Question

Statement-I : $\sum _{r=0}^{n-1}\frac{1}{n}\left(\sqrt{\frac{r}{n}}+1\right)<\underset{0}{\overset{1}{\int }}(\sqrt{x}+1)dx<\sum _{r=1}^n\frac{1}{n}\left(\sqrt{\frac{r}{n}}+1\right),n\in N$. because
Statement-II : If $f(x)$ is continuous and increasing in [0, 1], then $\sum _{r=0}^{n-1}\frac{1}{n}f\left(\frac{r}{n}\right)<\underset{0}{\overset{1}{\int }}f(x)dx<\sum _{r=1}^n\frac{1}{n}f\left(\frac{r}{n}\right)$, where $n\in N$

• A. Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.
• B. Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for statement-I.
• C. Statement-I is true, Statement-II is false.
• D. Statement-I is false, Statement-II is true

Answer 1

Answer: (A)

Correct answer is (a) Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.