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

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 2

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

Question 3

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

Question 4

Number of digits in the square root of 62478078 is:

Question 5

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 6

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 7

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

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

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 19

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

Question 20

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

Question 21

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

Question 22

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 23

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

Question 24

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 25

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 26

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 27

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

Question 28

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

Question 29

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

Question 30

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


Question 31

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

Question 32

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

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