List of top Questions asked in MHT CET- 2021

A particle having a charge $100e$ is revolving in a circular path of radius $0.8\text{ m}$ with $1\text{ r.p.s.}$. The magnetic field produced at the centre of the circle in SI unit is ($\mu_0 = \text{permeability of vacuum}$, $e = 1.6 \times 10^{-19}\text{ C}$)

Two satellites of same mass are launched in circular orbits at heights '$R$' and '$2R$' above the surface of the earth. The ratio of their kinetic energies is ($R = \text{radius of the earth}$)

In a parallel plate capacitor, the electric field between the plates is '$E$'. If the charge on the plates is '$Q$', then the force on each plate is

A tuning fork of frequency '$n$' is held near the open end of a tube which is closed at the other end and the lengths are adjusted until resonance occurs. The first resonance occurs at length $L_1$ and the immediate next resonance occurs at length $L_2$. The speed of sound in air is

A ball rises to the surface of a liquid with constant velocity. The density of the liquid is four times the density of the material of the ball. The viscous force of the liquid on the rising ball is greater than the weight of the ball by a factor of

Which of the following gates will give an output '1' for the given inputs?

For a common-emitter amplifier, the voltage gain is $40$. Its input and output impedances are $100\ \Omega$ and $400\ \Omega$, respectively. The power gain of the CE amplifier will be

A particle with position vector $\vec{r}$ has a linear momentum $\vec{P}$. Which one of the following statements is true in respect of its angular momentum 'L' about the origin?

Force is applied to a body of mass $2\text{ kg}$ at rest on a frictionless horizontal surface as shown in the force against time ($F-t$) graph. The speed of the body after 1 second is

A glass tube of $1\text{ m}$ length is filled with water. The water can be drained out slowly from the bottom of the tube. If a vibrating tuning fork of frequency $500\text{ Hz}$ is brought at the upper end of the tube, then the total number of resonances obtained are [Velocity of sound in air is $320\text{ m/s}$]

The rate of flow of heat through a copper rod with a temperature difference of $28^\circ\text{C}$ is $1400\text{ cal}\cdot\text{s}^{-1}$. The thermal resistance of the copper rod will be

If $$\int_{0}^{a} \sqrt{\frac{a-x}{x}} \, dx = \frac{k}{2}$$ then $k =$

Kirchhoff's current and voltage law are respectively based on the conservation of

Let $a : \sim(p \wedge \sim r) \vee (\sim q \vee s)$ and $b : (p \vee s) \leftrightarrow (q \wedge r)$. If the truth values of $p$ and $q$ are true and that of $r$ and $s$ are false, then the truth values of $a$ and $b$ are respectively

A capacitor of capacity '$C$' is charged to a potential '$V$'. It is connected in parallel to an inductor of inductance '$L$'. The maximum current that will flow in the circuit is

$$\int \frac{1}{\cos x + \sqrt{3}\sin x} \, dx =$$

The slant height of a right circular cone is $\sqrt{3}\text{ cm}$. The height of the cone for maximum volume is

$$\int \cos^{-1} x \, dx =$$

If $f(x) = [8x] - 3$, where $[x]$ is the greatest integer function of $x$, then $f(\pi) =$ (where $\pi = 3.14$)

If $\omega$ is the complex cube root of unity, then $(3 + 5\omega + 3\omega^2)^2 + (3 + 3\omega + 5\omega^2)^2 =$

If the line joining two points $A(2,0)$ and $B(3,1)$ is rotated about $A$ in anticlockwise direction through an angle of $15^\circ$, then the equation of the line in its new position is

The vector equation of the line whose Cartesian equations are $y = 2$ and $4x - 3z + 5 = 0$ is

If the mean and variance of a binomial distribution are 4 and 2 respectively, then probability of getting 2 successes is

The common region of the solution of the inequations $x+y \ge 5$, $y \le 4$, $x \ge 2$, $x, y \ge 0$ is

If $x^y \cdot y^x = 16$, then $\frac{dy}{dx}$ at $(2,2)$ is