SSC Algebra Questions with Answers

Algebra

An excellent collection of SSC Algebra questions and answers with detailed explanations for competitive exams. Given below are some of the most repeated practice questions on Algebra 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 questions from SSC Algebra with solutions to ace the exam.

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Instructions

For the following questions answer them individually

Question 1

If x + y = 15, then $$(x-10)^{3}+(y-5)^{3}$$ is

Question 2

If m = - 4, n = - 2, then the value of $$m^3 - 3m^2 + 3m + 3n + 3n^2 + n^3$$ is

Question 3

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

Question 4

If m - 5n = 2, then the vlaue of $$(m^{3} - 125n^{3}$$ - 30 mn) is

Question 5

If the cube root of 79507 is 43, then the value of $$\sqrt[3]{79.507}+\sqrt[3]{0.079507}+\sqrt[3]{0.000079507}$$
is

Question 6

If a + 1/a+2 = 0, then the value of $$(a+2)^{2}+\frac{1}{(a+2)^{3}}$$ is

Question 7

If $$x = \frac{2\sqrt{24}}{\sqrt{3}+\sqrt{2}}$$, then the value of $$\frac{x+\sqrt{8}}{x-\sqrt{8}}+\frac{x+\sqrt{12}}{x-\sqrt{12}}$$ is

Question 8

If ax + by = 6, bx - ay = 2 and x^2 + y^2 = 4, then the value of (a^2 + b^2) would be:

Question 9

If 5x + 9y = 5 and $$125x^{3}$$ + $$729y^{3}$$ = 120 then the value of the product of x and y is

Question 10

If $$x=(0.08)^2$$, $$y=\frac{1}{(0.08)^2}$$ and $$z=(1-0.08)^2 - 1$$, then out of the following, the true relation is

Question 11

If $$x=\sqrt{a^3\sqrt{b}\sqrt{a^3}\sqrt{b}}$$ then the value of x is

Question 12

If (x - y) = 7, then what is the value of $$(x-15)^{3}-(y-8)^{3}$$ ?

Question 13

If the operation ‘o’ among real numbers is defined by x o y = $$x^2 - 2y$$, then values of x satisfying 2xo 4 =2 ox is

Question 14

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

Question 15

If $$x = \frac{\sqrt{5}-2}{\sqrt{5}+2}$$, then $$x^4 + x^{-4}$$ is

Question 16

If $$ a =\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$$ and $$b=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$$ then $$\frac{a^2}{b}+\frac{b^2}{a}$$

Question 17

$$3 - \frac{3+\sqrt{5}}{4} - \frac{1}{3 + \sqrt{5}}$$

Question 18

If a = 2 + √3 ,then the value of $$(a^{2}+\frac{1}{a^{2}})$$ is

Question 19

If a + 1/a = 1, then the value of a^2 + 1/a^2 is :

Question 20

If (x - 2) and (x + 3) are the factors of the equation $$x^{2} + k_1x + k_2 = 0$$, then what are the values of $$k_1$$ and $$k_2$$ ?

Question 21

If (5x^2 - 3y^2): xy = 11:2, and x,y are positive, then the value of x/y is:

Question 22

If x = 2 + √3 , then the value, $$\sqrt{x} + \frac{1}{\sqrt{x}}$$

Question 23

The value of $$\sqrt{3\times{0.000729}^{1/3}}$$ is

Question 24

If $$x = \frac{2\sqrt{6}}{\sqrt{3}+\sqrt{2}}$$, then the value of $$\frac{x+\sqrt{2}}{x-\sqrt{2}} + \frac{x+\sqrt{3}}{x-\sqrt{3}}$$ is

Question 25

If $$2\sqrt{x} = \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}} + \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$$

Question 26

If $$a=\frac{2+\sqrt{3}}{2-\sqrt{3}}$$ and $$b=\frac{2-\sqrt{3}}{2+\sqrt{3}}$$, then the value of $$a^2+b^2+a \times b$$ is

Question 27

If $$x=[\frac{1}{(\sqrt{5}+\sqrt{3})}], y=[\frac{1}{(\sqrt{7}+\sqrt{5})}]$$ and $$z=[\frac{1}{(\sqrt{7}+\sqrt{3})}]$$, then what is the value of (x+y+z) ?

Question 28

If $$x^2 - 3x + 1= 0$$ and x > 1, then the value of $$(x - \frac{1}{x})$$

Question 29

If $$x+\frac{1}{x}=2$$ then the value of $$x^{12}+\frac{1}{x^{12}}$$ is

Question 30

If $$x+\frac{1}{x}=1$$ then the value of $$\frac{x^2+3x+1}{x^2+7x+1}$$

Question 31

The value of $$\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}$$ is

Question 32

If $$a^x = (x+y+z)^y$$ , $$a^y =(x+y+z)^z$$ and $$a^z = (x + y + z)^x$$ , then the value of x + y + z (given a ≠ 0) is

Question 33

If a^3 - b^3 = 56 and a - b = 2, then the value of (a^2 + b^2 + ab) is :

Question 34

The value of x when 5% of √2x is 0.01 will be :

Question 35

If $$\frac{3-5x}{x} + \frac{3-5y}{y} + \frac{3-5z}{z} = 0 $$, the value of $$\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$$ is

Question 36

If $$\frac{x}{y}$$=$$\frac{3}{4}$$ the ratio of $$(2x+3y)$$ and $$(3y-2x)$$ is

Question 37

If √6 x √15 = x√10, then the value of x is

Question 38

If $$x = 1 + \sqrt{2} + \sqrt{3}$$ , then the value of $$(2x^4 - 8x^3 - 5x^2 + 26x- 28)$$ is __?

Question 39

If $$x + \frac{1}{x} = 12 $$, the value of $$x^2 + \frac{1}{x^2}$$ is

Question 40

If $$a^2+b^2+c^2=2(a-2b-c-3)$$ then the value of a+b+c is

Question 41

If a * b = 2a + 3b - ab, then the value of (3 * 5 + 5 * 3) is

Question 42

The value of $$\sqrt{6+\sqrt{6+\sqrt{6+...}}}$$ is equal to

Question 43

If (a - b) = 3, (b - c) = 5 and (c - a) = 1, then the value of $$\frac{a^3 + b^3 + c^3 - 3abc}{a + b + c}$$ is

Question 44

The value of $$(\sqrt{5}+\sqrt{3})(\frac{3\sqrt{3}}{\sqrt{5}+\sqrt{2}} - \frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}})$$ is

Question 45

If $$\sqrt{4x-9}+\sqrt{4x+9}=5+\sqrt{7}$$, then the value of $$x$$ is

Question 46

If x = 27 and $$\sqrt[3]{x} + \sqrt[3]{y} = \sqrt[3]{729}$$, the y =

Question 47

If a + b = 6, a - b = 2, then the value of 2*(a^2 + b^2 ) is :

Question 48

If $$x^4 + \frac{1}{x^4} = 23$$, then the value of $$(x-\frac{1}{x})^2$$ will be

Question 49

If a + b + 1 = 0, then the value of $$(a^3 + b^3 +1 - 3ab)$$ is

Question 50

$$\sqrt{8 + \sqrt{57 + \sqrt{38 + \sqrt{108 + \sqrt{169}}}}}$$

Question 51

If a * b = $$a^{b}$$, then the value of 5 * 3 is

Question 52

A number of boys raised ₹12,544 for a famine fund, each boy has given as many rupees as there were boys. The number of boys was?

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