Assertion And Reason Questions For Class 10 Maths Chapter 1 Real Numbers PDF

Assertion and Reason Questions for Class 10 Maths Chapter 1 Real Numbers are available in this Maths article. Assertion and Reason Questions for Class 10 Maths Chapter 1 Real Numbers are very useful to solve the problems easily. This article helps the students to know the key questions and answers about Real Numbers. Real numbers include rational and irrational numbers, along with concepts like HCF, LCM, and Euclid’s Division Lemma, which we use in everyday calculations. Our subject experts have provided detailed solutions for these problems based on the CBSE syllabus and the NCERT textbook. This material helps students revise the chapter easily and perform well in the final examination. A free downloadable PDF is also available for easy practice and revision.

Important Assertion And Reason Questions on Real Numbers

Directions: In the following questions a statement of assertion (A) is followed by a statement of reason(R). Mark the correct choice as:

Choose the correct option for the following questions:

• A. Both Assertion (A) and Reason (R) are true, and Reason is the correct explanation of Assertion.

• B. Both Assertion (A) and Reason (R) are true, but Reason is not the correct explanation of Assertion.

• C. Assertion (A) is true, but Reason (R) is false.

• D. Assertion (A) is false, but Reason (R) is true.

Question 1:

Assertion (A): Every composite number can be expressed as a product of prime numbers.

Reason (R): According to the Fundamental Theorem of Arithmetic, every composite number has a unique prime factorisation.

Options:

(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.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 2:

Assertion (A): The decimal expansion of (13125) is terminating.

Reason (R): 125 can be written as (53).

Options:

(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.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A. 125=53

Question 3:

Assertion (A): (5) is an irrational number.

Reason (R): Irrational numbers cannot be expressed in the form (pq).

Options:

(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.

Correct Answer: (B). Both A and R are true, but R is not the correct explanation of A.

Question 4:

Assertion (A): The HCF of two consecutive integers is always 1.

Reason (R): Consecutive integers have no common factor other than 1.

Options:

(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.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 5:

Assertion (A): The decimal expansion of (712) is non-terminating recurring.

Reason (R): 12 has a prime factor other than 2 or 5.

Options:

(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.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.12=22×3

Question 6:

Assertion (A): Every rational number is a real number.

Reason (R): Real numbers include both rational and irrational numbers.

Options:

(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.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 7:

Assertion (A): The product of two irrational numbers is always irrational.

Reason (R): Irrational numbers cannot be written in fractional form.

Options:

(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.

Correct Answer: (D). A is false, but R is true.2×2=2

Question 8:

Assertion (A): If two numbers are co-prime, then their LCM is equal to their product.

Reason (R): The HCF of co-prime numbers is 1.

Options:

(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.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A. HCF×LCM=Product of two numbers

Question 9:

Assertion (A): The decimal expansion of every irrational number is non-terminating and non-recurring.

Reason (R): Irrational numbers cannot be expressed in the form (pq).

Options:

(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.

Correct Answer: (B). Both A and R are true, but R is not the correct explanation of A.

Question 10:

Assertion (A): When a positive integer is divided by 5, the possible remainders are 0, 1, 2, 3, and 4.

Reason (R): According to Euclid’s Division Lemma,a=bq+r, 0≤r<b

Options:

(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.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 11:

Assertion (A): ( 227) has a non-terminating recurring decimal expansion.

Reason (R): The denominator 7 contains a prime factor other than 2 or 5.

Options:

(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.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 12:

Assertion (A): Every even number is divisible by 2.

Reason (R): Prime factorisation of every even number contains 2 as a factor.

Options:

(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.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 13:

Assertion (A): (3+2) is an irrational number.

Reason (R): The sum of a rational number and an irrational number is irrational.

Options:

(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.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 14:

Assertion (A): The square of any odd number is odd.

Reason (R): Every odd number can be written in the form ( 2n+1).

Options:

(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.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.(2n+1)2=4n2+4n+1

Question 15:

Assertion (A): The number5×7×11+7is composite.

Reason (R): 7 is a common factor of both terms.

Options:

(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.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.5×7×11+7=7(5×11+1)

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