Numbers  1.  Which one of the following is not a prime number?  
Answer: Option D
Explanation: 91 is divisible by 7. So, it is not a prime number. 
2.  (112 x 5^{4}) = ?  
Answer: Option B
Explanation:

3.  It is being given that (2^{32} + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?  
Answer: Option D
Explanation: 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. 
4.  What least number must be added to 1056, so that the sum is completely divisible by 23 ?  
Answer: Option A
Explanation: 23) 1056 (45
92

136
115

21

Required number = (23  21)
= 2.

5.  1397 x 1397 = ?  
Answer: Option A
Explanation:

6.  How many of the following numbers are divisible by 132 ? 264, 396, 462, 792, 968, 2178, 5184, 6336 

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. 
7.  (935421 x 625) = ?  
Answer: Option B
Explanation:
= 584638125 
8.  The largest 4 digit number exactly divisible by 88 is:  
Answer: Option A
Explanation: Largest 4digit number = 9999
88) 9999 (113
88

1199
88

319
264

55

Required number = (9999  55)
= 9944.

9.  Which of the following is a prime number ?  
Answer: Option D
Explanation: Clearly, 97 is a prime number. 
10.  What is the unit digit in {(6374)^{1793} x (625)^{317} x (341^{491})}?  
Answer: Option A
Explanation: Unit digit in (6374)^{1793} = Unit digit in (4)^{1793} = Unit digit in [(4^{2})^{896} x 4] = Unit digit in (6 x 4) = 4 Unit digit in (625)^{317} = Unit digit in (5)^{317} = 5 Unit digit in (341)^{491} = Unit digit in (1)^{491} = 1 Required digit = Unit digit in (4 x 5 x 1) = 0. 
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