List of top Questions asked in MHT CET- 2021

A particle performing S.H.M. when displacement is 'x', the potential energy and restoring force acting on it are denoted by 'E' and 'F' respectively. The relation between x, E and F is
Two charged metallic spheres are joined by a very thin metal wire. If the radius of the larger sphere is four times that of the smaller sphere, the electric field near the larger sphere is
A wooden block of mass $m$ moves with velocity $V$ and collides with another block of mass $4m$, which is at rest. After collision the block of mass $m$ comes to rest. The coefficient of restitution will be
In hydrogen atom an electron revolves around a proton (in nucleus) at a distance 'r' m. The intensity of electric field due to the proton at distance 'r' is $5 \times 10^{11}\ \text{NC}^{-1}$, the magnitude of force between the electron and proton is [charge on electron = $1.6 \times 10^{-19}\ \text{C}$]
The magnifying power of a refracting type of astronomical telescope is $m$. If focal length of eyepiece is doubled then the magnifying power will become
The mass of a spherical planet is 4 times the mass of the earth, but its radius ($R$) is same as that of the earth. How much work is done in lifting a body of mass 5 kg through a distance of 2 m on the planet? ($g = 10\ \text{ms}^{-2}$)
If $m$ represents the mass of each molecule of a gas and $T$ its absolute temperature, then the root mean square speed of the gas molecule is proportional to
For series LCR circuit, which one of the following is a CORRECT statement?
In an LCR series a.c. circuit, the voltage across each of the components L, C and R is 60 V. The voltage across the LC combination is
Two waves $Y_1 = 0.25 \sin(316t)$ and $Y_2 = 0.25 \sin(310t)$ are propagating in the same direction. The number of beats produced per second are
The speed of a ball of radius 2 cm in a viscous liquid is 20 cm/s. What will be the speed of a ball of radius 1 cm in same liquid?
Equation of planes parallel to the plane $x - 2y + 2z + 4 = 0$ which are at a distance of one unit from the point $(1, 2, 3)$ are
If $y = \log \sqrt{\tan x}$, then the value of $\frac{dy}{dx}$ at $x = \frac{\pi}{4}$ is
If $x = a\left(t - \frac{1}{t}\right)$ and $y = b\left(t + \frac{1}{t}\right)$, then $\frac{dy}{dx} =$
The area bounded by the parabola $y^2 = 4ax$ and its latus-rectum $x = a$ is
If $f(x) = \csc^{-1} \left[ \frac{10}{6 \sin(2^x) - 8 \cos(2^x)} \right]$, then $f'(x) =$
Out of 7 consonants and 4 vowels, the number of words consisting of 3 consonants and 2 vowels are
Given that the total of 16 values is 528 and the sum of the squares of deviation from 33 is 9158. The variance is
Negation of the statement : $3 + 6 > 8$ and $2 + 3 < 6$ is
Rooms in a hotel are numbered from 1 to 19. Rooms are allocated at random as guests arrive. The first guest to arrive is given a room which is a prime number. The probability that the second guest to arrive is given a room which is a prime number is
Evaluate the limit: $\lim_{x \to 1} \left[ \frac{\sqrt{x} - 1}{\log x} \right] =$
If $f(x) = \frac{1 - \sin x + \cos x}{1 + \sin x + \cos x}$, for $x \neq \pi$ is continuous at $x = \pi$, then the value of $f(\pi)$ is
If the surrounding air is kept at 25$^\circ$C and a body cools from 80$^\circ$C to 50$^\circ$C in 30 minutes, then temperature of the body after one hour will be
The combined equation of a pair of lines passing through the origin and inclined at $60^\circ$ and $30^\circ$ respectively with X-axis is
If $3\hat{j}$, $4\hat{k}$ and $3\hat{j} + 4\hat{k}$ are the position vectors of the vertices $A, B, C$ respectively of $\Delta ABC$, then the position vector of the point in which the bisector of $\angle A$ meets $BC$ is