The World of Numbers Class 9 MCQ Maths Chapter 3 - #NCSOLVE 📚

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MCQ on The World of Numbers Class 9

The World of Numbers MCQ Class 9

Class 9 Maths MCQ Chapter 3 The World of Numbers

Question 1.
The decimal representation of a rational number cannot be
(a) terminating
(b) non-terminating repeating
(c) non-terminating non-repeating
(d) Both (b) and (c)
Solution:
The decimal representation of a rational number cannot be non-terminating and non-repeating.
Hence, (c) is the correct answer.

Question 2.
According to Brahmagupta’s idea of rina (debt) and dhana (fortune), what is the result of multiplying two debts?
(a) a debt
(b) zero
(c) a fortune
(d) cannot be determined
Solution:
In Brahmagupta’s framework, negative numbers are treated as debts (rina) and positive numbers as fortunes (dhana).
He stated that “the product of two debts is a fortune,” which in modern terms means: (-) × (-) = +.
Hence, (c) is the correct answer.

Question 3.
Which of the following is a rational number?
(a) 1 + √3
(b) π
(c) 2√3
(d) 0
Answer:
(d) 0

Question 4.
Every rational number is:
(a) a natural number
(b) an integer
(c) a real number
(d) a whole number
Answer:
(c) a real number

Question 5.
A rational number lying between -3 and 3 is:
(a) 0
(b) -4.3
(c) -3.4
(d) 1.101 1001 10001 ….
Answer:
(a) 0

Question 6.
A rational number lying between √2 and √3 is :
(a) \(\frac{\sqrt{2}+\sqrt{3}}{2}\)
(b) √6
(c) 1.6
(d) 1.9
Answer:
(c) 1.6

Question 7.
The rational number between –\(\frac{1}{5}\) and –\(\frac{2}{5}\) is:
(a) 0
(b) \(-\frac{1}{4}\)
(c) \(-\frac{3}{10}\)
(d) \(-\frac{7}{25}\)
Answer:
(c) \(-\frac{3}{10}\)

Question 8.
Two rational numbers between \(\frac{2}{3}\) and \(\frac{5}{3}\) are:
(a) \(\frac{1}{6}\) and \(\frac{2}{6}\)
(b) \(\frac{1}{2}\) and \(\frac{2}{7}\)
(c) \(\frac{5}{6}\) and \(\frac{7}{6}\)
(d) \(\frac{2}{3}\) and \(\frac{4}{3}\)
Answer:
(c) \(\frac{5}{6}\) and \(\frac{7}{6}\)

Question 9.
If √x is irrational number, then x is:
(a) rational
(b) irrational
(c) 0
(d) real
Answer:
(d) real

Question 10.
The decimal form of \(\frac{56}{1000}\) is:
(a) 0.56
(b) 0.056
(c) 0.0056
(d) 5.6
Answer:
(b) 0.056

Question 11.
A terminating decimal is:
(a) natural number
(b) a whole number
(c) a rational number
(d) an integer
Answer:
(c) a rational number

Question 12.
A number is an irrational if and only if its decimal representation is:
(a) non-terminating
(b) non-terminating and repeating
(c) non-terminating and non-repeating
(d) terminating
Answer:
(c) non-terminating and non-repeating

Question 13.
Which of the following is a rational number?
(a) √5
(b) π
(c) 0.101 001 0001 00001
(d) 0.853 853 853
Answer:
(d) 0.853 853 853

Question 14.
Which one of the following is an irrational number?
(а) 0.14
(б) 0.1446
(c) 0.1446
(d) 0.401 4001 40001 ……
Answer:
(d) 0.401 4001 40001 ……

Question 15.
Which of the following is an irrational number?
(a) 0.15
(b) 0.1516
(c) 0.1516
(d) 0.501 5001 50001…….
Answer:
(d) 0.501 5001 50001…….

Question 16.
Which of the following numbers is an irrational number?
(a) \(\sqrt{23}\)
(b) \(\sqrt{225}\)
(c) 0.3796
(d) \(7 . \overline{478}\)
Answer:
(a) \(\sqrt{23}\)

Question 17.
Which of the following is an irrational number?
(a) 3.3
(b) 3.763
(c) 0.763
(d) 3.101 1001 10001……
Answer:
(d) 3.101 1001 10001……

Question 18.
The decimal expansion of √2 is:
(a) finite decimal
(b) 1.4121
(c) non-terminating recurring
(d) non-terminating non-recurring
Answer:
(d) non-terminating non-recurring

Question 19.
π is:
(a) a rational number
(b) an integer
(c) an irrational number
(d) a whole number
Answer:
(c) an irrational number

Question 20.
An irrational number between \(\frac{5}{7}\) and \(\frac{7}{9}\) is
(a) 0.75
(b) √6
(c) 0.750 7500 75000…………..
(d) 0.7512
Answer:
(c) 0.750 7500 75000…………..

Question 21.
The value of 2.9̄ in the form \(\frac{p}{q}\) where p and q are integers and q ≠ 0, is
(a) \(\frac{2999}{1000}\)
(b) \(\frac{19}{10}\)
(c) 3
(d) \(\frac{26}{9}\)
Answer:
(c) 3

Question 22.
The sum of 0.3̄ and 0.2̄ is :
(a) \(\frac{5}{99}\)
(b) \(\frac{5}{9}\)
(c) \(\frac{5}{10}\)
(d) \(\frac{5}{100}\)
Answer:
(b) \(\frac{5}{9}\)

Question 23.
(-2 – √3) (-2 + √3) when simplified is:
(a) positive and irrational
(b) positive and rational
(c) negative and irrational
(d) negative and rational
Answer:
(b) positive and rational

Question 24.
(√2 +1 / √2)² is equal to :
(a) 4√2
(b) \(\frac{9}{2}\)
(c) 4/√2
(d) 9
Answer:
(b) \(\frac{9}{2}\)

Question 25.
√12 x √8 is equal to :
(a) 2√6
(b) 3√6
(c) 4√6
(d) 6√6
Answer:
(c) 4√6

Question 26.
Value of \(\frac{1}{2}\) is equal to:
(a) √2
(6) -√2
(c) \(\frac{1}{\sqrt{2}}\)
(d) –\(\frac{1}{\sqrt{2}}\)
Answer:
(d) –\(\frac{1}{\sqrt{2}}\)

Question 27.
If √3 = 1.732 and √2 = 1.414, the value of \(\frac{1}{\sqrt{3}-\sqrt{2}}\) is:
(a) 0.318
(b) 3.146
(c) \(\frac{1}{3.146}\)
(d) \(\sqrt{1.732}-\sqrt{1.414}\)
Answer:
(b) 3.146

Question 28.
The difference of \(\frac{5}{8}\) and \(\frac{4}{7}\) is:
(a) \(\frac{9}{56}\)
(b) \(\frac{3}{56}\)
(c) \(\frac{3}{28}\)
(d) none of these
Answer:
(c) \(\frac{3}{28}\)

Question 29.
The quotient of \(\left(\frac{-5}{8}\right) \div \frac{3}{4}\) is:
(a) \(\frac{-6}{5}\)
(b) \(\frac{4}{7}\)
(c) \(\frac{5}{6}\)
(d) \(\frac{-5}{6}\)
Answer:
(d) \(\frac{-5}{6}\)

Question 30.
The number of rational numbers between \(\) and \(\) is:
(a) 0
(b) 1
(c) 3
(d) uncountable
Answer:
(d) uncountable

Question 31.
The repeating block of the fraction which of the following will not be a cyclic number.
(a) 19
(b) 17
(c) 13
(d) 7
Answer:
(c) 13

Question 32.
7.5 can be expressed in the form \(\frac{p}{q}\) as:
(a) \(\frac{69}{9}\)
(b) \(\frac{79}{99}\)
(c) \(\frac{7}{9}\)
(d) none of these
Answer:
(d) none of these

Question 33.
Which of the following can be expressed as 0.1375?
(a) \(\frac{1375}{500}\)
(b) \(\frac{41}{160}\)
(c) \(\frac{27}{32}\)
(d) \(\frac{11}{80}\)
Answer:
(d) \(\frac{11}{80}\)

Question 34.
The number of digits in repeating block of \(\frac{1}{19}\) is:
(a) 20
(b) 19
(c) 18
(d) 21
Answer:
(c) 18

Question 35.
The sum of \(\frac{2}{3}\) and \(\frac{1}{6}\) is:
(a) \(\frac{5}{6}\)
(b) \(\frac{1}{2}\)
(c) –\(\frac{2}{3}\)
(d) none of these
Answer:
(a) \(\frac{5}{6}\)

Question 36.
Product of –\(\frac{2}{11}\) and –\(\frac{11}{8}\) is:
(a) –\(\frac{1}{4}\)
(b) \(\frac{1}{8}\)
(c) \(\frac{1}{4}\)
(d) none of these
Answer:
(c) \(\frac{1}{4}\)

Question 37.
Which of the following are not equal?
(a) \(\frac{1}{2}\) and \(\frac{3}{6}\)
(b) \(\frac{1}{5}\) and \(\frac{13}{10}\)
(c) \(\frac{8}{29}\) and \(\frac{32}{36}\)
(d) \(\frac{3}{7}\) and \(\frac{21}{49}\)
Answer:
(b) \(\frac{1}{5}\) and \(\frac{13}{10}\)

The World of Numbers Class 9 Assertion and Reason Questions

Two statements are given, one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer from the options (a), (b), (c), and (d) given below.
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of the Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.

Question 1.
Assertion (A): The product of a debt and a fortune is always a debt.
Reason (R): In Brahmagupta’s rules, a negative number represents a debt and a positive number represents a fortune.
Solution:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
According to Brahmagupta, multiplying a debt (-) by a fortune (+) results in a debt (-), i.e., (- × + = -).

Question 2.
Assertion (A): √n is rational if n is not a perfect square.
Reason (R): \(\frac{1}{a^n}=a^{-n}\)
Solution:
(d) Assertion (A) is false, but Reason (R) is true.
√n is an irrational number if n is not a perfect square number.
For example, √20 = 2√5 is an irrational number.

Question 3.
Assertion (A): Every point on the number line corresponds to a real number which may be either rational or irrational.
Reason (R): The decimal representation of the rational number \(\frac {2}{25}\) is 0.08.
Solution:
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

Question 4.
Assertion (A): Every integer is a rational number.
Reason (R): Every integer (Z) that can be expressed in the form of \(\frac {Z}{1}\).
Solution:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of the Assertion (A).
Positive integers, like 2, 3, 4,… can be written as \(\frac{2}{1}, \frac{3}{1}, \frac{4}{1}, \ldots\)
Integer zero can be written as \(\frac {0}{1}\).
Negative integers like -2, -3, -4, … can be written as \(-\frac{2}{1}, \frac{-3}{1}, \frac{-4}{1}\)
So, we can say that every integer is a rational number.

Question 5.
Assertion (A): 1.25 is a terminating decimal.
Reason (R): A decimal in which a ‘digit’ or a ‘set of digits’ is repeated periodically, is called a recurring or repeating a decimal.
Solution:
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Terminating decimals always have a finite number of digits. Recurring or repeating decimals are also referred to as ‘periodic decimals’.

Question 6.
Assertion (A): Every rational number is an integer.
Reason (R): \(\frac {7}{4}\) is not an integer.
Solution:
(d) Assertion (A) is false, but Reason (R) is true.
Few rational numbers can be integers like (\(\frac {4}{1}\) = 4), (\(\frac {11}{1}\) = 11), but most of them are not integers, like \(\frac{4}{7}, \frac{7}{11}\).
\(\frac {7}{4}\) gives 1.75 which is clearly not an integer.

Question 7.
Assertion (A): 5√13 and \(\sqrt{5+19}\) are the irrational numbers.
Reason (R): Every integer is a rational number.
Solution:
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
√13 is an irrational number, and we know that rational × irrational = irrational.
Also, \(\sqrt{5+19}=\sqrt{24}=2 \sqrt{6}\) which is also irrational number.

Question 8.
Assertion (A): √13 is an irrational number.
Reason (R): Square root of x, where ‘x’ is not a perfect square is an irrational number.
Answer:
(a) Both assertion (A) and reason (R) are true, and reason (R) is the correct explanation of assertion (A)

Question 9.
Assertion (A): 1.121221222… is a rational number.
Reason: (R): A number having non-terminating recurring decimal representation is a rational number.
Answer:
(d) Assertion (A) is false, but the reason (R) is true.

Question 10.
Assertion (A): Square root of a. where ‘a’ is a perfect square is a rational number.
Reason (R): To even’ real number corresponds a point on the number line.
Answer:
(b) Both assertion (A) and reason (R) are true, and reason (R) is not the correct explanation of assertion (A)

Question 11.
Assertion (A): Both 2.212121,.. and 2.212212221…are real numbers.
Reason (A) : Both rational and irrational numbers are real numbers.
Answer:
(a) Both assertion (A) and reason (R) are true, and reason (R) is the correct explanation of assertion (A)

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