number system Model Questions & Answers, Practice Test for ssc mts tier 1 2024

Answer: (c)

The number is divisible by 18 i.e., it has to be divisible by 2 and 9.

∴ B may be 0, 2, 4, 6, 8.

A + 4 + 5 + 7 + 1 + 2 + 0 + 3 + B

= A + B + 22.

A + B could be 5, 14

(as the sum can't exceed 18, since A and B are each less than 10).

So, A and B can take the values of 6, 8.

Answer: (c)

81 × 82 × 83 × 84 × ... × 99

It can be written as

= 81 × 82 × 83 × 84 × ... 90 × 99

When we multiply any number by multiple of 10, then resultant number always carry zero at unit place.

Answer: (b)

$?/432 = 243/? ⇒ (?)^2 = 432 × 243$

$? = √104976 = 324$

Answer: (d)

$3^N > N^3$ holds for all the natural numbers except N = 3 at which $3^N = N^3⇒ 3^3 = 3^3$

Answer: (b)

7! + 8! + 9! + 10! + ....... + 100 = 7.6! + 8.7.6! + 9.8.7.6! + ....... + 100! is completely divisible by 7 as each of the terms contain at least one 7 in it.

Now, 1! + 2! + 3! + 4! + 5! + 6!

= 1 + 2 + 6 + 24 + 120 + 720 = 873

which leaves a remainder of 5 when divided by 7.