List of top Questions asked in MHT CET- 2021

A parallel plate air capacitor is charged upto $100\ \text{V}$. A plate $2\ \text{mm}$ thick is inserted between the plates. Then to maintain the same potential difference, the distance between the plates is increased by $1.6\ \text{mm}$. The dielectric constant of the thick plate is
An inductive coil has a resistance of $100\ \Omega$. When an a.c. signal of frequency $1000\ \text{Hz}$ is applied to the coil the voltage leads the current by $45^\circ$. The inductance of the coil is ($\tan 45^\circ = 1$)
The P.E. 'U' of a moving particle of mass 'm' varies with 'x'-axis as shown in figure. The deBroglie wavelength of the particle in the regions $0 \le x \le 1$ and $x > 1$ are $\lambda_1$ and $\lambda_2$ respectively. If the total energy of the particle is 'nE', then the ratio $\lambda_1 / \lambda_2$ is
Two consecutive harmonics of an air column in a pipe closed at one end are of frequencies 150 Hz and 250 Hz. The fundamental frequency of an air column is
Two masses $m_a$ and $m_b$ moving with velocities $v_a$ and $v_b$ in opposite directions collide elastically. After the collision $m_a$ and $m_b$ move with velocities $v_b$ and $v_a$ respectively, then the ratio $m_a : m_b$ is
A sample of radioactive element contains $8 \times 10^{16}$ active nuclei. The half-life of the element is 15 days. The number of nuclei decayed after 60 days is
In Young's double slit experiment, with a source of light having wavelength $6300\ \text{\AA}$, the first maxima will occur when the
A body of density $\rho$ is dropped from (at rest) height $h$ into a lake of density $\delta$ ($\delta > \rho$). The maximum depth to which the body sinks before returning to float on the surface is [Neglect all dissipative forces]
What should be the radius of water drop so that excess pressure inside it is $72\ \text{Nm}^{-2}$? (The surface tension of water $7.2 \times 10^{-2}\ \text{Nm}^{-1}$)
In the case of insulators, a band gap and conduction band is respectively
A monoatomic gas is suddenly compressed to (1/8)th of its initial volume adiabatically. The ratio of the final pressure to the initial pressure is
Which one of the following statements is true?
In a single slit diffraction pattern, the distance between the first minimum on the left and the first minimum on the right is $5\ \text{mm}$. The screen on which the diffraction pattern is displayed is at a distance of $80\ \text{cm}$ from the slit. The wavelength is $6000\ \text{\AA}$. The slit width is about
A particle executes S.H.M. of period $\frac{2\pi}{\sqrt{3}}$ second along a straight line $4\ \text{cm}$ long. The maximum velocity of the particle is
A conducting rod of length $1\ \text{m}$ has area of cross-section $10^{-3}\ \text{m}^2$. One end is immersed in boiling water ($100^\circ\text{C}$) and the other end in ice ($0^\circ\text{C}$). If coefficient of thermal conductivity of copper is $92\ \text{cal}/\text{m-s-}^\circ\text{C}$ and latent heat of ice is $8 \times 10^4\ \text{cal}/\text{kg}$, then the amount of ice which will melt in one minute is
The output of an 'OR' gate is 'one'
A particle at rest starts moving with a constant angular acceleration of $4\ \text{rad}/\text{s}^2$ in a circular path. At what time the magnitudes of its tangential acceleration and centripetal acceleration will be equal?
A black rectangular surface of area $A$ emits energy $E$ per second at $27^\circ \text{C}$. If length and breadth are reduced to one third of initial value and temperature is raised to $327^\circ \text{C}$, then energy emitted per second becomes
A convex lens of focal length $f$ is used to form an image whose size is one fourth that of size of the object. Then the object distance is
A disc of radius 0.4 metre and mass 1 kg rotates about an axis passing through its centre and perpendicular to its plane. The angular acceleration is $10\ \text{rad}/\text{s}^2$. The tangential force applied to the rim of the disc is
A metal conductor of length $1\ \text{m}$ rotates vertically about one of its ends at an angular velocity of $5\ \text{rad/s}$. If the horizontal component of earth's magnetic field is $0.2 \times 10^{-4}\ \text{T}$, then the emf developed between the two ends of the conductor is
The relation obeyed by a perfect gas during an adiabatic process is $PV^{3/2} = \text{constant}$. The initial temperature of the gas is $T$. When the gas is compressed to half of its initial volume, the final temperature of the gas is
$\int \frac{2 x^2-1}{x^4-x^2-20} d x=$
In the arrangement of the capacitors as shown in figure, each capacitor is of $6\ \mu\text{F}$, then equivalent capacity between points A and B is
What is the additional energy that should be supplied to a moving electron to reduce its de Broglie wavelength from $1\ \text{nm}$ to $0.5\ \text{nm}$?