number system Model Questions & Answers, Practice Test for ssc steno grade c d 2024

Answer: (c)

An army commander has 5180 men in the form of a solid square.

If he get four more men and form the solid square then no. of men in the front row

$√{5180 + 4} = √5184 = 72$

Answer: (d)

According to question number = x

x × 2 + 42 × 3 = 238

2x = 112 or x = 56

Again 3 × 56 + 42 × 2 = 168 + 84 = 252.

Answer: (b)

Let two consecutive odd numbers = (2x + 1) and (2x + 3)

According to question

= $(2x + 3)^2 – (2x + 1)^2$

= $4x^2 + 12x + 9 – 4x^2 – 1 – 4x$

= 8x + 8 = 8(x + 1)

So, it is divisible by 8.

Answer: (d)

For square integer 25, 4k + 1 mean 4 × 6 + 1 and for 36

4k mean 4 × 9

Now, if k is a positive integer, then every square integer is of the form 4k or 4k + 1

Answer: (a)

$(0.11)^3 + (0.22)^3 + ..... + (0.99)^3$

= $(0.11)^3 [1^3 +2^3 + ....... 9^3]$

= $(0.11)^3$ × 2025 = 2.695