number system Model Questions & Answers, Practice Test for ibps rrb clerk asst multipurpose prelims 2024

Answer: (b)

Square of the odd numbers can be written as

$1^n = 8 × 0 + 1, 3^2 = 8 × 1 + 1, 8 × 3 + 1$ & so on i. e.,

square of the odd number is of the form 8q + 1.

Answer: (a)

On taking p = 5,

$2^p – 1 = 2^5$ – 1 = 31 which is prime

On taking p = 11,

$2^p – 1 = 2^11$ – 1 = 2047

Since, 2047 is divisible by 23, so it is not prime.

Thus , the required least positive prime number is 11.

Answer: (b)

Zero is a whole number and every integer is not a whole number, because negative integers are not whole numbers.

Therefore, A is correct and R is wrong.

Answer: (d)

$7^10 – 5^10$ is divisible by 11.

Answer: (c)

$1/8$ th Part is black. Half of the remaining.

i.e. $1/2 × 7/8 = 7/16$ is yellow

Therefore, the part left = $7/16$

Which is equal to $3{1}/2$ cm = 3.5cm

Hence, length of Pencil

= ${3.5}/{7/16}$ 8cm