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

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 2

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

Question 3

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

Question 4

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 5

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 6

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

Question 7

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

Question 8

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

Question 9

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

Question 10

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 11

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

Question 12

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

Question 13

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

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

Question 16

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

Question 17

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 18

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

Question 19

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

Question 20

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 21

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

Question 22

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

Question 23

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 24

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


Question 25

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

Question 26

Number of digits in the square root of 62478078 is:

Question 27

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

Question 28

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

Question 29

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

Question 30

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

Question 31

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

Question 32

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

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