number system Model Questions & Answers, Practice Test for ssc cgl tier 1 2023

Answer: (a)

Remainder of ($_32{32}^32$ divided by 7) = Remainder of ($_4{32}^32$ divided by 7)

Now find cyclicity of remainder of ($_4{32}^n$ divided by 7).

Remainder when $_4{32}^1$ divided by 7 = 2

Remainder when $_4{32}^2$ divided by 7 = 4

Remainder when $_4{32}^3$ divided by 7 = 2

So, the cyclicity is 2, 4, 2, 4 and so on.

For every even value of n, remainder = 4

Answer: (b)

A number is divisible by 9 if the sum of its digits is divisible by 9.

Here 5 + 4 + 3 + 2 + * + 7 = 21 + *

So, the digit in place of * is 6

Answer: (a)

Last digit in 19 – 9

$18^2$ – 1

$19^3$ – 1

for odd powers of 19

Last digit is 9 and for even it is 1

Last digit in $19^81$ is 9

Last digit in 41 is 4

42 is 6

43 is 4

for odd powers of 4

$3^9$k is odd irrespective of the value of k

∴ last digit in $4^9$k is 4. Last digit in $19^81 + 4^9$k is last digit in 9 + 4 i.e, in 13 = 3

Answer: (d)

$1/4$ = 0.25 and $3/4$ = 0.75

Only option (d) with $252/1000$ = 0.252 and $748/1000$ = 0.748 lies between 0.25 and 0.75.

Answer: (b)

On taking p = 11,

p + 2 = 13 (prime number)

I. 11 × 13 + 1 = 144 (a square number)

II. 11 + 13 = 24 (12 is a divisor of 24)

Hence, both statements I and II are correct.