List of top Questions asked in MHT CET- 2025

The instantaneous value of current in an a.c. circuit is \(I = 3 \sin (50\pi t + \frac{\pi}{4})\text{A}\). The current will be maximum for the first time at

Three identical polaroids \(P_1, P_2\) and \(P_3\) are placed one after another. The pass axis of \(P_2\) and \(P_3\) are inclined at an angle of \(60^\circ\) and \(90^\circ\) with respect to axis of \(P_1\). The source has an intensity \(256 \text{ W/m}^2\). The intensity of light at point ‘O’ is

Light of wavelength \(\lambda\) strikes a photoelectric surface and electrons are ejected with energy \(E\). If \(E\) is to be increased to twice the original value, the wavelength changes to \(\lambda_1\)

In Young's double slit interference experiment, using two coherent sources of different amplitudes, the intensity ratio between bright to dark fringes is \(5 : 1\). The value of the ratio of resultant amplitudes of bright fringe to dark fringe is

When a ceiling fan is switched off, its angular velocity falls to \((\frac{1}{3})^{\text{rd}\) while it makes 24 rotations. How many more rotations will it make before coming to rest?

A string of mass \(0.1\text{ kg m}^{-1}\) has length \(0.9\text{ m}\). It is fixed at both ends and stretched such that it has a tension of \(40\text{ N}\). The string vibrates in three segments with amplitude \(0.3\text{ cm}\). The amplitude (maximum) of the particle velocity is (in \(\text{m/s}\))

For a thin prism, \(\delta_1\) is the angle of deviation produced, when prism is placed in air. When the prism is immersed in water, the angle of deviation produced is \(\delta_2\). Given \({}_{\text{a}}\mu_{\text{g}} = \frac{3}{2}\) and \({}_{\text{a}}\mu_{\text{w}} = \frac{4}{3}\) . The ratio \(\delta_2 : \delta_1\) is

A mass suspended from a vertical spring performs S.H.M. of period \(0.1\) second. The spring is unstretched at the highest point of suspension. Maximum speed of the mass is (Gravitational acceleration \(g = 10\text{ m/s}^2\))

The frequency of fourth overtone of a closed pipe is in unison with the fifth overtone of an open pipe. The ratio of length of closed pipe to that of open pipe is

Three samples \(X, Y\), and \(Z\) of same gas have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for X , adiabatic for Y and isobaric for Z . If the final pressures are equal for the three samples, the ratio of the initial pressures is ( \(\gamma = 3/2\) )

If '\(\lambda_1\)' and '\(\lambda_2\)' are the wavelengths of the first member of the Balmer and Paschen series, in hydrogen atom respectively, then the ratio of respective frequencies, \(f_1/f_2\) , is

A stone of mass \(1\text{ kg}\) tied to a light inextensible string of length \(L = \frac{5}{3}\text{ m}\) is rotating in a circular path of radius \(L\) in a vertical plane. If the ratio of maximum tension in the string to the minimum tension in the string is 3 , the speed of the stone at the highest point of the circle is ( \(g =\) acceleration due to gravity)

If $\int \tan^4 x dx = a \tan^3 x + b \tan x + cx + k$ (where k is the constant of integration) then the value of $a - b + c =$

The equation of the plane passing through the line of intersection of the planes $x + y + z = 1$ and $3x + 4y + 5z = 2$ and perpendicular to the XY- plane is

The projection of the line segment joining the points \( (2, 1, -3) \) and \( (-1, 0, 2) \) on the line whose direction ratios are \( 3, 2, 6 \) is

Let X be a discrete random variable. The probability distribution of X is given below

and E(X) = 4, then the value of AB is equal to

In Young's double slit experiment let 'd' be the distance between two slits and 'D' be the distance between the slits and the screen. Using a monochromatic source of wavelength ' $\lambda$ ', in an interference pattern, third minimum is observed exactly in front of one of the slits. If at the same point on the screen first minimum is to be obtained, the required change in the wavelength is [ d&D are not changed].

To determine the internal resistance of a cell with potentiometer, when the cell is shunted by a resistance of $5\Omega$ the balancing length is $250 \text{ cm}$. When the cell is shunted by $20\Omega$, the balancing length of potentiometer wire is $400 \text{ cm}$. The internal resistance, of the cell is

Bohr model is applied to a particle of mass m and charge $q$ is moving in a plane under the influence of a transverse magnetic field (B). The energy of the charged particle in the second level will be ( h = Planck's constant)

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 $x + y + z =$

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

The distance of the point $A(3,-4,5)$ from the plane $2x+5y-6z=16$ measured along the line $\frac{x}{2}=\frac{y}{1}=\frac{z}{-2}$ is}

What is pH of weak dibasic acid, that is 2% dissociated in its M/100 solution at 298 K?

If \( f(x) = 3x^3 + 2x^2 f'(1) + x f''(2) + f'''(3) \) then \( f(x) = ....... \)}

Let the plane passing through point (2, 1, -1) containing line joining the points (1, 3, 2) and (1, 2, 1) makes intercepts \( p, q, r \) on co-ordinate axes, then \( p + q + r = \)}