SSC Number Systems Questions with Answers

Number Systems

An excellent collection of SSC Number systems questions and answers with detailed explanations for competitive exams. Given below are some of the most repeated practice questions on Number systems for SSC CGL, CHSL, JE, GD constable, Stenographer, MTS, and CPO exams. Go through this very important online quiz based on model and previous year asked problems from SSC Number systems with solutions to ace the exam.

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For the following questions answer them individually

Question 1

$$\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-2}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{3-\sqrt{8}}$$ is

Question 2

If $$2+x\sqrt{3}$$=$$\frac{1}{2+\sqrt{3}}$$ then the simplest value of x is

Question 3

The term to be added to $$121a^{2}+64b^{2}$$ to make a perfect square is

Question 4

Which one of the following will completely divide 571 + 572 + 573 ?

Question 5

If $$\frac{x^{24}+1}{x^{12}}=7$$ then the value of $$\frac{x^{72}+1}{x^{36}}$$ is

Question 6

If the operation Θ is defined for all real numbers a and b by the relation $$aΘ b =a^{2}\frac{b}{{3}}$$ then $$2Θ {3Θ(­-1)} = ?$$

Question 7

If $$\frac{m-a^2}{b^2+c^2}+\frac{m-b^2}{c^2+a^2}+\frac{m-c^2}{a^2+b^2}=3$$ then the value of m is

Question 8

If $$x-\frac{1}{x}=1$$, then the value of $$\frac{x^{4}-\frac{1}{x^{2}}}{3x^{2}+5x-3}$$ is

Question 9

I multiplied a natural number by 18 and another by 21 and added the products. Which one of the following could be the sum?

Question 10

A certain number when divided by 899 leaves the remainder 65. When the same number is divided by 31, the remainder is :

Question 11

The next term of the series ­-1, 6,25, 62,123, 214,_____ is :

Question 12

The value of $$(3^2 - 2^2 )^2 + (5^2 - 4^2 )^2 + (6^2 - 5^2 )^2$$ is

Question 13

The unit digit in the sum of (124)372 + (124)373 is

Question 14

If 15% of x is same as 20 % of y then x: y is

Question 15

The least number which when divided by 35, 45, 55 leaves the remainder 18, 28, 38
respectively is

Question 16

A student was asked to divide a number by 6 and add 12 to the quotient. He, however, first added 12 to the number and then divided it by 6, getting 112 as the answer. The correct answer should have been

Question 17

A number, when divided by 114, leaves remainder 21. If the same number is divided by 19, then the remainder will be

Question 18

By what least number should 675 be multiplied to obtain a number which is a perfect cube ?

Question 19

If $$\frac{b-c}{a}+\frac{a+c}{b}+\frac{a-b}{c}=1$$ and a - b + c ≠ 0 then which one of the following relations is true ?

Question 20

The greatest number that will divide 19,35 and 59 to leave the same remainder in each case is:

Question 21

For what valsue (s) of k the expression $$p+\frac{1}{4}\sqrt{p}+k^{2}$$ is a perfect square ?

Question 22

The least number which when divided by 6, 9, 12, 15 and 18 leaves the same remainder 2 in each case is :

Question 23

If A and B are in the ratio 4 : 5 and the difference of their squares is 81, what is the value of A?

Question 24

On what sum of money will the difference between S.I and C.I for 2 years at 5% per annum be equal to 25 ?

Question 25

A certain sum will amount to 12,100 in 2 years at 10% per annum of compound interest, interest being compounded annually. The sum is

Question 26

The unit digit in the product $$122^{173}$$ is

Question 27

The greatest number, which when subtracted from 5834, gives a number exactly divisible by each of 20, 28, 32 and 35, is

Question 28

Choose the correct relation(s) from the following:
(i) $$\sqrt{6}+\sqrt{2}=\sqrt{5}+\sqrt{3}$$
(ii) $$\sqrt{6}+\sqrt{2}<\sqrt{5}+\sqrt{3}$$
(iii) $$\sqrt{6}+\sqrt{2}>\sqrt{5}+\sqrt{3}$$

Question 29

What is the arithmetic mean of first 20 odd natural numbers ?

Question 30

The value of 2 × (2.11 + 2.23 + 2.16) is

Question 31

If a and b be positive integers such that $$a^2-b^2 = 19$$, then the value of a is

Question 32

The least positive integer which is a perfect square and also divisible by each of 21, 36 and 66 is :

Question 33

$$\frac{1+876542\times876544}{876543\times876543}$$ is equal to

Question 34

The ninth term of the sequence 0, 3, 8, 15, 24, 35, is

Question 35

If x = √3 + √2 then the value of $$x^{3}-\frac{1}{x^{3}}$$ is

Question 36

The least number which when divided by 25, 40 and 60 leaves the remainder 7 in each case is

Question 37

The least number which is divisible by all the natural numbers upto and including 10 is

Question 38

The odd element in the sequence 3, 7, 13, 21, 33, 43, 57, is :

Question 39

If $$x=\frac{\cos\theta}{1-\sin\theta}$$, then $$\frac{\cos\theta}{1+\sin\theta}$$ is equal to

Question 40

If 21 is added to a number, it becomes 7 less than thrice of the number. Then the number is

Question 41

The next term of the series 1, 5, 12, 24, 43 is

Question 42

The number nearest to 75070 which is divisible by 65, is

Question 43

When 'n' is divided by 5 the remainder is 2. What is the remainder when n2 is divided by 5?

Question 44

What is the product of the roots of the equation $$x^{2}-\sqrt{3}=0?$$

Question 45

The HCF of $$x^{8}-1$$ and $$x^{4}+2x^{3}-2x-1$$ is

Question 46

The least number that should be added to 2055, so that the sum is exactly divisible by 27 is

Question 47

The least number which should be multiplied to 243 to get a perfect cube is

Question 48

The least number which must be added to 1728 to make it a perfect square is ……………..

Question 49

The least multiple of 13 which when divided by 4, 5, 6, 7 leaves remainder 3 in each case is

Question 50

If $$17^{200}$$ is divided by 18, the remainder is

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