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 = 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
Answer : Option D
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
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
