List of top Questions asked in MHT CET- 2021

A ray of light is incident at an angle 'i' on one face of thin prism. The ray emerges normally from the other face. Refractive index of the glass prism is 'n' and angle of prism is 'A'. The value of 'i' is

The resultant capacity between points A and B in the given circuit is

In diffraction experiment, from a single slit, the angular width of central maximum does NOT depend upon

When an electron in hydrogen atom jumps from third excited state to the ground state, the de-Broglie wavelength associated with the electron becomes

For a transistor, $\frac{1}{\alpha_{DC}} - \frac{1}{\beta_{DC}}$ is equal to [$\alpha_{DC}$ and $\beta_{DC}$ are current amplification factors]

Light of frequency two times the threshold frequency is incident on photosensitive material. If the incident frequency is made 1/3 rd and intensity is doubled, then the photoelectric current will

The magnetic potential energy stored in a certain inductor is $25\ \text{mJ}$, when the current in the inductor is $50\ \text{mA}$. This inductor is of inductance

A charge moves with velocity 'V' through electric field (E) as well as magnetic field (B). then the force acting on it is

A pendulum is oscillating with frequency 'n' on the surface of the earth. It is taken to a depth $\frac{R}{2}$ below the surface of earth. New frequency of oscillation at depth $\frac{R}{2}$ is [R is the radius of earth]

The molar specific heats of an ideal gas at constant pressure and volume are denoted by ' $C_p$ ' and ' $C_v$ ' respectively. If $\gamma = \frac{C_p}{C_v}$ and ' R ' is universal gas constant, then $C_v$ is equal to

In a pure silicon, number of electrons and holes per unit volume are $1.6 \times 10^{16}\ \text{m}^{-3}$. If silicon is doped with Boron in a way that on doping hole density increases to $4 \times 10^{22}\ \text{m}^{-3}$. Then electron density in doped semiconductor will be

For two data sets each of size 5, the variance are given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively. The variance of the combined data set is

The product of the perpendicular distances from $(2,-1)$ to the pair of lines $2 x^2-5 x y+2 y^2=0$ is

$\int e^{\tan x}(\sec ^2 x+\sec ^3 x \sin x) d x=$

The curves $\frac{x^2}{a^2} + \frac{y^2}{4} = 1$ and $y^3 = 16x$ intersect each other orthogonally, then $a^2 =$

If $p, q$ are true statements and $r$ is false statement, then which of the following is correct.

The number of ways in which 8 different pearls can be arranged to form a necklace is

A stone is thrown into a quiet lake and the waves formed move in circles. If the radius of a circular wave increases at the rate of $4\ \text{cm/sec}$, then the rate of increase in its area, at the instant when its radius is $10\ \text{cm}$, is _________ $\text{cm}^2/\text{sec}$.

The function $f(x) = \cot^{-1} x + x$ is increasing in the interval.

$\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}=$

If $f(x) = 3[x] + 5\{x + 1\}$, where $[x]$ is greatest integer function of $x$ and $\{x\}$ is fractional part function of $x$, then $f(-1.32) =$

$\tan ^{-1}\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)=\frac{\pi}{4}$, then the values of $x$ are

If $X$ is a random variable with p.m.f. as follows.
$$P(X = x) = \begin{cases} \frac{5}{16}, & x = 0, 1 \\ \frac{kx}{48}, & x = 2 \\ \frac{1}{4}, & x = 3 \end{cases}$$
then $E(X) =$

The general solution of the differential equation $\frac{dy}{dx} = \frac{x+2y-1}{x+2y+1}$ is

If $|\bar{a}| = 3, |\bar{b}| = 4, |\bar{a} - \bar{b}| = 5$, then $|\bar{a} + \bar{b}| =$