Practicing Class 9 Maths MCQ and Ganita Manjari Class 9 Maths Chapter 3 The World of Numbers MCQ Questions Online Test with Answers daily helps in time management.
MCQ on The World of Numbers Class 9
The World of Numbers MCQ Class 9
Class 9 Maths The World of Numbers MCQ
Question 1.
The temperature at a place is 6°C in the afternoon. At night it decreases by 11°C. What is the night temperature?
(a) 5°C
(b) -5°C
(c) -17°C
(d) 17°C
Answer:
(b) -5°C
Question 2.
The valuer of (-9) × (-4) is
(a) 9
(b) 4
(c) 36
(d) -36
Answer:
(c) 36
Question 3.
Which pair shows equivalent rational number?
(a) \(\frac{3}{4}, \frac{6}{8}\)
(b) \(\frac{5}{6}, \frac{5}{12}\)
(c) \(\frac{3}{2}, \frac{3}{4}\)
(d) None of these
Answer:
(a) \(\frac{3}{4}, \frac{6}{8}\)
Explanation:
\(\frac{3}{4}, \frac{6}{8}\)
\(\frac{4}{3}\)
[on dividing numerator and denominator by 2]
Question 4.
Which of the following is equivalent to \(\frac{4}{5}\) ?
(a) \(\frac{5}{4}\)
(b) \(\frac{16}{25}\)
(c) \(\frac{16}{20}\)
(d) \(\frac{15}{25}\)
Answer:
(c) \(\frac{16}{20}\)
Explanation:
\(\frac{4 \times 4}{5 \times 4}=\frac{16}{20}\)
Question 5.
-3 can be written in the form of \(\frac{p}{q}\) as
(a) \(\frac{-3}{-1}\)
(b) \(\frac{-3}{0}\)
(c) \(\frac{0}{-3}\)
(d) \(\frac{-3}{1}\)
Answer:
(d) \(\frac{-3}{1}\)
Explanation:
-3 can be written in the form of as \(\frac{p}{q}\) as \(\frac{-3}{1}\)
Question 6.
In which of the following options, does point K represent –\(\frac{1}{5}\) on the number line?
Answer:
(d)
Explanation:
–\(\frac{1}{5}\) is less than 0 and greater than -1.
So, it will lie on the left of O on the number line.
Divide the gap between O and —1 into 5 equal parts.
Thus, the point Kon the number line represents the rational number –\(\frac{1}{5}\) as shown below.
Question 7.
In the standard form of a rational number, the common factor of numerator and denominator is always
(a) 0
(b) 1
(c) -2
(d) 2
Answer:
(b) 1
Explanation:
In the standard form of a rational number, the common factor of numerator and denominator is always 1.
Question 8.
The standard form of \(\frac{-32}{40}\) is
(a) \(\frac{-32}{40}\)
(b) \(\frac{-4}{5}\)
(c) \(\frac{4}{5}\)
(d) \(\frac{-32}{40}\)
Answer:
(b) \(\frac{-4}{5}\)
Explanation:
\(\frac{-32 \div 8}{40 \div 8}=-\frac{4}{5}\)
Question 9.
To reduce a rational number to its standard form, we divide its numerator and denominator by their
(a) LCM
(b) HCF
(c) product
(d) multiple
Answer:
(b) HCF
Explanation:
To reduce a rational number to its standard form, we divide its numerator and denominator by their HCF.
Question 10.
Which of the following are equal?
(a) \(\frac{3}{5}\) and \(\frac{9}{15}\)
(b) \(\frac{2}{3}\) and \(\frac{5}{6}\)
(c) \(\frac{4}{7}\) and \(\frac{8}{15}\)
(d) \(\frac{5}{8}\) and \(\frac{10}{17}\)
Answer:
(a) \(\frac{3}{5}\) and \(\frac{9}{15}\)
Question 11.
\(\frac{7}{9}-\frac{2}{3}\) is equal to
(a) \(\frac{5}{6}\)
(b) \(\frac{1}{9}\)
(c) \(\frac{3}{9}\)
(d) \(\frac{2}{9}\)
Answer:
(b) \(\frac{1}{9}\)
Question 12.
The numerical expression \(\frac{3}{8}+\frac{(-5)}{7}=\frac{-19}{56}\), shows that
(a) rational numbers are closed under addition.
(b) rational numbers are not closed under addition.
(c) rational numbers are closed under multiplication.
(d) addition of rational numbers is not commutative.
Answer:
(a) rational numbers are closed under addition.
Explanation:
The given expression shows the rational numbers are closed under addition.
Question 13.
Which of the following is not true?
(a) Rational numbers are closed under addition.
(b) Rational numbers are closed under subtraction.
(c) Rational numbers are closed under multiplication.
(d) Rational numbers are closed under division.
Answer:
(d) Rational numbers are closed under division.
Explanation:
Rational numbers are not closed under division.
Question 14.
Which of the following is not true?
(a) \(\frac{10}{11}+\frac{11}{12}=\frac{11}{12}+\frac{10}{11}\)
(b) \(\frac{10}{11} \times \frac{11}{12}=\frac{11}{12} \times \frac{10}{11}\)
(c) \(\frac{10}{11} \div \frac{11}{12}=\frac{11}{12} \div \frac{10}{11}\)
(d) \(\frac{10}{11} \div \frac{11}{12}=\frac{10}{11} \times \frac{12}{11}\)
Answer:
(c) \(\frac{10}{11} \div \frac{11}{12}=\frac{11}{12} \div \frac{10}{11}\)
Explanation:
From option (C), we have
∴ LHS ≠ RHS
Question 15.
Which of the following operation is not associative for rational numbers?
(a) Addition
(b) Division
(c) Subtraction
(d) Both (b) and (c)
Answer:
(d) Both (b) and (c)
Explanation:
Both subtraction and division are not associative for rational number.
Question 16.
Zero (0) is
(a) the identity for addition of rational numbers.
(b) the identity for subtraction of rational numbers.
(c) the identity for multiplication of rational numbers.
(d) the identity for division of rational numbers.
Answer:
(a) the identity for addition of rational numbers.
Explanation:
0 is the identity for addition of rational numbers.
Question 17.
One (1) is
(a) the identity for addition of rational numbers.
(b) the identity for subtraction of rational numbers.
(c) the identity for multiplication of rational numbers.
(d) the identity for division of rational numbers.
Answer:
(c) the identity for multiplication of rational numbers.
Explanation:
1 is the identity for multiplication of rational numbers.
Question 18.
Multiplicative inverse of 0 is
(a) -1
(b) 1
(c) 0
(d) not defined
Answer:
(d) not defined
Explanation:
Multiplicative inverse of 0 is not defined.
Question 19.
Multiplicative inverse of a negative rational number is
(a) 0
(b) -1
(c) a negative rational number
(d) a positive rational number
Answer:
(d) a positive rational number
Explanation:
Multiplicative inverse of a negative rational number is a positive rational number.
Question 20.
Which of the following number does not have multiplicative inverse?
(a) 1
(b) -1
(c) 0
(d) None of these
Answer:
(d) None of these
Explanation:
\(-\frac{3}{8} \times\left(-\frac{24}{13}\right)=\frac{(-3) \times(-3)}{13}=\frac{9}{13}\) and \(\frac{9}{13} \times \frac{13}{9}\)
So, multiplicative inverse of given expression is \(\frac{13}{9}\)
Question 21.
Which of the following number does not have multiplicative inverse?
(a) 1
(b) -1
(c) 0
(d) None of these
Answer:
(c) 0
Explanation:
0 does not have multiplicative inverse.
Question 22.
If is the multiplicative inverse of a number x then multiplicative inverse of \(\frac{a}{b}\) is
(a) \(\frac{1}{x}\)
(b) x
(c) \(\frac{a x}{b}\)
(d) \(\frac{x b}{a}\)
Answer:
(b) x
Explanation:
Since, the multiplicative inverse of \(\frac{a}{b}\) is \(\frac{b}{a}\) and given \(\frac{b}{a}\) = x.
So, the multiplicative inverse of \(\frac{a}{b}\) is x.
Question 23.
Which of the following is an example of distributive property over addition for rational number?
(a) \(-\frac{5}{4} \times\left(\frac{6}{17}+\frac{15}{9}\right)=\left(\frac{6}{17}+\frac{15}{9}\right) \times\left(-\frac{5}{4}\right)\)
(b) \(\frac{2}{3} \times\left(-\frac{7}{18}-\frac{19}{2}\right)=\frac{2}{3} \times\left(-\frac{7}{18}\right)-\frac{2}{3} \times \frac{19}{2}\)
(c) \(\frac{2}{3} \times\left(-\frac{7}{15}+\frac{19}{2}\right)=\frac{2}{3} \times\left(-\frac{7}{18}\right)+\frac{2}{3}+\frac{19}{2}\)
(d) \(\frac{15}{8} \times\left[\frac{6}{17}+\left(-\frac{5}{4}\right)\right]=\frac{15}{8} \times \frac{6}{17}+\left(-\frac{5}{4}\right)\)
Answer:
(b) \(\frac{2}{3} \times\left(-\frac{7}{18}-\frac{19}{2}\right)=\frac{2}{3} \times\left(-\frac{7}{18}\right)-\frac{2}{3} \times \frac{19}{2}\)
Explanation:
Distributive property states that
a × (b + c) = (a × b) ÷ (a × c)
From option (B),
Let a = \(\frac{2}{3}\), b = \(\frac{-7}18}\) and c = \(\frac{-19}{2}\)
Then, from Eq. (1), we get
\(\frac{2}{3} \times\left(-\frac{7}{18}-\frac{19}{2}\right)=\frac{2}{3} \times\left(-\frac{7}{18}\right)-\frac{2}{3} \times \frac{19}{2}\)
Question 24.
A rational number between 3.1455 and 3.1456.
(a) 3.1355
(b) 3.3246
(c) 3.1555
(d) 3.14555
Answer:
(d) 3.14555
Explanation:
\(\frac{3.1455+3.1456}{2}\) = 3.14555
Question 25.
A rational number between √2 and √3 is
(a) \(\frac{\sqrt{3}-\sqrt{2}}{2}\)
(b) 1.52
(c) 1.92
(d) \(\frac{\sqrt{3}+\sqrt{2}}{2}\)
Answer:
(d) \(\frac{\sqrt{3}+\sqrt{2}}{2}\)
Explanation:
We know that rational number between a and b is \(\frac{a+b}{2}\)
Question 26.
Decimal representation ola rational number cannot be
(a) terminating
(b) non-terminating
(c) non-terminating repeating
(d) non-terminating non-repeating
Answer:
(d) non-terminating non-repeating
Explanation:
Decimal representation of a rational number cannot be non .terminating non-repeating because the decimal expansion of rational number is either terminating or non-terminating recurring (repeating).
Question 27.
The value of 1.999… in the form of \(\frac{p}{q}\), where p and q are integers and q ≠ 0, is
(a) \(\frac{19}{10}\)
(b) \(\frac{1999}{1000}\)
(c) 2
(d) \(\frac{1}{9}\)
Answer:
(c) 2
Explanation:
Let x = 1.999… …..(i)
Here, the number of repeating digits is 1.
So. on multiplying both sides Eq. (i) by 101, we get
10x = 19.999… …(ii)
On subtracting Eq. (i) from Eq. (ii), we get
Question 28.
1.272727 ….. can be expressed in rational form as
(a) \(\frac{14}{99}\)
(b) \(\frac{14}{11}\)
(c) \(\frac{11}{14}\)
(d) \(\frac{99}{14}\)
Answer:
(b) \(\frac{14}{11}\)
Explanation:
Let x = 1.2727…
Here, the number of repeating digits is 2.
So, on multiplying both sides of Eq. (i) by 102
i.e. 100, we get
100x = 127.2727… …(ii)
On subtracting Eq. (i) from Eq.(ii), we get
99x = 126 ⇒ x = \(\frac{14}{11}\)
Question 29.
The value of 2.6̄ – 0.9̄ is
(a) \(\frac{4}{3}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{5}{3}\)
(d) \(\frac{7}{3}\)
Answer:
(c) \(\frac{5}{3}\)
Explanation:
Let x = 2.6̄ =2.666 ……(i)
Here, the number of repeating digit is 1.
So, on multiplying both sides Eq. (i) by 101.
we get
10x = 26.666 … …(ii)
On subtracting Eq. (j) from Eq. (ii), we get
9x = 24
⇒ x = \(\frac{24}{9}=\frac{8}{3}\) …(iii)
Let y = 0.9 = 0.9999 …(iv)
On multiplying both sides of Eq. (iv) by 10, we get
10y = 9.999… …(v)
On subtracting Eq. (iv) from Eq. (y). we get
10y – y = 9
⇒ y = 1 …(vi)
2.6̄ – 0.9̄ = x – y [using Eqs. (i) and (iv)]
= \(\frac{8}{3}\) (using Eqs. (iii) arid (vi))
= \(\frac{5}{3}\)
Question 30.
If 0.142857142857… express in the form of \(\frac{m}{n}\) then the value of 2m + n is
(a) 1
(b) 2
(c) 7
(d) 9
Answer:
(d) 9
Explanation:
Let x = 0.142857142857… …(i)
Here, the number of repeating digits are 6.
So, on multiplying both sides of Eq.(i) by 10 6 i.e. 1000000, we get
1000000x = 142857.142857… …(ii)
On subtracting Eq. (i) from Eq. (ii), we get
1000000x – x = 142857.142857… – 0.142857…
⇒ 999999x = 142857
⇒ x = \(\frac{142857}{999999}\)
⇒ x = \(\frac{1}{7}\)
Here, m = 1 and n = 7
∴ 2m + n = 2 × 1 + 7 =9
Question 31.
Decimal form of \(\frac{1}{17}\) is
(a) terminating
(b) non-terminating
(c) non-terminating repeating
(d) non-terminating non-repeating
Answer:
(d) non-terminating non-repeating
Explanation:
\(\frac{1}{17}\) = 0.058823529411764705 …
= \(0 . \overline{0588235294117647}\)
The World of Numbers Class 9 Assertion and Reason Questions
Direction (Question Nos 1-5) In the questions given below, there are two statement marked as
Assertion (A) and Reason (R). Read the statements and choose the correct option.
Question 32.
Assertion (A) The product of two negative numbers is always positive number.
Reason (R) The sum of two fortunes is a debt.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(c) A is true but R is false.
Explanation:
We know that product of two debts (negative numbers) is a fortune (positive number) and sum of two fortunes (positive number) is a fortune. Hence, Assertion is true but Reason is false.
Question 3.
Assertion (A) Product of two rational numbers are rational.
Reason (R) Rational numbers are closed under multiplication.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(a) Both A and R are true and R is the correct explanation of A.
Explanation:
We know that rational numbers are closed under multiplication. Therefore, product of two rational numbers is rational.
Question 4.
Assertion (A) For any three rational numbers x, y and z, x + (y x z) = (x + y) x (x + z).
Reason (R) For any three rational numbers a, b and c,a(b+c) =ab+ac.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(d) A is false but R is true.
Explanation:
Here, Assertion is false but Reason is true.
Question 5.
Assertion (A) The decimal value of is 0.437437…, which is rational.
Reason (R) A non-terminating repeating decimal number is a rational number.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(a) Both A and R are true and R is the correct explanation of A.
Explanation:
Assertion When we divide 437 by 999, we get 0.437437…
Here, we see that decimal number is a non-terminating but it is repeated, so it is a rational number.
Hence, Assertion is true.
Reason It is true, that a non-terminating repeating decimal number is a rational number and it is a correct explanation of Assertion.
Question 6.
Assertion (A) The decimal expansion of is terminating.
Reason (R) 5 \(\frac{1}{8}\) has non-terminating decimal 8 expansion.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(c) A is true but R is false.
Explanation:
Assertion We have, \(\frac{39}{100}\) = 0.39, so it has terminating decimal expansion.
Reason We have, 5\(\frac{1}{8}\) = \(\frac{41}{8}\) = 5.125, so it has terminating decimal expansion.
Hence, Assertion is true but Reason is false.