List of top Mathematics Questions

If $x=\sec\theta-\cos\theta$, $y=\sec^{10}\theta-\cos^{10}\theta$ then $\left(\frac{dy}{dx}\right)^{2}$ is equal to
Let $y=x^{\sin\frac{\pi}{2}x}$. Then at $x=1$, $\frac{dy}{dx}$ is equal to
Let $y = \tan^{-1}\left(\frac{\sin x + \cos x}{\sin x - \cos x}\right), \; 0<x < \frac{\pi}{2}$

Let $f(x) = \frac{\log(e + x)}{\log(\pi + x)}, \; -2 < x < \infty$. Then $f$ is

Let $g(x)=\begin{vmatrix}x^{4}&-\cos x&-\sin 2x\\ -8& 4& 3\\ 2& 4& 8\end{vmatrix}$. Then $g'''(0)$ is equal to

Let $f(x) = a_{0} + a_{1}x^{2} + a_{2}x^{4} + a_{3}x^{6}, \; x \in \mathbb{R}$ where $0 < a_{0} < a_{1} < a_{2} < a_{3}$. The minimum value of $f(x)$ is

The value of $\lim_{x\rightarrow\frac{\pi^{-}}{2}}(\tan x-\sec x)$ is equal to
If the function $f(x)=\begin{cases}\frac{x^{2}}{2},& 0\le x<1\\ 2x^{2}-ax+1.5,& 1\le x\end{cases}$ is continuous on $[0, 5]$, then the value of a is

Let $f(x)=\begin{cases}1-x,&x<1\\ (1-x)(2-x),& 1\le x\le2\end{cases}$. Which one of the following is not true?

Consider the function $f(x)=xe^{-\frac{2}{x}}$. Which one of the following is not true?
Let $[x]$ denote the greatest integer less than or equal to x. Then $\lim_{x\rightarrow0^{-}}\frac{\sin[x]}{[x]}$ is equal to
Let $f(x)=-\sqrt{49-x^{2}}$. Then $\lim_{x\rightarrow1}\frac{f(x)-f(1)}{x-1}$ is equal to
Let $x_{1},x_{2},\dots,x_{n}$ be the data with respective frequencies $f_{1},f_{2},\dots,f_{n}$. If $\sum_{i=1}^{n}f_{i}(|x_{i}-\overline{x}|)=400$ and the mean deviation from the mean $\overline{x}$ is 10, then $\sum_{i=1}^{n}f_{i}$ is equal to
The shortest distance between the lines $\vec{r}=(2\hat{i}+6\hat{j}+3\hat{k})+t(2\hat{i}+3\hat{j}+4\hat{k}), t\in\mathbb{R}$ and $\vec{r}=(2\hat{j}-3\hat{k})+s(\hat{i}+2\hat{j}+3\hat{k}), s\in\mathbb{R}$, is
A number x is randomly chosen from the set of natural numbers less than or equal to 100. Then the probability of the event that the chosen number satisfies the inequality $\frac{(x-15)(x-70)}{x-30}\ge0$ , is
Let A and B be two events such that $P(A)=\frac{1}{8}$ and $P(A/B)=\frac{1}{4}$, $P(B/A)=\frac{2}{5}$. Then $P(B)$ is equal to
Consider the data $x_{1},x_{2},\dots,x_{10}$. If $\sum_{i=1}^{10}(|x_{i}-\overline{x}|)^{2}=662,$ where $\overline{x}$ is the mean, then the standard deviation is approximately, equal to
The position vectors of the vertices of a triangle are $\hat{i}+2\hat{j}-4\hat{k}$, $-\hat{i}-2\hat{j}-4\hat{k}$ and $2\hat{i}+3\hat{j}+5\hat{k}$. The perimeter of the triangle is
The straight line $\vec{r}=(2-3t)(\hat{i}+\hat{j})+(6t+1)(\hat{j}+\hat{k})+(12t-11)(\hat{k}+\hat{i}), t\in\mathbb{R}$, is parallel to the vector
The equation of a line passing through (-1,6,5) and (-2,4,3), is
If $\alpha,\beta,\gamma$ are the angles made by the straight line $\frac{x-5}{2}=\frac{y+1}{3}=\frac{z-2}{\sqrt{7}}$ with the x-axis, y-axis and z-axis respectively, then $\cos\alpha, \cos\beta, \cos\gamma$ are respectively,
Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors such that $|\vec{a}|=2, |\vec{b}|=3, |\vec{c}|=4$ and $\vec{a}\cdot\vec{b}=\vec{a}\cdot\vec{c}=0$. If the angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{3}$, then $\vec{a}$ is equal to
Let $|\vec{a}|=2,|\vec{b}|=\sqrt{13+6\sqrt{3}}$ and $|\vec{c}|=3$. If $\vec{a}-\vec{b}+\vec{c}=0$, then the angle between $\vec{a}$ and $\vec{c}$ is
Let the eccentricity of an ellipse be $\frac{1}{2}$. If $S(3,2)$ is a focus and $x-9=0$ is the corresponding directrix of the ellipse, then the equation of the ellipse is}
The length of the latus rectum of the ellipse $225x^{2}+125y^{2}=28125$ is}