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

Question 2

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

Question 3

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

Question 4

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 5

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 6

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

Question 7

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?

Question 8

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 9

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 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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 22

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

Question 23

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

Question 24

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

Question 25

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

Question 26

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

Question 27

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

Question 28

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

Question 29

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

Question 30

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

Question 31

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

Question 32

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

Question 33

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

Question 34

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

Question 35

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 36

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

Question 37

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

Question 38

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 39

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

Question 40

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 41

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

Question 42

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

Question 43

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 44

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 45

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

Question 46

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

Question 47

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

Question 48

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

Question 49

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

Question 50

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

Question 51

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 52

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