ISI2021-MMA: 9

Question

The set of all $a$ satisfying the inequality

$$\frac{1}{\sqrt{a}} \int_{1}^{a} \left( \frac{3}{2} \sqrt{x} + 1 – \frac{1}{\sqrt{x}}  \right) dx < 4$$

Is equal to the interval

• A. $( – 5, – 2)$
• B. $(1, 4)$
• C. $(0, 2)$
• D. $(0, 4)$

Answer 1

Comments

@Udit Narayan why (1,4 ) is wrong because we just need to find the value “a” and we can find it by using a+Root(a) < 4+2 from here we can say that the value of a is 4 ….so interval must be (1,4) 

please confirm me !!!

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@NarutoUzumaki Because in the interval (1, 4) we are excluding 1 but it satisfies this inequality. Thats why (0,4) will be the answer.