List of top Mathematics Questions asked in MHT CET

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

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

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

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 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 eccentricity of a rectangular hyperbola is

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

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

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

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

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 $\omega$ is a complex cube root of unity and $A=\begin{pmatrix}\omega & 0\\0 & \omega\end{pmatrix}$, then $A^{-1}=$

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 $f(x)=$

The c.d.f. $F(x)$ of a discrete random variable $X$ is given by
\[ \begin{array}{c|cccccccc} X & -3 & -1 & 0 & 1 & 3 & 5 & 7 & 9 \\ F(X) & 0.1 & 0.3 & 0.5 & 0.65 & 0.75 & 0.85 & 0.90 & 1 \end{array} \] Then $P(X=3)=$

The direction ratios of the line perpendicular to the lines having direction ratios $2,3,1$ and $1,2,1$ are

The distance of the point $(1,2,-1)$ from the plane $x-2y+4z+10=0$ is

If $B$ is the end point of minor axis of the ellipse $b^2x^2+a^2y^2=a^2b^2\ (a>b)$ and $S$ and $S'$ are the foci of the ellipse such that $\triangle BSS'$ is an equilateral triangle, then the eccentricity $e$ is

The negation of the statement “If $5<7$ and $7>2$, then $5>2$” is

The order and degree of the differential equation $\sqrt{1+\dfrac{1}{\left(\dfrac{dy}{dx}\right)^2}}=\left(\dfrac{d^2y}{dx^2}\right)^{\tfrac{3}{2}}$ are respectively

If $a,b,c$ are distinct positive numbers and the vectors $a\hat i+a\hat j+c\hat k,\ \hat i+\hat k$ and $c\hat i+c\hat j+b\hat k$ lie in a plane, then