List of top Questions asked in MHT CET- 2025

If $f(x) = \frac{\cos ax - \cos bx}{\cos cx - \cos bx}$ for $x \ne 0$ and $f(0) = -1$ is continuous at $x = 0$, then $a^2, b^2, c^2$ are in ______.

The ratio of the frequencies of two simple pendulums is 4 : 3 at the same place. The ratio of their respective lengths is ______.

In case of free expansion, which one of the following statements is WRONG ______.

Which of the following changes takes place at positive electrode during recharging of lead accumulator?

The potentiometer wire is 5 m long and potential difference of 4 V is maintained between the ends. The e.m.f. of the cell which balances against a length of 200 cm of the potentiometer wire is ______.

If $\sin^{-1}(4x) + \sin^{-1}(4\sqrt{3}x) = -\frac{\pi}{2}$, then the value of $x$ is ______.

The compound forming ccp structure contains $9.6\times10^{23}$ atoms. Find the number of tetrahedral voids formed in it.

The heat energy that must be supplied to 14 gram of nitrogen at room temperature to raise its temperature by $48^\circ C$ at constant pressure is (Molecular weight of nitrogen = 28, R = gas constant, $C_p = 7/2 R$ for diatomic gas) ______.

A manufacturer sells $x$ items at a price of ₹$(6 - \frac{x}{40})$ each. The cost price of $x$ items is ₹$(\frac{x}{5} + 193)$. The maximum profit in ₹ is ______.

A triangle ABC is formed by A(1, -1, 0), B(3, 5, 3), C(-11, -5, 6). The equation of the internal angle bisector of angle A is ______.

A single slit diffraction pattern is formed with white light. For what wavelength of light the 4th secondary maximum in diffraction pattern coincides with the 3rd secondary maximum in the pattern of light of wavelength '$\lambda$'?

If $|\vec{a}| = \sqrt{26}$, $|\vec{b}| = 7$, $|\vec{a} \times \vec{b}| = 35$, find $\vec{a} \cdot \vec{b}$

The number of positive integral solutions of $\tan^{-1} x + \cos^{-1} \left( \frac{y}{\sqrt{1+y^2}} \right) = \sin^{-1} \left( \frac{3}{\sqrt{10}} \right)$ are ______.

A bar of iron having magnetic moment 2.4 Am$^2$ weighs 66 g. If the density of the material of the bar is 7700 kg/m$^3$, the intensity of magnetisation in Am$^{-1}$ is ______.

Calculate rate constant of a first order reaction having pre-exponential factor $1.6\times10^{-13}\text{s}^{-1}$. ($E_{a}/2.303RT=21$)}

When a resistance of 100 $\Omega$ is connected in series with a galvanometer of resistance 'G', its range is 'V'. To double its range, a resistance of 1000 $\Omega$ is connected in series. The value of 'G' is ______.

If $y = \alpha \log x + \beta x^2 - x$ has extreme values at $x = -1$ and $x = 1$, then $\alpha$ and $\beta$ are respectively ______.

Rate of the reaction $\text{A}+\text{B}\rightarrow$ product is $3.6\times10^{-2}\text{ mol dm}^{-3}\text{s}^{-1}$ and rate law is $r=k[\text{A}][\text{B}]^{2}$. What is rate constant of the reaction if $[\text{A}]=0.2$ M and $[\text{B}]=0.1$ M?

In Paschen series, wavelength of first line is '$\lambda_1$' and for Brackett series, wavelength of first line is '$\lambda_2$' then ratio $\frac{\lambda_1}{\lambda_2}$ is ______.

The angle between the tangents drawn from the point (1, 4) to the parabola $y^2 = 4x$, is ______.

Which among the following gases is least adsorbed on solid at similar conditions of temperature and pressure?

A rigid body rotates about a fixed axis with variable angular velocity $(\alpha - \beta t)$ at time $t$, where $\alpha$ and $\beta$ are constants. The angle through which it rotates before it comes to rest is ______.

The general solution of the differential equation $\frac{dy}{dx} = \cot x \cdot \cot y$ is ______.

$\lim_{x \to \infty} \frac{(2x+1)^{50} + (2x+2)^{50} + (2x+3)^{50} + \dots + (2x+100)^{50}}{(2x)^{50} + (10)^{50}} = $ ______.

$\int_{1/2}^{2} \frac{1}{x} \csc^{101} \left( x - \frac{1}{x} \right) dx = $ ______.