List of top Questions asked in MHT CET- 2026

Find the heat energy that must be supplied to 14 g of nitrogen at room temperature to raise its temperature by \(48^\circ\text{C}\) at constant pressure. (Molecular weight of nitrogen = 28; \(R\) is the gas constant; \(C_p = \frac{7}{2}R\) for a diatomic gas.)

If \(y = f\left(\frac{3 + 2x}{3 - 2x}\right)\), where \(f(x) = \tan(\log x)\), and \(\frac{dy}{dx} = \frac{A}{B + Cx^2} \cdot \sec^2\left(\log \frac{3 + 2x}{3 - 2x}\right)\), then find \(A, B, C\).

A particle starts oscillating simple harmonically from its mean position with time period \(T\). At time \(t = \frac{T}{6}\), find the ratio of potential energy to kinetic energy of the particle.

Evaluate the integral: \(\int \frac{x}{x + 2} \, dx\).

A plane is formed by the axes whose centroid is \(\left(2, -\frac{2}{3}, \frac{1}{2}\right)\). Find the distance of the plane from the origin.

When two sound waves having amplitudes 3 and 5 units are superimposed, find the ratio of maximum to minimum intensity of the resultant wave.

If \(\tan^{-1}(-1) + \tan^{-1}(5) + \tan^{-1}(3) + \tan^{-1}\left(\frac{1}{4}\right) = \pi + \tan^{-1}\left(\frac{\alpha}{2}\right)\), find \(\alpha\).

For the curve \(y = 3x^3 - 3x^2 + 1\) at \(x = 1\), find the equation of the tangent.

Evaluate the integral: \(\int \frac{2x}{x^2 - 5x + 4} \, dx\)

If \(A, B, C\) are vertices of a triangle with position vectors \(\vec{a}, \vec{b}, \vec{c}\) respectively, then find the position vector of the point \(D\) where the angle bisector from vertex \(A\) meets \(BC\).

Consider the following logical statements:
R: If \(p \rightarrow q\) is false, then \(p \vee q\) is false.
S: If \(p \leftrightarrow q\) is false, then \(p \vee q\) is false.
Evaluate the truth values of R and S.

Two progressive waves \(Y_1 = \sin 2\pi \left(\frac{t}{0.4} - \frac{x}{4}\right)\) and \(Y_2 = \sin 2\pi \left(\frac{t}{0.4} + \frac{x}{4}\right)\) superpose to form a standing wave (\(x\) and \(y\) in SI units). Find the amplitude of the particle at \(x = 0.5\) m.

Find the eigenvalues of the matrix \(A = \begin{pmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{pmatrix}\).

If \(\cos 4x = \cos 3x\), find the general solution for \(x\).

Evaluate the integral: \(\int \frac{\sin x}{\sin 4x} \, dx\)

A gas having \(\gamma = \frac{5}{2}\) and volume 360 cc is suddenly compressed to 90 cc. If the initial pressure of the gas is \(P\), find the final pressure.

An air column is of length 17 cm. Find the ratio of the frequency of the 5th overtone when the column is closed at one end to that when it is open at both ends. (Speed of sound in air = 340 m/s.)

Given \(\int_1^a (2x + 1) \, dx = 5\), find the sum of all values of \(a\).

Find the approximate value of \(\sqrt[3]{63}\).

Evaluate: \(\int_0^3 \sqrt{9 - x^2} \, dx\).

Evaluate: \(\tan^{-1}(1) + \tan^{-1}(4) + \tan^{-1}(5) + \tan^{-1}\left(\frac{1}{4}\right) = \pi + \tan^{-1}\left(\frac{\alpha}{2}\right)\). Find the value of \(\alpha\).

The equation \(x^2 - Ky^2 - 4x + 6y - 5 = 0\) represents a pair of straight lines. Find the point of intersection.