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

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

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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

Question 22

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

Question 23

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 24

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

Question 25

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

Question 26

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

Question 27

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

Question 28

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

Question 29

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 30

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

Question 31

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

Question 32

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 33

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 34

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

Question 35

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 36

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

Question 37

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

Question 38

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

Question 39

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 40

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 41

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 42

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 43

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

Question 44

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

Question 45

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 46

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 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 $$\sqrt{3\sqrt{0.000729}}$$ is

Question 50

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

Question 51

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 $$k_2$$ ?

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