List of top Questions asked in MHT CET- 2025

A thin metal wire of length ' L ' and mass ' M ' is bent to form semicircular ring as shown. The moment of inertia about XX' is

Calculate the volume occupied by a particle in fcc unit cell if volume of unit cell is 1.6 \(\times\) 10\(^{-23}\) cm\(^3\).

A particle executes S.H.M. starting from the mean position. Its amplitude is ' a ' and its periodic time is ' T '. At a certain instant, its speed ' u ' is half that of maximum speed \( V_{\text{max}} \). The displacement of the particle at that instant is

A radioactive element A decays into radioactive element C by the following processes in succession. \( A \rightarrow B + _2\text{He}^4; B \rightarrow C + 2e^- \) Then elements}

At any time \( t \), the co-ordinates of moving particle are \( x = at^2 \) and \( y = bt^2 \). The speed of the particle is

Which amino acid from following contains \(\text{--CH}_3\) as side chain?

A car is driven on the banked road of radius of curvature 20 m with maximum safe speed. In order to increase its safety speed by 20%, without changing the angle of banking, the increase in the radius of curvature will be [Assume friction is same on the road]}

The percentage error in the measurement of mass and speed of a particular body is 3% and 4% respectively. The percentage error in the measurement of kinetic energy is

Which of the following molecules contains maximum number of electrons in antibonding molecular orbitals?

Three charges each of magnitude \(3\mu C\), are placed on the vertices of an equilateral triangle of side 6 cm . The net potential energy of the system will be nearly \(\left[ \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ SI unit} \right]\)}

Identify from following reactions that exhibits negative work done.

A small spherical ball of radius ' r ' is rolling on a curved surface which is frictionless and has a radius of curvature ' R '. Its motion is simple harmonic. Then its time period of oscillation is proportional to ( g = acceleration due to gravity)}

In a box containing 100 apples, 10 are defective. The probability that in a sample of 6 apples, 3 are defective is

The equation of the curve passing through $(2, \frac{9}{2})$ and having the slope $(1 - \frac{1}{x^2})$ at $(x, y)$ is

The value of the integral $\int_1^2 \frac{x \text{ d}x}{(x+2)(x+3)}$ is

The general solution of the differential equation $\frac{\text{d}y}{\text{d}x} + \sin \left( \frac{x+y}{2} \right) = \sin \left( \frac{x-y}{2} \right)$ is

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

Four defective oranges are accidentally mixed with sixteen good ones. Three oranges are drawn from the mixed lot. The probability distribution of defective oranges is

If four digit numbers are formed by using the digits 1, 2, 3, 4, 5, 6, 7 without repetition, then out of these numbers, the numbers exactly divisible by 25 are

The lines $x + 2ay + \text{a} = 0, x + 3by + \text{b} = 0, x + 4cy + \text{c} = 0$ are concurrent then $a, b, c$ are in}

$\int \sec^{\frac{2}{3}} x \cdot \csc^{\frac{4}{3}} x dx =$

Three urns respectively contain 2 white and 3 black, 3 white and 2 black and 1 white and 4 black balls. If one ball is drawn from each um, then the probability that the selection contains 1 black and 2 white balls is

An open tank with a square bottom is to contain 4000 cubic cm . of liquid. The dimensions of the tank so that the surface area of the tank is minimum, is

$\int \text{e}^{2x} \frac{(\sin 2x \cos 2x-1)}{\sin^2 2x} \text{d}x =$

If the lengths of three vectors $\bar{a}, \bar{b}$ and $\bar{c}$ are 5, 12, 13 units respectively, and each one is perpendicular to the sum of the other two, then $|\bar{a} + \bar{b} + \bar{c}| = ..............$