number systems Model Questions & Answers, Practice Test for ssc chsl tier 1

Answer: (b)

Since, D is a point of BC.

As BC is rational so BD must be rational but AD need not to be rational.

Answer: (c)

Let the larger and smaller numbers be x and y respectively.

Then, x – y = 3 . ...(i)

and, $x^2 – y^2 = 63$

(x + y) (x – y) = 63

$(x + y) = 63/3 = 21$ ...(ii)

From equation (i) and (ii),

x = 12

Answer: (a)

We know that, between any two rational numbers, there are an infinite number of rational and irrational numbers.

Hence, statement II is correct.

Answer: (c)

Number is of the form = 7n + 3; n = 1 to 13

So, S = $$∑ ↙{n = 1}↖13 (7n + 3) = {7n(n + 1)}/2 + 3n$$

putting n = 13, We get,

7 × 13 × 7 + 39 = 676

Answer: (a)

Let the GP series be $a, ar, ar^2 , ar^3 , ar^4$ ,...

By given condition,

$T_3 = T_1 + 9$

⇒ $ar^2 = a + 9$

⇒ $a(r^2 – 1) = 9$ ...(i)

and $T_2 = T_4 + 18$

⇒ ar = $ar^3$ + 18

⇒ $ar (1 – r^2)$ = 18 ...(ii)

On dividing Eq. (i) by Eq. (ii), we get

∴ ${a(r^2 - 1)}/{-ar(r^2 - 1)} = 9/18$

⇒ – r = 2

From Eq. (i)

a (4 – 1) = 9 ∴ a = 3