List of top Questions asked in MHT CET

Find the general solution of the differential equation \( \dfrac{dy}{dx} + \dfrac{y}{x} = x^2 \).

Calculate the area of the region bounded by the curve \( y^2 = 4x \) and the line \( x = 3 \).

Find the value of \( k \) if the function \( f(x) = \dfrac{k\sin x + 2\cos x}{\sin x + \cos x} \) is increasing for all \( x \).

Which of the following aqueous solutions will show maximum vapour pressure at 300 K?

Which of the following reagents is used to prepare alkyl isocyanides from alkyl halides $(RX)$?

Identify the product when a ketone reacts with hydrazine $(NH_2-NH_2)$

The monomer used to prepare Orlon is

The solution of the differential equation $\frac{dy}{dx} = \frac{x+y}{x-y}$ is

The coordinates of the foot of the perpendicular from the origin to the plane $2x - 3y - 6z = 4$ are

In $\triangle ABC$, $(b-c)^2 \cos^2 \frac{A}{2} + (b+c)^2 \sin^2 \frac{A}{2} =$

In $\triangle ABC$, if $2a^2 = b^2 + c^2$, then the value of $\frac{\cos 3A}{\cos A} + 2$ is

The value of $\tan^{-1}(\sqrt{3}) + \sec^{-1}(-2) - \sin^{-1}\left(-\frac{1}{2}\right)$ is

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

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

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

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.

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.)

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.

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.)

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

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.

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

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 \(\alpha\).

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

Determine the shortest distance between the lines \( \dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{4} \) and \( \dfrac{x-2}{3} = \dfrac{y-4}{4} = \dfrac{z-5}{5} \).