List of top Questions asked in MHT CET

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: \[HCl_{(aq)} + H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)} + Cl^-_{(aq)}\]}

What is the pH of $2 \times 10^{-3}$ M solution of monoacidic weak base if it ionises to the extent of 5%?

Calculate the pH of 0.02 M monobasic acid having 2% dissociation.

The integral $\displaystyle\int \frac{1}{\sqrt[4]{(x-1)^3(x+2)^5}}\,dx$ is equal to: (where $C$ is a constant of integration)}

In a $\triangle ABC$, $a = 1$, $b = \sqrt{3}$ and $\angle C = \dfrac{\pi}{6}$. Then the measure of the third side $c =$}

If the area of triangle $ABC$ is $b^2 - (c-a)^2$, then $\tan B =$

In a triangle $\triangle ABC$, if $a$, $b$, and $c$ are in arithmetic progression, then $\cos A + 2\cos B + \cos C =$

If $I = \int \frac{\sin x + \sin^3 x}{\cos 2x}\,dx = P \cos x + Q \log \left| \frac{\sqrt{2}\cos x - 1}{\sqrt{2}\cos x + 1} \right| + C$, then the values of $P$ and $Q$ are respectively:

If the direction ratios of two lines are given by \[ l+m+n=0 \] \[ mn-2ln+lm=0 \] then the angle between the lines is

Let the function \[ f(x)=\frac{x-|x|}{x} \] Then

Gas is being pumped into a spherical balloon at the rate of \(30~ft^3/min\). Find the rate at which the radius increases when the radius becomes \(15~ft\).

Let \[ f(x)=\int \frac{x\sqrt{x}}{(1+x)^2}\,dx \qquad (x\ge0) \] Then $f(3)-f(1)$ is equal to:

Which from following compounds is NOT in gaseous phase at \(25^\circ C\)?

% Question A pendulum clock gives correct time at $20^\circ$C. If the coefficient of linear expansion of the pendulum's material is \alpha = 1.2 \times 10^{-5} /^\circC, the clock will lose time per day at $40^\circ$C by approximately:

A particle executes simple harmonic motion of amplitude A and time period T. The time taken by the particle to travel from the mean position to a distance of A/2 is:

A Carnot engine operates between temperatures T₁ and T₂ (T₁ > T₂). If T₁ is increased by ∆T and T₂ is decreased by ∆T, its efficiency will:

An ideal gas undergoes a cyclic process ABCA wherein AB is an isothermal expansion, BC is an isochoric pressure drop, and CA is an adiabatic compression. The work done by the gas in the complete cycle is:

The equation of the normal to the curve \[ y=\log_e x \] at the point $P(1,0)$ is:

If the direction ratios of two lines are given by \[ l+m+n=0, \qquad mn-2ln+lm=0, \] then the angle between the lines is:

Let the function $f(x)$ be defined as \[ f(x)=\frac{x-|x|}{x} \] then: