Question

If a is between 0 and 1, which of the following statements is (are) true?

(i) a² - 1> 0

(ii) a² + 1 > 0

(iii) a²  - a > 0

1. only (ii)
2. (i) & (ii)
3. (iii) only
4. All three

Answer 1

Correct Answer - Option 1 : only (ii)

Calculation:

Gien, 0 < a < 1, squaring both sides, 0 < a² < 1

Let us go through the statements:

(i): subtracting 1 from the inequality equation:

-1 < a2 - 1 < 0 

That is, a2 - 1 < 0 , hence (i) is false.

(ii): adding 1 to the inequality equation:

1 < a2 + 1 < 2

That is, 1 < a2 + 1, hence (i) is true

Now in the options, w can see that, only option 1 is possible as options 2 and 4 are not possible as the statement (i) is false.

Also, option 3 is not possible as we know statement (ii) is already true.

∴ Only statement 2 is possible.