List of top Mathematics Questions

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:

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

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

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

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

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

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

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

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

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

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

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

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

The mean deviation about the mean from the data 400, 410, 420, 430, 440 is:

The point at which the line $\frac{x+3}{11}=\frac{y-2}{-1}=\frac{z+1}{3}$ meets the $zx$-plane is:

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

The Cartesian equation of the line $\vec{r}=(2\hat{i}-7\hat{j}+11\hat{k})+\lambda(3\hat{i}+7\hat{j}-13\hat{k})$ is:

Let $\vec{OP}=2\hat{j}$ be the position vector of a point $P$. Let $\vec{r}=\hat{j}+\lambda(\hat{i}+\hat{j})$ be a straight line. The distance of the point $P$ from the line is:

$\vec{a}, \vec{b}, \vec{c}, \vec{d}$ 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:

Let $\vec{a}=3\hat{i}+2\hat{j}+2\hat{k}$ and $\vec{b}=\hat{i}+2\hat{j}-2\hat{k}$. Then $(\vec{a}+\vec{b}) \cdot (\vec{a}-\vec{b}) =$

If $\vec{a} \cdot \vec{b}=12$, then $(3\vec{a}) \cdot (3\vec{b})$ is equal to:

Let $\vec{a}, \vec{b}, \vec{c}$ be any three vectors and $m, n$ be scalars. Which one of the following is not true?

The eccentricity of the hyperbola $\frac{(x-1)^{2}}{25}-\frac{(y+2)^{2}}{11}=1$ is:

Let $P$ be any point on the ellipse $4(x+2)^{2}+9(y-4)^{2}=144$. If $F_{1}$ and $F_{2}$ are the foci of the ellipse, then $F_{1}P+F_{2}P=$