1. (935421 x 625) = ?

A. 542622125

B. 584632125

C. 544638125

D. 584638125

Explanation :

935421×625=935421×54=935421×(102)4=935421×1000016=584638125

2. (64 – 12)2 + 4 x 64 x 12 = ?

A. 5246

B. 4406

C. 5126

D. 5776

Explanation :

(a + b)2 = a2 + 2ab + b2

(a – b)2 = a2 – 2ab + b2

Here, the given statement is like (a – b)2 + 4ab where a= 64 and b = 12

(a – b)2 + 4ab = (a2 – 2ab + b2) + 4ab = a2 + 2ab + b2 = (a + b)2

Hence (64 – 12)2 + 4 x 64 x 12 = (64 + 12)2 = 762 = 5776

3. When (6767 +67) is divided by 68, the remainder is?

A. 0

B. 22

C. 33

D. 66

Explanation :

(xn+1) is divisible by (x + 1) only when n is odd

=> (6767 + 1) is divisible by (67 + 1)

=> (6767 + 1) is divisible by 68

=> (6767 + 1) ÷  68 gives a remainder of 0

=> [(6767 + 1) + 66] ÷ 68 gives a remainder of 66

=> (6767 + 67) ÷ 68 gives a remainder of 66

4. (23341379 x 72) = ?

A. 1680579288

B. 1223441288

C. 2142579288

D. 2142339288

Explanation :

23341379 x 72 = 23341379(70 + 2) = (23341379 x 70) + (23341379 x 2)

= 1633896530 + 46682758 = 1680579288

5.Which one of the following is a prime number ?

A. 307

B. 437

C. 247

D. 203

Explanation :

307−−−√<18

Prime numbers < 18 are 2, 3, 5, 7, 11, 13, 17

307 is not divisible by 2

307 is not divisible by 3

307 is not divisible by 5

307 is not divisible by 7

307 is not divisible by 11

307 is not divisible by 13

307 is not divisible by 17

Hence 307 is a prime number