List of top Mathematics Questions

If A and B are positive acute angles satisfying 3cos²A+2cos²B=4 and (3sin A)/(sin B)=(2cos B)/(cos A), then the value of A+2B is equal to:

Let f(x)=dfracax+bcx+d, then f∘ f(x)=x, provided that:

The angle of elevation of a cloud $C$ from a point $P , 200 m$ above a still lake is $30^{\circ} .$ If the angle of depression of the image of $C$ in the lake from the point $P$ is $60^{\circ}$, then $P C$ (in $m$ ) is equal to :

The mean and variance of 7 observations are 8 and $16,$ respectively. If five observations are $2,4,10,12,14,$ then the absolute difference of the remaining two observations is :

The inverse function of $f\left(x\right) = \frac{8^{2x}-8^{-2x}}{8^{2x} + 8^{-2x}}, x\epsilon \left(-1, 1\right),$ is __________.

If \( A=\begin{bmatrix}2 & 3 \\ 1 & 2\end{bmatrix} \) and \( B=\begin{bmatrix}2 & -3 \\-1 & 2\end{bmatrix} \), then \( (B^{-1}A^{-1})^{-1} \) is

If \( x + y = \frac{\pi}{2} \), then the maximum value of \( \sin x \cdot \sin y \) is

If $\displaystyle \int_{1}^{k} (3x^2 + 2x + 1)\,dx = 11$, then $k =$

Evaluate \[ \int \frac{5^x}{\sqrt{5^{-2x}} - 5^{2x}}\,dx \]

Given $X\sim B(n,p)$, if $E(X)=4$ and $\text{Var}(X)=2.4$, then $n=$

If $A$ and $B$ are two angles such that $A,B\in(0,\pi)$ and they are not supplementary angles such that $\sin A-\sin B=0$, then

The general solutions of $\sin^2x\cdot\sec x=\tan x-\sin x+1$ are

The coordinates of the point where the line $\dfrac{x-1}{2}=\dfrac{y-2}{-3}=\dfrac{z+3}{4}$ meets the plane $2x+4y-z=1$ are

If the points $A(2,1,-1)$, $B(0,-1,0)$, $C(4,0,4)$ and $D(2,0,x)$ are coplanar, then $x=$

$\cosec 2\theta-\cot 2\theta=$

If the p.m.f. of a random variable $X$ is given by
\[ \begin{array}{c|ccc} x & 0 & 1 & 2 \\ P(X=x) & q^2 & 2pq & p^2 \end{array} \] then, the standard deviation of $X$ is (given $p+q=1$)

The area of the region bounded by the parabola $x^2=16y$, the lines $y=1$, $y=4$ and the $y$-axis lying in the first quadrant is

If $3\sin^2x-8\sin x+4=0$, $x\in\left(\dfrac{\pi}{2},\pi\right)$, then $\tan x=$

The eccentricity of a rectangular hyperbola is

If $\vec a,\vec b,\vec c$ are nonzero vectors along the coterminous edges of a parallelepiped with volume $7$ cubic units, then the volume of the parallelepiped with $\vec a+\vec b,\ \vec b+\vec c,\ \vec c+\vec a$ as the coterminous edges is

If $f(x)=\dfrac{4\sin \pi x}{5x}$ for $x\neq 0$ and $f(x)=2k$ for $x=0$, and $f(x)$ is continuous at $x=0$, then the value of $k$ is

The joint equation of bisectors of the angle between the lines represented by $3x^2+2xy-y^2=0$ is

If $f'(x)=k(\cos x-\sin x)$, $f'(0)=3$, $f\!\left(\dfrac{\pi}{2}\right)=15$, then $f(x)=$