Question

(i) A rational number between `1/2` and `1/5` is `1/10`.

(ii) `(sqrt(7) + 1)/(sqrt(7) - 1)` can be written as `(sqrt(7) + 1)^2`.

विकल्प

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Neither (i) nor (ii)

Explanation:

Let’s analyze both statements:

(i) A rational number between `1/2` and `1/5` is `1/10`.

`1/2 = 0.5` and `1/5 = 0.2`.

A rational number between 0.5 and 0.2 should be greater than 0.2 and less than 0.5.

But `1/10 = 0.1` which is less than 0.2.

So, `1/10` is not between `1/2` and `1/5`.

Hence, statement (i) is false.

(ii) `(sqrt(7) + 1)/(sqrt(7 - 1)` can be written as `(sqrt(7) + 1)^2`. 

Simplifying `(sqrt(7) + 1)/(sqrt(7 - 1)` by rationalizing the denominator:

`(sqrt(7) + 1)/(sqrt(7) - 1) xx (sqrt(7) + 1)/(sqrt(7) + 1)`

= `(sqrt(7) + 1)^2/((sqrt(7))^2 - 1^2)`

= `(sqrt(7) + 1)^2/(7 - 1)`

= `(sqrt(7) + 1)^2/6`

So, `(sqrt(7) + 1)/(sqrt(7) - 1) = (sqrt(7) + 1)^2/6`, not simply `(sqrt(7) + 1)^2`.

Hence, statement (ii) is false.