List of top Mathematics Questions asked in MHT CET

The value of c of Lagrange's mean value theorem for $f(x)=\sqrt{25-x^{2}}$ on $[1,5]$ is

If $\int \frac{x^2}{\sqrt{1-x }}dx = p\sqrt{1-x} (3x^2 + 4x + 8) + c$ where $c$ is a constant of integration, then the value of $p$ is

The value of \[ \int e^{x} \left(\frac{x^{2} + 4x + 4}{(x+4)^{2}}\right)\, dx \] is:

If $\sum_{r=1}^{50} \tan^{-1}\frac{1}{2r^{2 = p}}$ then $\tan p$ is

If \[ x = \sqrt{e^{\sin^{-1} t}} \quad \text{and} \quad y = \sqrt{e^{\cos^{-1} t}}, \] then find \[ \frac{d^2 y}{dx^2}. \]

The volume of parallelopiped, whose coterminous edges are given by $\overline{u}=\hat{i}+\hat{j}+\lambda\hat{k}, \vec{v}=\hat{i}+\hat{j}+3\hat{k}, \overline{w}=2\hat{i}+\hat{j}+\hat{k}$ is 1 cu. units. If $\theta$ is the angle between $\overline{u}$ and $\overline{w}$, then the value of $\cos\theta$ is

If the Cartesian equation of a line is $6x-2=3y+1=2z-2$, then the vector equation of the line is

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

If $[(\overline{a}+2\overline{b}+3\overline{c})\times(\overline{b}+2\overline{c}+3\overline{a})]\cdot(\overline{c}+2\overline{a}+3\overline{b})=54$ then the value of $[\overline{a}\overline{b}\overline{c}]$ is

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

The scalar product of the vector $\hat{i}+\hat{j}+\hat{k}$ with a unit vector along the sum of the vectors $2\hat{i}+4\hat{j}-5\hat{k}$ and $\lambda\hat{i}+2\hat{j}+3\hat{k}$ is equal to 1, then value of $\lambda$ is

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

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

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

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

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

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 $f(x)$ 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 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