List of top Questions asked in MHT CET- 2026

In \(\triangle ABC\), if \(\angle C = \frac{2\pi}{3}\), then the value of \(\cos^2 A + \cos^2 B - \cos A \cos B\) is:

Evaluate the indefinite integral: \[ \int e^x (\sin x + \cos x)\, dx \]

If the scalar triple product of three vectors \( \vec{a}, \vec{b}, \vec{c} \) is given as \([\vec{a}\ \vec{b}\ \vec{c}] = 3\), then find the value of the scalar triple product of their cross products, denoted as \([ \vec{a} \times \vec{b} \quad \vec{b} \times \vec{c} \quad \vec{c} \times \vec{a} ]\).

Find the distance between the point \(2\hat{i} + \hat{j} - \hat{k}\) and the plane \(\vec{r} \cdot (\hat{i} - 2\hat{j} + 4\hat{k}) = 9\).

If \(\int x^3 e^x \, dx = e^x(px^3 + qx^2 + rx + s) + C\), then find the value of \(p + q + r + s\).

The displacement of a particle executing SHM is given by $x = 0.01 \sin(100\pi t + 0.05)$. Its maximum velocity is:

A refrigerator has a coefficient of performance of 5. If the temperature inside the freezer is $-20^{\circ}C$, the temperature of the surroundings to which it rejects heat is:

In an isothermal expansion of an ideal gas, the heat supplied to the gas is:

If the absolute temperature of a black body is doubled, the frequency corresponding to maximum emissive power becomes:

The parametric equations of the circle $x^2 + y^2 - 4x - 6y - 12 = 0$ are:

The value of $\int \frac{x^2-1}{(x^4+3x^2+1)\tan^{-1}(x+\frac{1}{x})} dx$ is:

If $n \in \mathbb{Z}$, then the expression $\frac{2^n}{(1-i)^{2n}} + \frac{(1+i)^{2n}}{2^n}$ is equal to:

If $\sin x \cos x = \frac{1}{4}$, then the general solution is:

Which of the following electrolytic solutions of the same electrolyte has Maximum electrolytic conductivity at the same temp?

Which of the following mixtures of gases represent water gas?

Identify unit of rate constant for first order reaction from the following.

Which of the following is a correct set of four quantum numbers for 4d orbital?

The rate of reaction $A \rightarrow P$ is $1.25 \times 10^{-2}$ mol dm$^{-3}$ s$^{-1}$ when $[A] = 0.5$ M. Calculate the rate constant if the reaction is second order in A.

An infinite line charge of uniform linear charge density $\lambda$ is placed along the $z$-axis. The work done in moving a charge $q$ from $(a,\,0,\,0)$ to $(2a,\,0,\,0)$ is:

A parallel plate capacitor has capacitance $C$. If a dielectric slab of dielectric constant $K$ and thickness equal to half the plate separation is introduced parallel to the plates, the new capacitance is:

Unpolarized light of intensity $I_0$ is incident on two polaroids placed coaxially. The transmission axis of the second polaroid is at an angle of $60^\circ$ to the first. The intensity of emerging light is:

An open pipe resonates with a tuning fork of frequency 500 Hz. It is observed that two successive nodes are separated by 34 cm. The velocity of sound in air is:

Calculate the pH of 0.01 M sulphuric acid.

Identify $\text{base}_2$ for the following equation according to Br\o{}nsted--Lowry theory: \[HCl_{(aq)} + H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)} + Cl^-_{(aq)}\]}