List of top Mathematics Questions asked in MHT CET

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

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

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

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

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 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:
$a:\sim(p\wedge\sim r)\vee(\sim q\vee s)$
$b:(\sim q\wedge\sim r)\leftrightarrow(p\vee s)$
$c:(\sim p\vee q)\rightarrow(r\wedge\sim s)$

The rate of change of $\sqrt{x^{2}+16}$ with respect to $\frac{x}{x-1}$ at $x=5$ is

The maximum value of $xy$ when $x+2y=8$ is

If $\sin^{-1}x+\cos^{-1}y=\frac{3\pi}{10}$, then the value of $\cos^{-1}x+\sin^{-1}y$ is

The value of $\alpha$, so that the volume of the parallelopiped formed by $\hat{i}+\alpha\hat{j}+\hat{k}$, $\hat{j}+\alpha\hat{k}$ and $\alpha\hat{i}+\hat{k}$ becomes maximum, 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

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

The area (in sq. units) of the region bounded by the parabola $x = \frac{y^2}{2}$ and the line $x = y + 4$ is

The approximate value of $\log_{10} 998$ is (given that $\log_{10}e=0.4343$)

The number of solutions in $[0,2\pi]$ of the equation $16^{\sin^{2}x}+16^{\cos^{2}x}=10$ is

The differential equation of all parabolas, whose axes are parallel to Y-axis, is

If $Z_{1}=4i^{40}-5i^{35}+6i^{17}+2$, $Z_{2}=-1+i$ where $i=\sqrt{-1}$, then $|Z_{1}+Z_{2}|=$

The value of the integral $\int\frac{x+1}{x(1+xe^{x})^{2dx$ is

Let two non-collinear vectors $\hat{a}$ and $\hat{b}$ form an acute angle. A point P moves, so that at any time t the position vector $\overline{OP}$, where O is origin, is given by $\hat{a}\sin t+\hat{b}\cos t.$ when P is farthest from origin O, let M be the length of OP and $\hat{u}$ be the unit vector along $\overline{OP,}$ then

In a Binomial distribution with $n=4$ if $2P(X=3)=3P(X=2)$, then the variance is

If two vertices of a triangle are $A(3,1,4)$ and $B(-4,5,-3)$ and the centroid of the triangle is $G(-1,2,1),$ then the third vertex C of the triangle is