Definite Integration

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AIEEE 2003 (Offline)Question 383

$\lim\limits_{n\to\infty}\frac{1+2^{4}+3^{4}+\cdots+n^{4}}{n^{5}}-\lim\limits_{n\to\infty}\frac{1+2^{3}+3^{3}+\cdots+n^{3}}{n^{5}}$

$\frac15$$\frac1{30}$zero$\frac14$

AIEEE 2004 (Offline)Question 384

$\lim\limits_{n\to\infty}\sum\limits_{r=1}^{n}\frac1ne^{\frac rn}$ is

Definite Integration

$e+1$$e-1$$1-e$$e$

AIEEE 2005 (Offline)Question 385

$\lim\limits_{n\to\infty}\left[\frac{1}{n^{2}}\sec^{2}\frac{1}{n^{2}}+\frac{2}{n^{2}}\sec^{2}\frac{4}{n^{2}}+\cdots+\frac1n\sec^{2}1\right]$ equals

Definite Integration

$\frac12\sec1$$\frac12\operatorname{cosec}1$$\tan1$$\frac12\tan1$

JEE Main 2013 (Online) 22nd AprilQuestion 386

The integral $\int_{7\pi/4}^{7\pi/3}\sqrt{\tan^{2}x}\,dx$ is equal to :

Definite Integration

$\log2\sqrt2$$\log2$$2\log2$$\log\sqrt2$

JEE Main 2019 (Online) 9th January Morning ShiftQuestion 387

The value of $\int_0^\pi|\cos x|^3\,dx$ is

Definite Integration

$\frac23$$0$$\frac43$$-\frac43$