Mastering Real Numbers: Class 10 Maths Board Exam Prep Quiz

Question 1

Which of the following is a rational number?

Accepted Answer

$0.3333...$

Answer

$\sqrt{3}$

Answer

$\pi$

Answer

$2 + \sqrt{2}$

Question 2

The HCF of $96$ and $404$ using the prime factorization method is:

Accepted Answer

$4$

Answer

$96$

Answer

$101$

Answer

$24 	imes 101$

Question 3

If the HCF of $65$ and $117$ is expressible in the form $65m - 117$, then the value of $m$ is:

Accepted Answer

$2$

Answer

$1$

Answer

$3$

Answer

$4$

Question 4

The decimal expansion of the rational number $14587/1250$ will terminate after how many decimal places?

Accepted Answer

$4$

Answer

$1$

Answer

$2$

Answer

$3$

Question 5

If $p$ and $q$ are two positive integers such that $p = a^3b^2$ and $q = a^2b^3$, where $a$ and $b$ are prime numbers, then LCM $(p, q)$ is:

Accepted Answer

$a^3b^3$

Answer

$a^2b^2$

Answer

$a^5b^5$

Answer

$ab$

Question 6

Which of the following statements is true?

Accepted Answer

The product of a non-zero rational number and an irrational number is always irrational.

Answer

The product of two rational numbers is always irrational.

Answer

The sum of a rational and an irrational number is always rational.

Answer

The sum of two irrational numbers is always irrational.

Question 7

Given that HCF $(306, 657) = 9$, then LCM $(306, 657)$ is:

Accepted Answer

$22338$

Answer

$1988$

Answer

$452$

Answer

$306 	imes 657$

Question 8

A number $x$ is called prime if it has exactly two factors, $1$ and $x$. Which of the following is NOT a prime number?

Accepted Answer

$27$

Answer

$19$

Answer

$23$

Answer

$29$

Question 9

The largest number which divides $70$ and $125$, leaving remainders $5$ and $8$ respectively, is:

Accepted Answer

$13$

Answer

$65$

Answer

$875$

Answer

$1750$

Question 10

The product of a non-zero rational number and an irrational number is:

Accepted Answer

Always irrational

Answer

Always rational

Answer

Rational or irrational

Answer

One

Question 11

The least number that is divisible by all numbers from $1$ to $5$ is:

Accepted Answer

$60$

Answer

$10$

Answer

$20$

Answer

$120$

Question 12

If $n$ is a natural number, then $6^n - 5^n$ always ends with:

Accepted Answer

$1$

Answer

$3$

Answer

$5$

Answer

$7$

Question 13

For some integer $m$, every odd integer is of the form:

Accepted Answer

$2m+1$

Answer

$m$

Answer

$m+1$

Answer

$2m$

Question 14

If $2$ is a prime number, then $2\sqrt{2}$ is:

Accepted Answer

An irrational number

Answer

A rational number

Answer

An integer

Answer

A composite number

Question 15

The decimal expansion of $23 / (2^2 	imes 5)$ will terminate after how many places?

Accepted Answer

$2$

Answer

$1$

Answer

$3$

Answer

$4$

Question 16

Which of the following numbers has a non-terminating repeating decimal expansion?

Accepted Answer

$64 / (455)$

Answer

$13 / (3125)$

Answer

$17 / (8)$

Answer

$23 / (2^3 	imes 5^2)$

Question 17

The HCF of two numbers is $27$ and their LCM is $162$. If one of the numbers is $54$, the other number is:

Accepted Answer

$81$

Answer

$36$

Answer

$45$

Answer

$9$

Question 18

If $p$ is a prime number, then $\sqrt{p}$ is:

Accepted Answer

Always irrational

Answer

Always rational

Answer

Always an integer

Answer

Sometimes rational, sometimes irrational

Question 19

If $a = 2^3 	imes 3^1 	imes 5^2$ and $b = 2^2 	imes 3^3 	imes 5^1$, then HCF $(a, b)$ is:

Accepted Answer

$2^2 	imes 3^1 	imes 5^1$

Answer

$2^3 	imes 3^3 	imes 5^2$

Answer

$2^5 	imes 3^4 	imes 5^3$

Answer

$2^1 	imes 3^1 	imes 5^1$

Question 20

The sum of two irrational numbers is:

Accepted Answer

Can be rational or irrational

Answer

Always rational

Answer

Always irrational

Answer

Always an integer

Question 21

Which of the following is NOT an irrational number?

Accepted Answer

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

Answer

$\sqrt{2} + \sqrt{3}$

Answer

$\sqrt{7}$

Answer

$3\sqrt{5}$

Question 22

If $LCM(x, 18) = 36$ and $HCF(x, 18) = 2$, then $x$ is:

Accepted Answer

$4$

Answer

$2$

Answer

$3$

Answer

$5$

Question 23

The number $7 	imes 11 	imes 13 + 13$ is a:

Accepted Answer

Composite number

Answer

Prime number

Answer

Neither prime nor composite

Answer

Rational number but not an integer

Question 24

A rational number between $\sqrt{2}$ and $\sqrt{3}$ is:

Accepted Answer

$1.5$

Answer

$1.9$

Answer

$1.3$

Answer

$1.8$

Question 25

If $a$ and $b$ are two positive integers, then HCF $(a, b) 	imes$ LCM $(a, b)$ is equal to:

Accepted Answer

$a 	imes b$

Answer

$a+b$

Answer

$a/b$

Answer

$a-b$

Question 26

Which of the following numbers can be written in the form $p/q$ where $q$ is of the form $2^n 5^m$?

Accepted Answer

$0.375$

Answer

$0.120120012000...$

Answer

$0.4\overline{7}$

Answer

$\sqrt{2}$

Question 27

The number of decimal places after which the decimal expansion of the rational number $43 / (2^4 	imes 5^3)$ will terminate is:

Accepted Answer

$4$

Answer

$1$

Answer

$2$

Answer

$3$

Question 28

If $n$ is any natural number, then $12^n$ cannot end with the digit:

Accepted Answer

$0$

Answer

$2$

Answer

$4$

Answer

$6$

Question 29

Consider the numbers $4^n$, where $n$ is a natural number. For $4^n$ to end with the digit $0$, the prime factorization of $4^n$ must contain:

Accepted Answer

Both $2$ and $5$

Answer

Only $2$

Answer

Only $5$

Answer

Only $3$

Question 30

What is the HCF of the smallest prime number and the smallest composite number?

Accepted Answer

$2$

Answer

$1$

Answer

$3$

Answer

$4$

Questions in this Quiz

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Mastering Real Numbers: Class 10 Maths Board Exam Prep Quiz

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