NCERT Exemplar Solutions
Class 9 - Mathematics - CHAPTER 1: NUMBER SYSTEMS
Exercise 1.1 - Multiple Choice Questions

Write the correct answer in each of the following:

Question.  1

Every rational number is

(A)

a natural number

(B)

an integer

(C)

a real number

(D)

a whole number

Question.  2

Between two rational numbers

(A)

there is no rational number

(B)

there is exactly one rational number

(C)

there are infinitely many rational numbers

(D)

there are only rational numbers and no irrational numbers

Question.  3

Decimal representation of a rational number cannot be

(A)

terminating

(B)

non-terminating

(C)

non-terminating repeating

(D)

non-terminating non-repeating

Question.  4

The product of any two irrational numbers is

(A)

always an irrational number

(B)

always a rational number

(C)

always an integer

(D)

sometimes rational, sometimes irrational

Question.  5

The decimal expansion of the number \(\sqrt{2}\) is

(A)

a finite decimal

(B)

\(1.41421\)

(C)

non-terminating recurring

(D)

non-terminating non-recurring

Question.  6

Which of the following is irrational?

(A)

\(\sqrt{\dfrac{4}{9}}\)

(B)

\(\dfrac{\sqrt{12}}{\sqrt{3}}\)

(C)

\(\sqrt{7}\)

(D)

\(\sqrt{81}\)

Question.  7

Which of the following is irrational?

(A)

\(0.14\)

(B)

\(0.14\overline{16}\)

(C)

\(0.\overline{1416}\)

(D)

\(0.4014001400014\ldots\)

Question.  8

A rational number between \(\sqrt{2}\) and \(\sqrt{3}\) is

(A)

\(\dfrac{\sqrt{2}+\sqrt{3}}{2}\)

(B)

\(\dfrac{\sqrt{2}\cdot\sqrt{3}}{2}\)

(C)

\(1.5\)

(D)

\(1.8\)

Question.  9

The value of \(1.999\ldots\) in the form \(\dfrac{p}{q}\), where \(p\) and \(q\) are integers and \(q\neq 0\), is

(A)

\(\dfrac{19}{10}\)

(B)

\(\dfrac{1999}{1000}\)

(C)

\(2\)

(D)

\(\dfrac{1}{9}\)

Question.  10

\(2\sqrt{3}+\sqrt{3}\) is equal to

(A)

\(2\sqrt{6}\)

(B)

\(6\)

(C)

\(3\sqrt{3}\)

(D)

\(4\sqrt{6}\)

Question.  11

\(\sqrt{10}\times\sqrt{15}\) is equal to

(A)

\(6\sqrt{5}\)

(B)

\(5\sqrt{6}\)

(C)

\(\sqrt{25}\)

(D)

\(10\sqrt{5}\)

Question.  12

The number obtained on rationalising the denominator of \(\dfrac{1}{\sqrt{7}-2}\) is

(A)

\(\dfrac{\sqrt{7}+2}{3}\)

(B)

\(\dfrac{\sqrt{7}-2}{3}\)

(C)

\(\dfrac{\sqrt{7}+2}{5}\)

(D)

\(\dfrac{\sqrt{7}+2}{45}\)

Question.  13

\(\dfrac{1}{\sqrt{9}-\sqrt{8}}\) is equal to

(A)

\(\dfrac{1}{2}(3-2\sqrt{2})\)

(B)

\(\dfrac{1}{3+2\sqrt{2}}\)

(C)

\(3-2\sqrt{2}\)

(D)

\(3+2\sqrt{2}\)

Question.  14

After rationalising the denominator of \(\dfrac{7}{3\sqrt{3}-2\sqrt{2}}\), we get the denominator as

(A)

\(13\)

(B)

\(19\)

(C)

\(5\)

(D)

\(35\)

Question.  15

The value of \(\dfrac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}\) is equal to

(A)

\(\sqrt{2}\)

(B)

\(2\)

(C)

\(4\)

(D)

\(8\)

Question.  16

If \(\sqrt{2}=1.4142\), then \(\sqrt{\dfrac{\sqrt{2}-1}{\sqrt{2}+1}}\) is equal to

(A)

\(2.4142\)

(B)

\(5.8282\)

(C)

\(0.4142\)

(D)

\(0.1718\)

Question.  17

\(\sqrt[4]{\sqrt[3]{2^{2}}}\) equals

(A)

\(2^{-\frac{1}{6}}\)

(B)

\(2^{-6}\)

(C)

\(2^{\frac{1}{6}}\)

(D)

\(2^{6}\)

Question.  18

The product \(\sqrt[3]{2}\cdot\sqrt[4]{2}\cdot\sqrt[12]{32}\) equals

(A)

\(\sqrt{2}\)

(B)

\(2\)

(C)

\(\sqrt[12]{2}\)

(D)

\(\sqrt[12]{32}\)

Question.  19

Value of \(\sqrt[4]{(81)^{-2}}\) is

(A)

\(\dfrac{1}{9}\)

(B)

\(\dfrac{1}{3}\)

(C)

\(9\)

(D)

\(\dfrac{1}{81}\)

Question.  20

Value of \((256)^{0.16}\times(256)^{0.09}\) is

(A)

\(4\)

(B)

\(16\)

(C)

\(64\)

(D)

\(256.25\)

Question.  21

Which of the following is equal to \(x\)?

(A)

\(x^{\frac{12}{7}}-x^{\frac{5}{7}}\)

(B)

\(\sqrt[12]{\left(x^{4}\right)^{\frac{1}{3}}}\)

(C)

\(\left(\sqrt{x^{3}}\right)^{\frac{2}{3}}\)

(D)

\(x^{\frac{12}{7}}\times x^{\frac{7}{12}}\)

NCERT Exemplar Solutions Class 9 – Mathematics – CHAPTER 1: NUMBER SYSTEMS – Exercise 1.1 - Multiple Choice Questions | Detailed Answers