List of top Mathematics Questions asked in MHT CET

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 $f(1)=1$, $f^{\prime}(1)=3$, 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 $A=\begin{bmatrix}2 & -1\\ -1 & 3\end{bmatrix}$, then the inverse of $(2A^{2}+5A)$ is
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 $f(x)$ 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
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 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 $\lambda^{2}=$
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
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
The maximum value of $xy$ when $x+2y=8$ 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:
$a:\sim(p\wedge\sim r)\vee(\sim q\vee s)$
$b:(\sim q\wedge\sim r)\leftrightarrow(p\vee s)$
$c:(\sim p\vee q)\rightarrow(r\wedge\sim s)$
The standard deviation of the following distribution}
is
The rate of change of $\sqrt{x^{2}+16}$ with respect to $\frac{x}{x-1}$ at $x=5$ is
Two sides of a triangle are $\sqrt{3}+1$ and $\sqrt{3}-1$ and the included angle is $60^\circ$, then the difference of the remaining angles is
If $\sin^{-1}x+\cos^{-1}y=\frac{3\pi}{10}$, then the value of $\cos^{-1}x+\sin^{-1}y$ is
A, B, C are three events, one of which must and only one can happen. The odds in favor of A are $4:6$, the odds against B are $7:3$. Thus, odds against C are
The approximate value of $\log_{10} 998$ is (given that $\log_{10}e=0.4343$)