List of top Questions asked in MHT CET- 2021

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

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

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

The derivative of $(\log x)^x$ with respect to $\log x$ is

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

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

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

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

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

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

The equation of a line passing through $(p \cos \alpha, p \sin \alpha)$ and making an angle $(90 + \alpha)$ with positive direction of X-axis is

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

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

A body at an unknown temperature is placed in a room which is held at a constant temperature of $30^{\circ}F$. If after 10 minutes the temperature of the body is $0^{\circ}F$ and after 20 minutes the temperature of the body is $15^{\circ}F$, then the expression for the temperature of the body at any time $t$ 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 _________ $\text{cm}^2/\text{sec}$.

If $f(x) = |x-1| + |x-2| + |x-3|, \forall x \in [1,4]$, then $\int_1^4 f(x) dx =$

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 $E(X) =$

If $\int \frac{x^3}{\sqrt{1+x^2}} dx = a(1+x^2)^{\frac{3}{2}} + b\sqrt{1+x^2} + c$, then $a+b =$, (where $c$ is constant of integration)

If $y = \operatorname{cosec}^{-1} \left[ \frac{\sqrt{x}+1}{\sqrt{x}-1} \right] + \cos^{-1} \left[ \frac{\sqrt{x}-1}{\sqrt{x}+1} \right]$, then $\frac{dy}{dx} =$

If $A^{-1} = \frac{-1}{2} \begin{bmatrix} 1 & -4 \\ -1 & 2 \end{bmatrix}$, then $2A + I_2 = \dots$ where $I_2$ is a unit matrix of order 2.

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

If the polar co-ordinates of a point are $\left(\sqrt{2}, \frac{\pi}{4}\right)$, then its Cartesian co-ordinates are

The shaded figure given below is the solution set for the linear inequations. Choose the correct option.