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.

Take a free SSC CHSL Mock

Thousands of students have taken Cracku's Free SSC CHSL Mock.

Instructions

For the following questions answer them individually

Question 1

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

Question 2

Number of digits in the square root of 62478078 is:

Question 3

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

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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 9

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

Question 10

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 11

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


Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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 17

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

Question 18

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

Question 19

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

Question 20

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 21

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 22

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

Question 23

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

Question 24

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

Question 25

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 26

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

Question 27

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

Question 28

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

Question 29

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 30

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

Question 31

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 32

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

Download SSC CHSL Previous Papers as PDF

Solve all previous papers at your convenience by downloading PDFs. Every question has a detailed solution.

SSC Questions from other topics

Download our Highly-Rated App

Get all the help you need to crack CAT in one place.
Our highly rated app (4.6/5) is a must-have for cracking CAT.

Get it on Google Play
/

Boost your Prep!

Download App