List of top Questions asked in MHT CET- 2025

In fundamental mode, the time required for the sound wave to reach up to closed end of a pipe filled with air is '\(t\)' second. The frequency of vibration of air column is (Neglect end correction)

For the following reaction, the particle ' x ' is \({}_6\text{C}^{11} \longrightarrow {}_5\text{B}^{11} + \beta^+ + \text{X}\)

When an observer moves towards a stationary source with velocity '\(V_1\)', the apparent frequency of emitted note is '\(F_1\)'. When observer moves away from stationary source with velocity '\(V_1\)' the apparent frequency is '\(F_2\)'. If '\(v\)' is velocity of sound in air and \(\frac{F_1}{F_2} = 2\), then \(\frac{v}{V_1}\) is equal to

Two discs A and B of same material and thickness have radii \(R\) and \(3R\) respectively. Their moments of inertia about their axis will be in the ratio

Which one of the following person is in an inertial frame of reference?

The potential difference \((V_A - V_B)\) between the points A and B in the given figure is

For a perfectly black body, coefficient of emission is

In hydrogen spectrum, the ratio of wavelengths of the last line of Lyman series and that of the last line of Balmer series is

The differential equation whose solution represents the family $x^2y = 4e^x + c$, where c is an arbitrary constant, is

The sum of the degree and order of the differential equation $\sqrt{\frac{d^2y}{dx^2}} = \sqrt[5]{\frac{dy}{dx}} - 5$ is

If $A = \begin{bmatrix} 1 & \tan x \\ -\tan x & 1 \end{bmatrix}$, then $A^T A^{-1} =$}

With usual notations, in a triangle $ABC$, if $\theta$ is any real number, then $a \cos(B - \theta) + b \cos(A + \theta)$ is

The shaded region in the following figure represents a solution set of

If $\tan 3\theta = \cot \theta$, then $\theta =$

In a triangle ABC with usual notations, if a, b, c are in arithmetic progression, then, $\tan \frac{A}{2} \cdot \tan \frac{C}{2} =$}

If $y = \log_e x^3 + 3 \sin^{-1} x + kx^2$ and $y'\left(\frac{1}{2}\right) = 2\sqrt{3}$, then $k =$}

If $f(1) = 1, f'(1) = 3$, then the derivative of $f(f(f(x))) + (f(x))^2$ at $x = 1$ is

In a triangle ABC, with usual notations if $\frac{2\cos A}{a} + \frac{\cos B}{b} + \frac{2\cos C}{c} = \frac{a}{bc} + \frac{b}{ca}$ then $\angle A =$}

If $\tan^{-1}\left(\frac{x}{2}\right) + \tan^{-1}\left(\frac{y}{2}\right) + \tan^{-1}\left(\frac{z}{2}\right) = \frac{\pi}{2}$ then $xy + yz + zx =$}

If the plane $\frac{x}{3} + \frac{y}{2} - \frac{z}{4} = 1$ cuts the co-ordinate axes at points A, B and C, then the area of the triangle ABC is

If $y = x^x + x^{\frac{1}{x}}$, then $\frac{dy}{dx}$ is equal to}

The distance between the lines represented by the equation $4x^2 + 4xy + y^2 - 6x - 3y - 4 = 0$ is

The magnitude of a vector which is orthogonal to the vector $\hat{i} + \hat{j} + \hat{k}$ and is coplanar with the vectors $\hat{i} + \hat{j} + 2\hat{k}$ and $\hat{i} + 2\hat{j} + \hat{k}$ is

If $A + B = \frac{\pi}{2}$ then the maximum value of $\cos A \cdot \cos B$ is

$\int \frac{dx}{2+\cos x} =$}