List of top Questions asked in MHT CET

If (X \sim B(35, p)) such that (7P(X = 0) = P(X = 1)) then the value of (\frac{P(X=15){P(X=20)}) is equal to

The value of (\tan [2 \tan^{-1} \frac{1}{5} - \frac{\pi}{4}]) is

In a triangle (ABC), with usual notations, the sides (a, b, c) are such that they are roots of the equation (x^3 - 11x^2 + 38x - 40 = 0) then (\frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} = )

The general solutions of the equation (\tan^2 \theta + \sec 2\theta = 1) are

Two adjacent sides of a parallelogram ABCD are given by $\vec{AB} = 2\hat{i} + 10\hat{j} + 11\hat{k}$ and $\vec{AD} = -\hat{i} + 2\hat{j} + 2\hat{k}$. The side AD is rotated by an acute angle $\alpha$ in the plane of parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then $\cos \alpha =$

If $\vec{a} = \frac{1}{\sqrt{10}}(3\hat{i} + \hat{k}), \vec{b} = \frac{1}{7}(2\hat{i} + 3\hat{j} - 6\hat{k})$, then the value of $(\vec{a} - 2\vec{b}) \cdot \{(\vec{a} \times \vec{b}) \times (2\vec{a} + \vec{b})\}$ is

With usual notation, in a triangle ABC $\frac{b+c}{11} = \frac{c+a}{12} = \frac{a+b}{13}$, then the value of $\cos B$ is equal to

$\cot^{-1}(2 \cdot 1^2) + \cot^{-1}(2 \cdot 2^2) + \cot^{-1}(2 \cdot 3^2) + \dots \dots \infty =$

The equation $x^2 - 3xy + 2y^2 + 3x - 5y + 2 = 0$ represents a pair of straight lines. If $\theta$ is the angle between them, then the value of $\cos \theta$ is equal to

If $\vec{c} = 5\vec{a} + 6\vec{b}$ and $3\vec{c} = \vec{a} - 4\vec{b}$ then}

A line L is passing through points A(1, 3, 2) and B(2, 2, 1). If mirror image of point P(1, 1, -1) in the line L is (x, y, z) then $x + y + z =$

ABCD is a quadrilateral with $\overline{AB} = \overline{a}, \overline{AD} = \overline{b}$ and $\overline{AC} = 2\overline{a} + 3\overline{b}$. If its area is $\alpha$ times the area of the parallelogram with AB, AD as adjacent sides, then the value of $\alpha$ is

The integrating factor of $x \cdot \frac{dy}{dx} + y \log x = x \cdot e^x x^{-1/2} \log x$ is

The solution of $\log(\frac{dy}{dx}) = 2x - 5y, y(0) = 0$ is

If p : switch $S_1$ is closed, q : switch $S_2$ is closed then correct interpretation from the following circuit is

If $x \cdot \log_e(\log_e x) - x^2 + y^2 = 4(y > 0)$, then $\frac{dy}{dx}$ at $x = e$ is

A spherical balloon is filled with (4500\pi) cubic meters of helium gas. If a leak causes gas to escape at (72\pi) m(^3)/min, then the rate at which the radius decreases 49 minutes after leakage began is

The solution of the equation (\frac{dy}{dx} = \frac{1}{x+y+1}) is

The value of \[ \int \frac{\sin 7x}{\cos 9x \, \cos 2x} \, dx \] is:

If \[ A= \begin{bmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{bmatrix} \] where \[ a=7^x,\quad b=7^{7^x},\quad c=7^{7^{7^x}} \] then the value of \[ \int |A| \, dx \] is:

The population ( p ) of the city at time ( t ) is given by ( \frac{dp}{dt} = \frac{p}{2} - 100 ). If initial population is 100 then ( p = )

The value of \[ \int_{0}^{\pi} \left|\sin^{3}x\right| \, dx \] is:

If $( \sin(\alpha + \beta) = 1, \sin(\alpha - \beta) = \frac{1}{2}, \alpha, \beta \in [0, \pi/2] ), then ( \tan(\alpha + 2\beta) \cdot \tan(2\alpha + \beta) = ) $

The area of the region bounded by the parabola ( y^2 = 27x ) and the line ( x = 1 ) is ________ sq.units.