Question

If 0 < x < 1 , which of the following lists the numbers in increasing order ??

(a) √x , x , x²
(b) x² , x , √x
(c) x² , √x , x

Answer 1

answer B


`x = (1)/(4)`

`\sqrt{ (1)/(4) }= (1)/(2)`

`((1)/(4))^2 = (1)/(16)`


`(1)/(16)\ \textless \ (1)/(4)\ \textless \ (1)/(2)`

Answer 2

(b) x² , x , √x

Explanation:

Since, when x is a real number,

Such that 0 < x < 1

Then with increasing the exponent of x the value of x decreases,

That is, x with highest exponent is lowest,

Since,

`2 > 1 > (1)/(2)`

Thus, by the above statement,

`x^2 < x < x^(1)/(2)`

Hence, the numbers in increasing order is,

x² , x , √x

Where, 0 < x < 1

Option (b) is correct.