^2 => 81
Quote:
4) how many factors are there for the number equal to 40^3 – 17^3 – 23^3?

if a+b+c = 0, then a^3 + b^3 + c^3 = 3abc
now, since 40 -23-17 = 0,
40^3 – 17^3 – 23^3 can be written as,
40*17*23*3 = 2^3*3*5*17*23, so the total number of factors wud be,
(3+1)(1+1)(1+1)(1+1)(1+1) = 64

Quote:
5) what is the value of 2^256 mod 19 ?

Help! ( seems to be taking more time than anticipated, so left it )

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