Assertion:

Question:

Assertion: $\sqrt{3}$ is an irrational number.

Reason: The sum of rational number and an irrational number is an irrational number.
(a) Both Assertion and Reason are true and Reasom is a correct explanation of Assertion.
(b) Both Assertion and Reason and Reasom are true but Reasom is not a correct explanation of Assertion.
(c) Assertion is true and Reasom is false.
(d) Assertion is false and Reasom is true.

Solution:

(b) Both Assertion and Reason are true, but Reason is not a correct explanation of Assertion.

$\sqrt{3}$ is not a perfect square and is irrational.

Reason: Let the sum of a rational numbe $r a$ and an irrational number $\sqrt{b}$ be a rational number $c$.

Thus, we have :

$a+\sqrt{b}=c$

$\Rightarrow \sqrt{b}=c-a$

Now, $c-a$ is rational because both $c$ and $a$ are rational, but $\sqrt{b}$ is irrational; thus, we arrive at a contradiction. Hence, the sum of a rational number and an irrational number is an irrational number.

Thus, Reason $\mathrm{R}$ is not a correct explanation.