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

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 3

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 4

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

Question 5

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

Question 6

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


Question 7

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

Question 8

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

Question 9

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 10

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

Question 11

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

Question 12

Number of digits in the square root of 62478078 is:

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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

Question 22

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 23

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

Question 24

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

Question 25

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

Question 26

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 27

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

Question 28

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 29

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 30

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

Question 31

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

Question 32

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

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