List of top Questions asked in MHT CET- 2021

A mass $0.4\ \text{kg}$ performs S.H.M. with a frequency $\frac{16}{\pi}\ \text{Hz}$. At a certain displacement it has kinetic energy $2\ \text{J}$ and potential energy $1.2\ \text{J}$. The amplitude of oscillation is

The translational kinetic energy of the molecules of a gas at absolute temperature ($T$) can be doubled

A polyatomic gas ($\gamma = 4/3$) is compressed to $\left(\frac{1}{8}\right)^{\text{th}}$ of its volume adiabatically. If its initial pressure is $P_0$, its new pressure will be

A wire of length $1\ \text{m}$ is moving at a speed of $2\ \text{m/s}$ perpendicular to a homogeneous magnetic field of $0.5\ \text{T}$. If the ends of the wire are joined to a resistance of $6\ \Omega$, the rate at which work is being done to keep the wire moving at that speed is

If $\omega_1$ is the angular velocity of the hour hand of a clock and $\omega_2$ is the angular velocity of the earth's rotation about its axis, then the ratio $\omega_1 : \omega_2$ is

In Young's double slit experiment, the $10^{\text{th}}$ maximum of wavelength '$\lambda_1$' is at a distance of '$Y_1$' from the central maximum. When the wavelength of the source is changed to '$\lambda_2$', the $5^{\text{th}}$ maximum is at a distance '$Y_2$' from the central maximum. The ratio $\frac{Y_1}{Y_2}$ is

When a light of wavelength '$\lambda$' falls on the emitter of a photocell, the maximum speed of emitted photoelectrons is '$V$'. If the incident wavelength is changed to $\frac{2\lambda}{3}$, the maximum speed of emitted photoelectrons will be

A circular coil of radius $R$ has $N$ turns of a wire. The coefficient of self-induction of the coil will be ($\mu_0 = $ permeability of free space)

Two rotating bodies $P$ and $Q$ of masses $m$ and $2m$ with moment of inertia $I_P$ and $I_Q$ ($I_Q > I_P$) have equal Kinetic energy of rotation. If $L_P$ and $L_Q$ be their angular momenta respectively, then

An a.c. source of angular frequency $\omega$ is fed across a resistor $R$ and a capacitor $C$ in series. The current registered is $I$. If now the frequency of source is changed to $\frac{\omega}{3}$ (but maintaining the same voltage), the current in the circuit is found to be halved. The ratio of reactance to resistance at the original frequency $\omega$ will be

A sound wave is travelling with a frequency of $50\ \text{Hz}$. The phase difference between the two points in the path of a wave is $\frac{\pi}{3}$. The distance between those two points is (Velocity of sound in air $= 330\ \text{m/s}$)

A logic gate which gives output 'HIGH' only when its two input terminals are at different logic levels with respect to each other is

A transverse wave given by $y = 2 \sin(0.01x + 30t)$ moves on a stretched string from one end to another end in $0.5\ \text{second}$. If '$x$' and '$y$' are in $\text{cm}$ and '$t$' is in $\text{second}$, then the length of the string is

The equation of the perpendicular bisector of the line segment joining $A(-2, 3)$ and $B(6, -5)$ is

The indefinite integral $\int \frac{\sec^8 x}{\csc x}\,dx$ is equal to

If $y = \tan^{-1}\left(\sqrt{\frac{1 + \sin x}{1 - \sin x}}\right)$, where $0 \le x < \frac{\pi}{2}$, then $\frac{dy}{dx}$ at $x = \frac{\pi}{6}$ is

The shortest distance between lines $\vec{r} = (2\hat{i} - \hat{j}) + \lambda(2\hat{i} + \hat{j} - 3\hat{k})$ and $\vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(2\hat{i} + \hat{j} - 5\hat{k})$ is

If $\vec{a}$, $\vec{b}$, $\vec{c}$ are mutually perpendicular vectors having magnitudes $1$, $2$, $3$ respectively, then $[\vec{a} + \vec{b} + \vec{c} \quad \vec{b} - \vec{a} \quad \vec{c}] =$

If the variance of the data $2, 4, 5, 6, 8, 17$ is $23.33$, then the variance of $4, 8, 10, 12, 16, 34$ will be

A random variable $X \sim B(n, p)$. If the values of the mean and variance of $X$ are $18$ and $12$ respectively, then $n =$

If $x = \frac{1 - t^2}{1 + t^2}$ and $y = \frac{2at}{1 + t^2}$, then $\frac{dy}{dx} =$

The value of $\int_0^1 \tan^{-1}\left(\frac{2x - 1}{1 + x - x^2}\right)\,dx$ is

The differential equation of all family of lines $y = mx + \frac{4}{m}$ obtained by eliminating the arbitrary constant $m$ is

$\tan^{-1}\left(\tan \frac{5\pi}{6}\right) + \cos^{-1}\left(\cos \frac{13\pi}{6}\right) =$

The integral $\int \sin^{-1}\left(\frac{2x}{1 + x^2}\right)\,dx$ for $|x| < 1$ is equal to