List of top Questions asked in MHT CET- 2025

If $f(x) = \sqrt{1 + \cos^2(x^2)}$, then $f'(\frac{\sqrt{\pi}}{2})$ is ______.

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

125 small water drops of same size fall through air with constant velocity 4 cm/s. They coalesce to form a big drop. The terminal velocity of the big drop 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 ______.

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 ______.

If $\tan(\pi \cos \theta) = \cot(\pi \sin \theta)$, then $\sin\left(\frac{\pi}{4} + \theta\right) = $ ______.

Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be vectors of magnitude 2, 3 and 4 respectively. If $\vec{a} \cdot (\vec{b} + \vec{c}) = 0$, $\vec{b} \cdot (\vec{c} + \vec{a}) = 0$ and $\vec{c} \cdot (\vec{a} + \vec{b}) = 0$, then the magnitude of $\vec{a} + \vec{b} + \vec{c}$ is ______.

An air column is of length 17 cm. The ratio of frequencies of 5th overtone if the air column is closed at one end to that open at both ends is (velocity of sound in air = 340 ms$^{-1}$) ______.

In Sonometer experiment, the frequency of a tuning fork used is 288 Hz. Harmonics will 'NOT' be produced at the frequency ______.

Find out the total number of electrons present in 3.2 g methane?

The probability that a person is not a sportsperson is $1/6$. Then the probability that out of 6 members of the family, 5 are sportspersons is ______.

Charges of $2\mu C$ and $-3\mu C$ are placed at two points A and B separated by distance of 1 m. The distance of the point from A where net potential is zero is ______.

Let $\vec{a} = \alpha\hat{i} + 3\hat{j} - \hat{k}$, $\vec{b} = 3\hat{i} - \hat{j} + \beta\hat{k}$ and $\vec{c} = \hat{i} + 2\hat{j} - 2\hat{k}$ where $\alpha, \beta \in \mathbb{R}$, be three vectors. If the projection of $\vec{a}$ on $\vec{c}$ is $\frac{10}{3}$ and $\vec{b} \times \vec{c} = -6\hat{i} + 10\hat{j} + 7\hat{k}$, then the value of $(\alpha + \beta)$ is ______.

The equation of the directrix of the parabola $y^2 + 4y + 4x + 2 = 0$ is ______.

If $\vec{a}$, $\vec{b}$, $\vec{c}$ are three coplanar vectors such that $|\vec{a}| = 1$, $|\vec{b}| = 2$, $\vec{b} \cdot \vec{c} = 8$, the angle between $\vec{b}$ and $\vec{c}$ is $45^\circ$, then $|\vec{a} \times (\vec{b} \times \vec{c})| = $ ______.

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 ______.

A source of sound emits sound wave of frequency 'f' and moves towards an observer with a velocity $V/3$ where $V$ is the velocity of sound. If the observer moves away from the source with a velocity $V/5$ the apparent frequency heard by him will be ______.

Equal masses of helium and oxygen are mixed in an empty container at $25^{\circ}\text{C}$. What is the fraction of the total pressure exerted by helium?

Calculate the change in internal energy of the system if work done by the system is 18 joule and absorbs heat 50 joule in a particular reaction.

Which from following compounds is an example of primary amines?

Let $R_1, R_2$ and $R_3$ be the radii of three mercury drops. A big mercury drop is formed from them under isothermal conditions. The radius of the resultant drop is ______.

What is the expected order of basic strength of different compounds from following (in gaseous phase)?

A capillary tube when immersed vertically in water, the rise of water column is upto height $h_1$ on earth's surface. When this arrangement is taken into a mine of depth 'd', below earth's surface, the height of the water column is $h_2$. If R is the radius of the earth, the ratio $h_2/h_1$ is ______.

Dissociation constant of 0.01 M weak acid is $10^{-4}$. What is percent dissociation of acid?