*439*

**1. (935421 x 625) = ?**

A. 542622125

B. 584632125

C. 544638125

D. 584638125

**Answer : **Option D

**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

**Answer : **Option D

**Explanation :**

**(a + b) ^{2} = a^{2} + 2ab + b^{2}**

**(a – b) ^{2} = a^{2} – 2ab + b^{2}**

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

(a – b)^{2} + 4ab = (a^{2} – 2ab + b^{2}) + 4ab = a^{2} + 2ab + b^{2} = (a + b)^{2}

Hence (64 – 12)^{2} + 4 x 64 x 12 = (64 + 12)^{2} = 76^{2} = 5776

**3. When (67 ^{67} +67) is divided by 68, the remainder is?**

A. 0

B. 22

C. 33

D. 66

**Answer : **Option D

**Explanation :**

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

=> (67^{67}+ 1) is divisible by (67 + 1) => (67^{67}+ 1) is divisible by 68 => (67^{67}+ 1) ÷ 68 gives a remainder of 0 => [(67^{67}+ 1) + 66] ÷ 68 gives a remainder of 66 => (67^{67}+ 67) ÷ 68 gives a remainder of 66

**4. (23341379 x 72) = ?**

A. 1680579288

B. 1223441288

C. 2142579288

D. 2142339288

**Answer : **Option A

**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

**Answer : **Option A

**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