Question

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

Reason (R): If p is prime then \[\frac{1}{\sqrt{p}}\] is irrational.

Options

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

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

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is false and Reason (R) is true.

Explanation:

Step 1 – Assertion: A is false. Since \[\frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}\] and \(\sqrt{3}\) is irrational, \[\frac{1}{\sqrt{3}}\] is irrational, not rational.

Step 2 – Reason: R is true. If p is prime, then \[\frac{1}{\sqrt{p}}\] is irrational; this applies to p = 3.