List of top Questions asked in MHT CET

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

The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its centre and perpendicular to its length is:

Find the energy of a photon with a wavelength of \(4000\,\text{\AA}\). (Take \( h = 6.63 \times 10^{-34}\,\text{Js} \), \( c = 3 \times 10^8\,\text{m/s} \)).

A disc of mass \(M\) and radius \(R\) has a concentric hole of radius \(R/2\). Its moment of inertia about an axis passing through its center and perpendicular to its plane is:

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

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

The species-area relationship is represented on a log scale as

If a polygon has 54 diagonals, find the number of sides of the polygon.

Where is sperm produced?

The ratio of specific heats $C_{p}/C_{v}$ for a mixture of 1 mole of helium and 1 mole of hydrogen is:

Which hormone is primarily responsible for the relaxation of pelvic ligaments during childbirth?

Let \(f(x)\) be defined by: \[ f(x)= \begin{cases} \displaystyle \int_x^6 (|t-2|+3)\,dt, & x>4 2x+8, & x\le4 \end{cases} \] Then at \(x=4\), \(f(x)\) 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 electrolytic solutions of the same electrolyte has maximum electrolytic conductivity at the same temperature?

What happens to the resistance of a wire if its radius is halved?

The solubility product of \(PbCl_2\) at \(298\ \text{K}\) is \(3.2 \times 10^{-5}\). What is its solubility in \(\text{mol dm}^{-3}\)?

What is the pH of a weak dibasic acid that is 2% dissociated in its M/100 solution at 298 K?

Find the moment of inertia of a uniform ring of mass \(M\) and radius \(R\) about a tangent perpendicular to its plane.

A uniform solid sphere of mass $M$ and radius $R$ is placed on a smooth horizontal surface. It is struck by a horizontal cue at a height $h$ above the center. For the sphere to roll without slipping immediately after the impact, the value of $h$ must be:

If \[ f(x)=\int \frac{x^2}{(1-x^2)(1+\sqrt{1-x^2})}\,dx \] and \( f(0)=2 \), then \( f\left(\frac12\right) \) is:

Identify \(Base_2\) for the following equation according to Brønsted-Lowry theory:
\( HCl(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + Cl^-(aq) \)

\[ \int \frac{1}{x^{1/2}+x^{1/3}}\,dx \] is equal to:

Which of the following is a soft metal?

What is the oxidation state of Chlorine in \( Cl_2O_7 \)?

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: