List of top Questions asked in MHT CET- 2025

An electric dipole of length \(2 \text{ cm}\) is placed at \(60^{\circ}\) to a uniform electric field of \(10^{5} \text{ N/C}\). If it experiences a torque of \(9\sqrt{3} \text{ Nm}\), the magnitude of the charge is:

The angular momentum of a rotating body is '\(L\)'. When frequency is tripled and kinetic energy is made one-third, the new angular momentum becomes

A beam of light of intensity \(I_0\) falls on a system of three polaroids such that each pass axis is turned through \(60^{\circ}\) with respect to preceding one. The fraction of intensity that passes through is:

An open organ pipe and closed organ pipe of same length produce \(2\) beats per second in fundamental mode. The length of open pipe is made half and that of closed pipe is doubled. The number of beats produced per second will be:

The value of alternating e.m.f. (\(E\)) in the given circuit is

A person observes two moving trains. First reaching the station and another leaves the station with equal speed of \(30 \text{ m/s}\). If both trains emit sounds of frequency \(300 \text{ Hz}\), difference of frequencies heard by the person will be (speed of sound in air \(330 \text{ m/s}\))

The electric flux through the surface

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

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}

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

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) = ) $