# Assertion Reason MCQ on Real Numbers – Class 10 Mathematics

The Chapter 1 of Class 10 Mathematics under the NCERT Syllabus is about the Real Numbers. The various topics that are discussed in the chapter are Euclid’s Division Lemma, The Fundamental Theorem of Arithmetic, Irrational Numbers, and Rational Numbers and Their Decimal Expansions. This section consists of Assertion Reason MCQ Practice Questions on Real Numbers for Class 10.

Each of the following questions contains two statements: Assertion (A) and Reason (R). Also, each of the questions has four options. Out of the four options, only one option is correct. Choose the correct answer for all the questions and then click on the submit button for results.

## Assertion Reason MCQ on Real Numbers - Class 10 Mathematics

1.
Assertion (A): $\sqrt{3}$ is a rational number.

Reason (R): Let $p$ be a prime number, then $\sqrt{p}$ is an irrational number.

2.
Assertion (A): $\pi$ is an irrational number.

Reason (R): $\pi$ can be expressed in the form $\frac{p}{q}$.

3.
Assertion (A): If the LCM of two integers 26 and 91 is 182, then $HCF(26,\,91)=13$.

Reason (R): $LCM\times Product of two Integers=HCF$

4.
Assertion (A): The factors of $91$ are $7$ and $13$.

Reason (R): 91 is not a composite number.

5.
Assertion (A): Every Positive odd integer is of the form $2q+1$

Reason (R): By Euclid's Algorithm, $a=2q+r$. For some positive integers $q$ if $r=1$, $a$ is odd.

6.
Assertion (A): $\frac{13}{3125}$ is a rational number.

Reason (R): $\frac{13}{3125}$ has non-terminating non-repeating decimal expansion.

7.
Assertion (A): The HCF of $(3,\,11)$ is $1$.

Reason (R): If $p$ and $q$ are prime, then the $HCF (p,\,q)=1$

8.
Assertion (A): HCF of $(10,\,12)$ is $2$

Reason (R): If $p$ and $q$ are prime, then $HCF(p,\,q)=1$

9.
Assertion (A): Every positive even integer is of the form $2q$

Reason (R): By Euclid's Algorithm, $a=2q+r$. For some positive integers $q$ if $r=0$, $a$ is even.

10.
Assertion (A): $\frac{1}{7}$ is an irrational number.

Reason (R): $\frac{1}{7}$ has non-terminating repeating decimal expansion.

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