List of top Mathematics Questions

$\int_{-\log 3}^{+\log 3} e^{|x|} dx = $ ________.

Let $\vec{OA}=2\hat{i}+3\hat{j}-5\hat{k}$, $\vec{OB}=3\hat{i}+\hat{j}-2\hat{k}$, $\vec{OC}=6\hat{i}-5\hat{j}+7\hat{k}$ be position vectors of A, B and C. Then ________.

If \([x]\) denotes the greatest integer less than or equal to \(x\), then \[ \lim_{x\to 0^-}\frac{\sin([x])}{[x]} \] is equal to ________.

If $f(x)=\sin(|x|)-|x|,x\in\mathbb{R}$, then $f$ is ________.

Find the mean deviation about the mean for the following data: $X: 2, 4, 6, 8, 10$ with frequencies $f: 7, 4, 5, 4, 5$.

Let $\vec{a}=\hat{i}+2\hat{j}+4\hat{k}$, $\vec{b}=2\hat{i}+4\hat{j}+8\hat{k}$ and $\vec{c}=2\hat{i}+4\hat{j}+3\hat{k}$. Then $(\vec{a}\times\vec{b})\cdot\vec{c}=$ ________.

Let $\vec{AB}=2\hat{i}+10\hat{j}+11\hat{k}$ and $\vec{AC}=-\hat{i}+2\hat{j}+2\hat{k}$. If $\theta$ is the angle between $\vec{AB}$ and $\vec{AC}$, then $\sin\theta=$ ________.

Let $A=\begin{pmatrix}0& 2\\ 3& 4\end{pmatrix}$ and $I=\begin{pmatrix}1& 0\\ 0& 1\end{pmatrix}$. If $(I+A)\begin{pmatrix}4&-3\\ 2&-1\end{pmatrix}=\begin{pmatrix}8&-5\\ 22& x\end{pmatrix}$, then the value of $x$ is equal to ________.

If $|\begin{matrix}1& 0& 0\\ x& x+2& 0\\ x^{2}& x& x+3\end{matrix}|=0$, then values of $x$ are ________.

Minimize $z=x+y$ subject to $2x+3y \ge 6, x \ge 0, y \ge 0$. The solution is ________.

The elimination of arbitrary constants $c_{1}, c_{2}, c_{3}, c_{4}$ from $y=(c_{1}+c_{2})\sin(2x+c_{3}) + c_{4}e^{5x}$ gives a differential equation of order ________.

The integrating factor of the differential equation $\frac{dy}{dx}-2y=2x-3$ is ________.

$\int_{-\pi/2}^{\pi/2}(x^{5}+x^{3}+x)\cos x dx = $ ________.

If $[x]$ is the greatest integer less than or equal to x, then $\int_{-3}^{3}[x]dx=$ ________.

$\int_{4}^{5}\frac{1}{x(1+x)}dx=$ ________.

$\int e^{x}[\frac{1}{1+x}-\frac{1}{(1+x)^{2}}]dx=$ ________.

$\int(\sin^{-1}\sqrt{x}+\cos^{-1}\sqrt{x})dx=$ ________.

$\int\frac{\cos \theta}{2-\sin^{2}\theta}d \theta=$ ________.

$\int\frac{\log(1+x)}{(1+x)}dx=$ ________.

$\int\frac{\sin 2x}{\sin x}dx=$ ________.

The maximum value of the function $f(x)=x\sqrt{4x-x^{2}}$ is ________.

The distance travelled by a moving particle is given by $s=t^{2}-6t+10$. The particle is at rest when $t=$ ________.

If $g(x)=x^{2}-x, x\in\mathbb{R},$ then $g(x)$ is increasing in ________.

The minimum of $f(x)=|x+2|$, $x\in\mathbb{R}$ occurs at ________.