List of top Mathematics Questions asked in MHT CET

The derivative of $f(\sec x)$ with respect to $g(\tan x)$ at $x=\frac{\pi}{4}$, where $f^{\prime}(\sqrt{2})=4$ and $g^{\prime}(1)=2$, is

$\int\frac{1}{\sin(x-a)\sin x}dx=$

The number of discontinuities of the greatest integer function $f(x)=[x]$, $x\in(-\frac{7}{2},100)$

A spherical raindrop evaporates at a rate proportional to its surface area. If originally its radius is 3 mm and 1 hour later it reduces to 2 mm, then the expression for the radius R of the raindrop at any time t is

The distance of the point having position vector $\hat{i}-2\hat{j}-6\hat{k}$ from the straight line passing through the point $(2,-3,-4)$ and parallel to the vector $6\hat{i}+3\hat{j}-4\hat{k}$ is

If $\cos^{-1}x-\cos^{-1}\frac{y}{3}=\alpha$, where $-1\le x\le1$, $-3\le y\le3$, $x\le\frac{y}{3}$, then for all $x, y$, $9x^{2}-6xy\cos\alpha+y^{2}$ is equal to

If $f(1)=1$, $f^{\prime}(1)=3$, then the derivative of $f(f(f(x)))+(f(x))^{2}$ at $x=1$ is

A vector $\vec{n}$ is inclined to X-axis at 45°, Y-axis at 60° and at an acute angle to Z-axis. If $\vec{n}$ is normal to a plane passing through the point $(-\sqrt{2},1,1)$ then equation of the plane is

If $A=\begin{bmatrix}2 & -1\\ -1 & 3\end{bmatrix}$, then the inverse of $(2A^{2}+5A)$ is

If $\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}$, then $\cos^{2}48^{\circ}-\sin^{2}12^{\circ}$ has the value

If $I=\int\frac{\sin x+\sin^{3}x}{\cos 2x}dx = P\cos x+Q\log\left|\frac{\sqrt{2}\cos x-1}{\sqrt{2}\cos x+1}\right|+c$ (where c is a constant of integration), then values of P and Q are respectively

The negation of the statement $(p\wedge q)\rightarrow(\sim p\vee r)$ is

The distance of a point (2, 5) from the line $3x+y+4=0$ measured along the line $L_{1}$ and $L_{2}$ are same. If slope of line $L_{1}$ is $\frac{3}{4}$, then slope of the line $L_{2}$ is

If at the end of certain meeting, everyone had shaken hands with everyone else, it was found that 45 handshakes were exchanged, then the number of members present at the meeting, are

The particular solution of the differential equation $(1+y^{2})dx-xy \, dy=0$ at $x=1$, $y=0$, represents

If the distance between the parallel lines given by the equation $x^{2}+4xy+py^{2}+3x+qy-4=0$ is $\lambda$, then $\lambda^{2}=$

The foot of the perpendicular drawn from the origin to the plane is $(4,-2,5)$, then the Cartesian equation of the plane is

If $f(x)$ is a function satisfying $f^{\prime}(x)=f(x)$ with $f(0)=1$ and $g(x)$ is a function that satisfies $f(x)+g(x)=x^{2}$. Then the value of the integral $\int_{0}^{1}f(x)g(x)dx$ is

If $f(x)=\frac{3x-2}{5x+3}$ where $f:\mathbb{R}-\{-\frac{3}{5}\}\rightarrow\mathbb{R}$ is defined, then $f\circ f(1)$ is

The value of $\cot\left(\sum_{n=1}^{23}\cot^{-1}\left(1+\sum_{k=1}^{n}2k\right)\right)$ is

If feasible region is as shown in the figure, then the related inequalities are}

An object is moving in the clockwise direction around the unit circle $x^{2}+y^{2}=1$. As it passes through the point $(\frac{1}{2},\frac{\sqrt{3{2})$, its y-coordinate is decreasing at the rate of 3 units per sec. The rate at which the x-coordinate changes at this point is

Two tangents to the circle $x^{2}+y^{2}=4$ at the points A and B meet at the point $P(-4,0)$. Then the area of the quadrilateral PAOB, O being the origin, is

The standard deviation of the following distribution}

is

If truth values of statements p, q are true, and r, s are false, then the truth values of the following statement patterns are respectively:
$a:\sim(p\wedge\sim r)\vee(\sim q\vee s)$
$b:(\sim q\wedge\sim r)\leftrightarrow(p\vee s)$
$c:(\sim p\vee q)\rightarrow(r\wedge\sim s)$