List of top Mathematics Questions asked in KEAM

Given that $\int_{0}^{1}\tan^{-1}(t)\,dt = \frac{\pi}{4} - \frac{1}{2}\log 2$, then $\int_{0}^{1}\tan^{-1}(1-t)\,dt =$

If $a+b=10$ and $ab$ is maximum, then the value of a is

$\int e^{\left(x+\frac{1}{x}\right)}\left(\frac{x^{2}-1}{x^{2}}\right)dx =$

$\int \frac{\sec x}{(\sec x+\tan x)^{9}}dx =$

$\int \frac{9e^{x}+4e^{-x}}{9e^{x}-4e^{-x}}dx =$

If $\int \frac{1}{x^{7}\left(\frac{1}{x^{8}}+1\right)^{p}}dx = -\frac{1}{2}\left(\frac{1}{\frac{1}{x^{8}}+1}\right)^{2} + c$, then $p =$

$\int e^{2\theta}(2\cos^{2}\theta-\sin 2\theta)\, d\theta =$

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a function such that $f(x)=x^3+x^2f'(1)+xf''(2)+f'''(3)$, then $f'''(3) =$

Let $f(x)=10-|x-3|,\; x\in\mathbb{R}$. The maximum of $f(x)$ occurs at:

The function $f(x)=e^x-x$ is increasing in the interval:

If $u=\sec^{-1}(-\sec 2\theta)$ and $v=\cos \theta$, then $\frac{du}{dv}$ at $\theta=\frac{\pi}{4}$ is equal to:

The distance travelled by a moving particle is given by $s=\frac{t^{2}}{2}-6t+8$, where $t$ denotes the time in seconds. The velocity becomes zero when $t$ is equal to:

Let $f(x)=10-|x-5|,\; x\in\mathbb{R}$. Then $f(x)$ is not differentiable at:

The function $f(x)=x(\sqrt{x+2}+\sqrt{x+1})$ is continuous on

For $x\in\mathbb{R}$, let $f(x)=\log(3-\sin x)$ and $g(x)=f(f(x))$. Then $g'(0) =$

Let $f(x)=[x]$, $x\in(0,6)$, where $[x]$ is the greatest integer function. Then the number of discontinuities of $f(x)$ is:

$\lim_{x\rightarrow 2}\frac{\sin x \cos 2 - \cos x \sin 2}{x-2} =$

If $y=\cos x \cos y$, then $\frac{dy}{dx}$ at $\left(\frac{\pi}{3},\frac{\pi}{6}\right)$ is:

The standard deviation of 1, 2, 3, ..., 100 is:

An integer is chosen from the first 100 positive integers. Probability that the chosen number is a multiple of 11 is:

An unbiased die is thrown and B is an event showing an odd number on top. Then $P(B)$ is:

$\lim_{\theta\rightarrow 0}\frac{\theta \sin 2\theta}{1-\cos 2\theta} =$

$\lim_{x\rightarrow 0}\frac{\sin x}{2\sqrt{2}\sin\frac{x}{\sqrt{2}}} =$

Which one of the following is a point on the straight line $\vec{r}=(13\hat{i}-14\hat{j}+23\hat{k})+\lambda(5\hat{i}-7\hat{j}-9\hat{k})$?

$\vec{a}, \vec{b}, \vec{c}, \vec{d}$ be non-zero vectors such that $\vec{a}\times\vec{b}=\vec{c}\times\vec{d}$ and $\vec{a}\times\vec{c}=\vec{b}\times\vec{d}$. Then: