List of top Questions asked in MHT CET

In an \(LC\) circuit, angular frequency at resonance is \(\omega\). The new angular frequency when inductance is made four times and capacitance is made eight times is

A student studies for (X) number of hours during a randomly selected school day. The probability that (X) can take the values, has the following form, where (k) is some constant.
(P(X = x) = 0.2, & if x = 0
kx, & if x = 1 or 2
k(6 - x), & if x = 3 or 4
0, & otherwise )
The probability that the student studies for at most two hours is

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

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

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

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 $\cos \alpha =$

The vectors $\vec{p} = \hat{i} + a\hat{j} + a^2\hat{k}, \vec{q} = \hat{i} + b\hat{j} + b^2\hat{k}$ and $\vec{r} = \hat{i} + c\hat{j} + c^2\hat{k}$ are non-coplanar and $\begin{vmatrix} a & a^2 & 1+a^3 \\ b & b^2 & 1+b^3 \\ c & c^2 & 1+c^3 \end{vmatrix} = 0$ then the value of $(abc)$ is

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

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

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

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

The equation of a line passing through the point $(-1, 2, 3)$ and perpendicular to the lines $\frac{x}{2} = \frac{y-1}{-3} = \frac{z+2}{-2}$ and $\frac{x+3}{-1} = \frac{y+3}{2} = \frac{z-1}{3}$ is

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

If $A = \begin{bmatrix} 1 & -2 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix}$ then $A(I + \text{adj } A) =$

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

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

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

The equation of plane passing through ( (1, 0, 0) ) and ( (0, 1, 0) ) and making an angle ( 45^\circ ) with the plane ( x + y - 3 = 0 ) is

Two cards are drawn successively with replacement from fair playing 52 cards. let X denote number of kings obtained when two cards are drawn, then ( E(X^2) = )

If one of the diameters of the circle, given by the equation ( x^2 + y^2 - 4x + 6y - 12 = 0 ), is a chord of a circle, 'S', whose centre is at ( (-3, 2) ), then the length of radius of 'S' is ________ units.