Answer: Option A

Explanation:

132 = 4 x 3 x 11

So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.

264 11,3,4 (/)

396 11,3,4 (/)

462 11,3 (X)

792 11,3,4 (/)

968 11,4 (X)

2178 11,3 (X)

5184 3,4 (X)

6336 11,3,4 (/)

Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.

Required number of number = 4.

23) 1056 (45 92 --- 136 115 --- 21 --- Required number = (23 - 21) = 2.

Answer: Option D

91 is divisible by 7. So, it is not a prime number.

Let 2^{32} = x. Then, (2^{32} + 1) = (x + 1).

Let (x + 1) be completely divisible by the natural number N. Then,

(2^{96} + 1) = [(2^{32})^{3} + 1] = (x^{3} + 1) = (x + 1)(x^{2} - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.