Question

Assertion: If `a = 5sqrt(2)` and `2a = sqrt(2x)` then x = 100.

Reason: `10sqrt(2) = sqrt(200)`.

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Given `a = 5sqrt(2)`, then:

`2a = 2 * 5sqrt(2) = 10sqrt(2)`

Now from the assertion:

`2a = sqrt(2x)`

⇒ `10sqrt(2) = sqrt(2x)`

Square both sides:

`(10sqrt(2))^2 = (sqrt(2x))^2`

⇒ `100 * 2 = 2x`

⇒ 200 = 2x

⇒ x = 100

So Assertion is true.

Now check the Reason:

`10sqrt(2) = sqrt(200)`

`sqrt(200) = sqrt(100 * 2) = 10sqrt(2)`

So Reason is also true and is the correct explanation for the assertion.