$\displaystyle \lim_{h \to 0} \frac{\sqrt{x + h} - \sqrt{x}}{h}$ is equal to …

1

$\displaystyle \lim_{x \to \frac{\pi}{4}} \frac{\sin x - \cos x}{x - \frac{\pi}{4}}$ is equal to …

Topic: JAMIA MCA 2016

1

If $\displaystyle \lim_{x \to a} \frac{x^{\alpha} - x^{a}}{x - a} = -1$, then $\alpha$ is equal to …

Topic: JAMIA MCA 2016

2

$\displaystyle \lim_{x\to a}\frac{x^{10}-a^{10}}{x^{2}-a^{2}}$ is equal to …

Topic: JAMIA MCA 2016

3

$\displaystyle \lim_{x\to1}\frac{x+x^{2}+\ldots+x^{10}-10}{5x-5}$ is equal to …

Topic: JAMIA MCA 2016

4

$\displaystyle \int_{1}^{x}(1+\log t)^{2}\,dt$ is equal to …

Topic: JAMIA MCA 2016

5

If $x>0$, then $\displaystyle \int |x|^{3} dx$ is equal to …

Topic: JAMIA MCA 2016

6

$\displaystyle \int_{0}^{\frac{\pi}{4}}\sec^{2}x\sin x\,dx=a+\sqrt{2}$, find $a$

Topic: JAMIA MCA 2016

7

$\displaystyle \int_{0}^{1}\frac{x}{(1-x)^{1/2}}dx$ is equal to …

Topic: JAMIA MCA 2016

8

$\displaystyle \int \sqrt{x}e^{\sqrt{x}}dx$ is equal to …

Topic: JAMIA MCA 2016

9

The value of $2\sin^{2}\theta \cdot \cos^{2}\theta (\sec^{2}\theta + \csc^{2}\theta)$ is …

Topic: JAMIA MCA 2016

10

If $\cos\theta + \sec\theta = 3$, then $\cos^{2}\theta + \sec^{2}\theta$ is …

Topic: JAMIA MCA 2016