1. Find the number of ways in which you can fill a 3x3 grid(with four courners defined as a,b,c,d) if u have 3 white marbles and 6 black marbles.
It is a 3*3 grid, so there are a total of 9 spaces where you can place the marbles. Let us first place the 3 white marbles, that can be done in 9C3 ways. There are 6 spaces available and 6 black marbles are to be placed in those 6 spaces. So, that can be done in 1 way.
Hence the answer would be 9C3.
2. If X=123456 and Z=X-Y then for how many values of Y, Z is divisible by 48, 98, 105?
X=123456
LCM of 48,98,105 is 11760. So if a number is divisible by 11760, then it will be divisble by 48,98,105.
On dividing X by 11760 we get dividend = 10.
So for 10 values of y, z is divisible by 11760.
Thus for 10 values of y ,z value found is divide by 48,,98,105.
These values of Y are 111696, 99936, 88176, 76416, 64656, 52896, 41136, 29376, 17616, 5856
3. There are 6 Bangles each of 4cms in diameter. These are to be placed in a salver(plate), what should be the minimum radius of the salver, so that each bangles are kept without overlapping (bangles touching each other)?
One bangle at the center and the remaining 5 surrounding them, so radius of the center + the diameter of the outer bangle = 4+2=6cms
4. Let Sn denote the sum of first n terms of an A.P. If S2n = 3Sn, then the ratio S3n/Sn is equal to?
We know that Sn = n(n+1)/2
now it is given that
S2n = 3Sn
=> 2n(2n+1)/2 = 3n(n+1)/2
=> 2(2n+1) = 3(n+1)
=> 4n+2 = 3n+3
=> n = 1
then S3n/Sn = [3n(3n+1)/2]/[n(n+1)/2] = 3*4/1*2 = 6
5. In a strange twist of hearts, P politicians of a country agreed to an average donation of Rs. D each. Q of these politicians, who had pledged an average of Rs. A never donated the pledged money. Which of the following expressions represents the percent of the pledged money that was actually donated.
We know that Sn = n(n+1)/2
now it is given that
S2n = 3Sn
=> 2n(2n+1)/2 = 3n(n+1)/2
=> 2(2n+1) = 3(n+1)
=> 4n+2 = 3n+3
=> n = 1
then S3n/Sn = [3n(3n+1)/2]/[n(n+1)/2] = 3*4/1*2 = 6
pledged money = P*D
Actually donated money = PD-QA
percent of the pledged money thas ws actually donated = 100*(PD-QA)/PD = 100-100(QA/PD)
