List of top Questions asked in MHT CET- 2026

If \( y = \cos^{-1} x \), find \( \frac{d^2y}{dx^2} \) in terms of \( y \).

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 \(A, B, C\).

If \(n\) is an odd natural number and \[ I_n=\int_0^1 e^x(x-1)^n\,dx \] then \( I_n+nI_{n-1} \) is equal to:

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

If slope of two lines represented by \( \dfrac{x^2}{a}+\dfrac{2xy}{h}+\dfrac{y^2}{b}=0 \) is twice the other, then \(ab:h^2=\ ?\)

At what temperature will the r.m.s. velocity of a hydrogen molecule be equal to that of an oxygen molecule at \(47^\circ\text{C}\)?

If \[ A= \begin{bmatrix} \sin\alpha & -\cos\alpha \cos\alpha & \sin\alpha \end{bmatrix} \] and \( \alpha\in\left(\frac{\pi}{2},\frac{3\pi}{2}\right) \). If \( A+A^T=I \), then \( \alpha= \)

A metal has BCC structure. Atomic radius \(=173\,\text{pm}\) and molar mass \(M=56\,\text{g mol}^{-1}\). The density of the metal is:

The rms velocity of hydrogen molecules at 27°C is v. At what temperature will the rms velocity of oxygen molecules equal v ?

Which of the following statements about Pollination by Water (Hydrophily) are correct?
i. It is found only in some 30 genera of aquatic monocots.
ii. In Hypohydrophily, the pollen grains are lighter than water and float on the water surface to reach the stigma.
iii. In Vallisneria (Epihydrophily), the female flowers reach the water surface temporarily to ensure pollination, and the male flowers float on the surface.
iv. Pollen grains of hydrophilous flowers are long and unwettable due to the presence of mucilage, and they lack exine in some species like Zostera (sea grass).

Calculate the moment of inertia of a uniform ring of mass \( M \) and radius \( R \) about a tangent in its own plane.

Evaluate the integral: \[ \int \frac{4x^2 \cot^{-1}(x^3)}{1+x^6}\,dx \] (where \(C\) is a constant of integration)

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

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 \(BC\).

Which of the following shows maximum hydrogen bonding?

A ball is thrown upwards with a velocity of \(20\,m/s\). Find the maximum height reached \((g=10\,m/s^2)\).

A particle in SHM has a speed of \(6\,cm/s\) at the mean position and an amplitude of \(4\,cm\). Find its position when its velocity is \(2\,cm/s\).

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 normal value of Tidal Volume (TV) in a healthy adult is approximately:

A particle moves with a constant velocity of \(5\ \text{m/s}\) in a circular path of radius \(2\ \text{m}\); calculate its centripetal acceleration.

A train moving at 20 m/s approaches a stationary observer. The frequency of the whistle emitted by the train is 640 Hz. If the velocity of sound is 340 m/s, the apparent frequency heard by the observer is:

The process during double fertilization in which non motile male gametes are carried through hollow pollen tube is called

What is the primary site of sperm production?

Name the phenomenon that proves the transverse nature of light.

The term used for species in which the last individual has died or is not recorded is