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Question 1:

Assertion (A): Every terminating decimal is a rational number.
Reason (R): A terminating decimal can be expressed in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

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.

Answer: (a)

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Question 2:

Assertion (A): The number $0.123123123…$ is a rational number.
Reason (R): A repeating decimal can always be converted into a fraction.

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.

Answer: (a)

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Question 3:

Assertion (A): The HCF of two co-prime numbers is always 1.
Reason (R): Two numbers are co-prime if they 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.

Answer: (a)

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Question 4:

Assertion (A): The number $\sqrt{7}$ is irrational.
Reason (R): The square root of any prime 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.

Answer: (a)

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Question 5:

Assertion (A): The LCM of two numbers is always divisible by their HCF.
Reason (R): For any two numbers, $\text{HCF} \times \text{LCM} = \text{Product of the numbers}$.

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.

Answer: (b)

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Question 6:

Assertion (A): The sum of two irrational numbers $2 + \sqrt{3}$ and $2 – \sqrt{3}$ is rational.
Reason (R): The sum of two irrational numbers is always 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.

Answer: (c)

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Question 7:

Assertion (A): The decimal expansion of $\frac{13}{3125}$ is terminating.
Reason (R): A rational number $\frac{p}{q}$ has a terminating decimal expansion if $q$ is of the form $2^n \times 5^m$.

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.

Answer: (a)

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Question 8:

Assertion (A): The number $6^n$ cannot end with the digit 5 for any natural number $n$.
Reason (R): A number ending with 5 must have 5 as a prime factor, but 6 has only 2 and 3 as prime factors.

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.

Answer: (a)

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Question 9:

Assertion (A): The product of a non-zero rational and an irrational number is always irrational.
Reason (R): Rational numbers are closed under multiplication.

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.

Answer: (b)

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Question 10:

Assertion (A): The HCF of 12 and 18 is 6.
Reason (R): HCF is the greatest common divisor of two 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.

Answer: (a)

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