List of top Mathematics Questions

$\int\frac{\tan x+\cot x}{1+\tan^{2}x}dx$ is equal to

The distance $s$ in meters travelled by a particle in $t$ seconds is given by $s=e^{t}(4\cos 3t+5\sin 3t)$. Then the velocity of the particle at time $t$ is given by

If $f(x)=\tan^{-1}\left(\frac{3\cos x-5\sin x}{5\cos x+3\sin x}\right)$ , then the value $f^{\prime}(1)$ is

If $f(x)=\frac{|x|}{x^{2}}$ then $f^{\prime}(2)$ is equal to

If $f(x)=(2x+3)e^{5x}$, then $f^{\prime\prime}(1)-10f^{\prime}(1)$ is equal to

If $f(x)=\frac{1}{2x-4}$ then the point(s) of discontinuity of $f(f(x))$ is/are

If $f^{\prime}(5)=\frac{3}{5}$ then the value of $\lim_{h\rightarrow 0}\frac{f(5+10h)-f(5)}{h}$ is equal to

The value of $\lim_{x\rightarrow 0}\frac{\sqrt{1+3x}-\sqrt{1-3x}}{x}$ is

The range of the function $f(x)=\left(\frac{1}{3}\right)^{3+\sin x}$ is

The domain of the function $f(x)=\sqrt{\frac{x+1}{2-x}}$ is

Let $f(x)=\begin{cases}ax+3 & x<1\\ \frac{4x}{a} & x\ge 1\end{cases}$. If $\lim_{x\rightarrow 1}f(x)$ exists, then the possible values of $a$ are

The value of $\lim_{x\rightarrow 2^{+}}\frac{[x]-2}{x-2}$ is

The vector form of the straight line $\frac{x-2}{1}=\frac{y-1}{-1}=\frac{z-1}{-2}$ is

If $P(A/B)=\frac{1}{2}, P(B/A)=\frac{1}{3}$ and $P(A\cap B)=\frac{1}{6}$ then $P(A\cup B)$ is

The combined mean age of a group of boys and girls in a school is 12. If the mean of the boys in that group is 14 and the mean of the girls is 9, then the percentage of boys in that group is

A box contains 5 white balls, one red ball and 4 black balls. If three balls are drawn at random, then the probability of getting no red ball is

If the mean and standard deviation of 10 observations are 24 and 4 respectively, then the sum of the squares of all observations is

The equation of line which is parallel to $\frac{2-x}{-3}=\frac{y-2}{2}=\frac{z-4}{1}$ and passing through the point $(1,1,1)$, is

The shortest distance between the lines $\vec{r}=\hat{i}+\hat{j}+3\hat{k}+\lambda(2\hat{i}+2\hat{j}+\hat{k})$ and $\vec{r}=(2\mu+1)\hat{i}+(2\mu-1)\hat{j}+(\mu+1)\hat{k}$ where $\lambda$ and $\mu$ are parameters, is

The angle between the lines $\vec{r}=(3+\alpha)\hat{i}+2(1+\alpha)\hat{j}+2(-2+\alpha)\hat{k}$ and $\vec{r}=(5+3\beta)\hat{i}+2(1+\beta)\hat{j}+6\beta\hat{k}$ , where $\alpha$ and $\beta$ are parameters, is

If $\vec{a}\times(\hat{i}-\hat{j}+\hat{k})=(\hat{i}-\hat{j}+\hat{k})\times\vec{b}$ and $|\vec{a}+\vec{b}|=3\sqrt{3}$, then the possible values of $(\vec{a}+\vec{b})\cdot(3\hat{i}+2\hat{j}+\hat{k})$ are

Let $\vec{OP}=2\hat{i}-2\hat{j}-\hat{k}$ and $\vec{OQ}=2\hat{i}+\hat{j}+2\hat{k}$. If the point $R$ lies on $\vec{PQ}$ and $\vec{OR}$ bisects the angle $\angle POQ$, then $2\vec{OR}$ is} \textit{Note: The initial vector has been mathematically corrected from the exam's typo ($2\hat{i}-2\hat{j}-2\hat{k}$) to standard format ($2\hat{i}-2\hat{j}-\hat{k}$) to permit a valid solution.

Let the three vectors $\vec{a}, \vec{b}$, and $\vec{c}$ be pairwise non-collinear vectors. If $\vec{a}+2\vec{b}$ is collinear with $\vec{c}$ and if $\vec{b}+2\vec{c}$ is collinear with $\vec{a}$, then $\vec{a}+2\vec{b}+5\vec{c}$ is equal to

The equation of a hyperbola is $9x^{2}-16y^{2}=144$. If $A$ and $S$ are, respectively, the focus and the vertex of one section of the hyperbola, then the length of $AS$ is

If the focus and vertex of a parabola are at a distance of 3 units and 6 units, respectively, from the origin on the positive x-axis, then the equation of the parabola is