List of top Questions asked in MHT CET- 2025

The liquid (mercury) meniscus in capillary tube will be convex if the angle of contact is
Two inductors of \(80 \text{ mH}\) each are joined in parallel. If the current is \(2.1 \text{ A}\), the energy stored in the combination is
A beam of light of intensity \(I_0\) falls on a system of three polaroids such that each pass axis is turned through \(60^{\circ}\) with respect to preceding one. The fraction of intensity that passes through is:
An electric dipole of length \(2 \text{ cm}\) is placed at \(60^{\circ}\) to a uniform electric field of \(10^{5} \text{ N/C}\). If it experiences a torque of \(9\sqrt{3} \text{ Nm}\), the magnitude of the charge is:
A person observes two moving trains. First reaching the station and another leaves the station with equal speed of \(30 \text{ m/s}\). If both trains emit sounds of frequency \(300 \text{ Hz}\), difference of frequencies heard by the person will be (speed of sound in air \(330 \text{ m/s}\))
In an \(LC\) circuit, angular frequency at resonance is \(\omega\). The new angular frequency when inductance is made four times and capacitance is made eight times is
The value of alternating e.m.f. (\(E\)) in the given circuit is
The electric flux through the surface
A student studies for (X) number of hours during a randomly selected school day. The probability that (X) can take the values, has the following form, where (k) is some constant.
(P(X = x) = 0.2, & if x = 0
kx, & if x = 1 or 2
k(6 - x), & if x = 3 or 4
0, & otherwise )
The probability that the student studies for at most two hours is
If (X \sim B(35, p)) such that (7P(X = 0) = P(X = 1)) then the value of (\frac{P(X=15){P(X=20)}) is equal to
If $\vec{a} = \frac{1}{\sqrt{10}}(3\hat{i} + \hat{k}), \vec{b} = \frac{1}{7}(2\hat{i} + 3\hat{j} - 6\hat{k})$, then the value of $(\vec{a} - 2\vec{b}) \cdot \{(\vec{a} \times \vec{b}) \times (2\vec{a} + \vec{b})\}$ is
The vectors $\vec{p} = \hat{i} + a\hat{j} + a^2\hat{k}, \vec{q} = \hat{i} + b\hat{j} + b^2\hat{k}$ and $\vec{r} = \hat{i} + c\hat{j} + c^2\hat{k}$ are non-coplanar and $\begin{vmatrix} a & a^2 & 1+a^3 \\ b & b^2 & 1+b^3 \\ c & c^2 & 1+c^3 \end{vmatrix} = 0$ then the value of $(abc)$ is
Two adjacent sides of a parallelogram ABCD are given by $\vec{AB} = 2\hat{i} + 10\hat{j} + 11\hat{k}$ and $\vec{AD} = -\hat{i} + 2\hat{j} + 2\hat{k}$. The side AD is rotated by an acute angle $\alpha$ in the plane of parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then $\cos \alpha =$
The value of (\tan [2 \tan^{-1} \frac{1}{5} - \frac{\pi}{4}]) is
In a triangle (ABC), with usual notations, the sides (a, b, c) are such that they are roots of the equation (x^3 - 11x^2 + 38x - 40 = 0) then (\frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} = )
The general solutions of the equation (\tan^2 \theta + \sec 2\theta = 1) are
If $\vec{c} = 5\vec{a} + 6\vec{b}$ and $3\vec{c} = \vec{a} - 4\vec{b}$ then}
The equation $x^2 - 3xy + 2y^2 + 3x - 5y + 2 = 0$ represents a pair of straight lines. If $\theta$ is the angle between them, then the value of $\cos \theta$ is equal to
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 $x + y + z =$
With usual notation, in a triangle ABC $\frac{b+c}{11} = \frac{c+a}{12} = \frac{a+b}{13}$, then the value of $\cos B$ is equal to
If $A = \begin{bmatrix} 1 & -2 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix}$ then $A(I + \text{adj } A) =$
$\cot^{-1}(2 \cdot 1^2) + \cot^{-1}(2 \cdot 2^2) + \cot^{-1}(2 \cdot 3^2) + \dots \dots \infty =$
If p : switch $S_1$ is closed, q : switch $S_2$ is closed then correct interpretation from the following circuit is
ABCD is a quadrilateral with $\overline{AB} = \overline{a}, \overline{AD} = \overline{b}$ and $\overline{AC} = 2\overline{a} + 3\overline{b}$. If its area is $\alpha$ times the area of the parallelogram with AB, AD as adjacent sides, then the value of $\alpha$ is
If $x \cdot \log_e(\log_e x) - x^2 + y^2 = 4(y > 0)$, then $\frac{dy}{dx}$ at $x = e$ is