# SSC Logarithms, Surds and Indices Questions with Answers

#### Logarithms, Surds and Indices

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

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Instructions

For the following questions answer them individually

Question 1

Determine the value of 'a' which satisfies the equation $$9^{\sqrt{a}}+40^{\sqrt{a}}=41^{\sqrt{a}}$$

Question 2

The simplified value of $$999\frac{1}{7}+999\frac{2}{7}+999\frac{3}{7}+999\frac{4}{7}+999\frac{5}{7}+999\frac{6}{7}$$ is

Question 3

If $$x-y-\sqrt{18}=-1$$ and $$x + y - 3\sqrt{2} = 1$$, then what is the value of $$12xy(x^{2} - y^{2})$$ ?

Question 4

The value of $$(1-\sqrt{2})+(\sqrt{2}-\sqrt{3})+(\sqrt{3}-\sqrt{4})+.....+(\sqrt{15}-\sqrt{16})$$ is

Question 5

Which value among $$\sqrt[3]{5},\sqrt[4]{6},\sqrt[6]{12},\sqrt[12]{276}$$ is the largest ?

Question 6

If $$x=1+\sqrt2+\sqrt3$$, then the value of $$x^2-2x-4$$ is

Question 7

If $$x=\sqrt[3]{28},y=\sqrt[3]{27}$$, then the value of $$x+y-\frac{1}{x^2+xy+y^2}$$ is

Question 8

If $$x+[\frac{1}{(x+7)}]=0$$, then what is the value of $$x-[\frac{1}{(x+7)}]$$ ?

Question 9

What is the value of $$\frac{1+a}{a^{\frac{1}{2}}+a^{\frac{-1}{2}}}-\frac{a^{\frac{1}{2}}+a^{\frac{-1}{2}}}{1+a}+a^{\frac{-1}{2}}$$ ?

Question 10

The simplest value of $$\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}$$ is

Question 11

Calculate the value of $$\frac{\sqrt{3}}{(3+\sqrt{3})}$$ if $$\sqrt{3}=1.7320$$

Question 12

If $$x=6+2\sqrt{6}$$, then what is the value of $$\sqrt{x-1}+\frac{1}{\sqrt{x-1}}$$ ?

Question 13

If $$\frac{p}{q}=\frac{r}{s}=\frac{t}{u}=\sqrt{5}$$, then what is the value of $$[\frac{(3p^{2} + 4r^{2} + 5t^{2})}{(3q^{2} + 4s^{2} + 5u^{2})}]$$  ?

Question 14

If $$\frac{x+\sqrt{x^2-1}}{x-\sqrt{x^2-1}}+\frac{x-\sqrt{x^2-1}}{x+\sqrt{x^2-1}}=194$$, then what is the value of x?

Question 15

If $$\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=3$$, then what is the value of x?

Question 16

If $$2x+\frac{1}{2x}=2$$, then what is the value of $$\sqrt{2(\frac{1}{x})^4+(\frac{1}{x})^5}$$ ?

Question 17

If $$x=8+2\sqrt{15}$$, then what is the value of $$\sqrt{x}+\frac{1}{\sqrt{x}}$$ ?

Question 18

$$x=\frac{2+\sqrt{3}}{2-\sqrt{3}}$$ then what is the value of $$x^{2}+x-9$$

Question 19

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

Question 20

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

Question 21

If $$x=\frac{2\sqrt{15}}{\sqrt{3}+\sqrt{5}}$$, then what is the value of $$\frac{x+\sqrt{5}}{x-\sqrt{5}}+\frac{x+\sqrt{3}}{x-\sqrt{3}}$$

Question 22

The approx value of $$5\frac{1}{3}+1\frac{2}{9}\times \frac{1}{4}(10+\frac{3}{1-\frac{1}{5}})$$ is

Question 23

If $$\sqrt{5x-6}+\sqrt{5x+6}=6$$, then what is the value of x ?

Question 24

Number of digits in the square root of 62478078 is:

Question 25

$$\frac{1}{\sqrt{a}}-\frac{1}{\sqrt{b}}=0$$, then the value of $$\frac{1}{a}+\frac{1}{b}$$ is

Question 26

The value of $$\sqrt{9-2\sqrt{16}+3\sqrt[3]{512}}$$ is

Question 27

If $$\sqrt{1+\frac{x}{144}}=\frac{13}{12}$$ then x equals to

Question 28

Arranging the following in descending order, we get
$$\sqrt[3]{4},\sqrt{2},\sqrt[6]{3},\sqrt[4]{5}$$

Question 29

Which is the largest of the following fractions ?
$$\frac{2}{5},\frac{3}{5},\frac{8}{11},\frac{11}{17}$$

Question 30

If, $$\frac{(a+b)}{\sqrt{ab}}=\frac{2}{1}$$, then the value of (a-b) is

Question 31

If $$x=\sqrt{a}+\frac{1}{\sqrt{a}},y=\sqrt{a}-\frac{1}{\sqrt{a}}, (a>o)$$ the the value of $$x^{4}+y^4-2x^2y^2$$ is

Question 32

If $$4x=\sqrt{5}+2$$, then $$x-\frac{1}{16x}$$ ?

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