assertion reasoning class x ch 1

Assertion : When a positive integer a is divided by 4, the values of remainder can be 0, 1, 2 or 3.

Reason : According to Euclid’s Division Lemma a = bq + r , where 0 ≤ r < b and r is an integer.

• Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

• Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

• Assertion (A) is true but reason (R) is false.

• Assertion (A) is false but reason (R) is true.

Assertion : The HCF of two numbers is 18 and their product is 3072. Then their LCM = 169.

Reason : If a, b are two positive integers, then HCF x LCM = a x b.

• Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

• Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

• Assertion (A) is true but reason (R) is false.

• Assertion (A) is false but reason (R) is true.

Assertion : 12ⁿ ends with the digit zero, where n is natural number.

Reason : Any number ends with digit zero, if its prime factor is of the form 2 ^mx 5ⁿ, where m, n are natural numbers.

• Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

• Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

• Assertion (A) is true but reason (R) is false.

• Assertion (A) is false but reason (R) is true.

Assertion : 29 / 625

is a terminating decimal fraction.

Reason : If q = 2^m x 5ⁿ where n, m are non-negative integers, then p/q is a

terminating decimal fraction

• Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

• Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

• Assertion (A) is true but reason (R) is false.

• Assertion (A) is false but reason (R) is true

1. Assertion : Denominator of 12.145. When expressed in the form p/q, q ≠ 0, is of the form 2^m x 5ⁿ, where m, n are non-negative integers.

Reason : 12.145 is a terminating decimal fraction.

• Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

• Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

• Assertion (A) is true but reason (R) is false

• Assertion (A) is false but reason (R) is true.

Assertion : √x is an irrational number, where x is a prime number.

Reason : Square root of any prime number is an irrational number.

• Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

• Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

• Assertion (A) is true but reason (R) is false.

• Assertion (A) is false but reason (R) is true.

1. Assertion : For any two positive integers a and b, HCF (a, b) x LCM (a, b) = a x b Reason : The HCF of two numbers is 8 and their product is 280. Then their LCM is 40.

• Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

• Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

• Assertion (A) is true but reason (R) is false.

• Assertion (A) is false but reason (R) is true.

Assertion : 3 is a rational number.

Reason : The square roots of all positive integers are irrationals.

• Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

• Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

• Assertion (A) is true but reason (R) is false.

• Assertion (A) is false but reason (R) is true.