List of top Questions asked in MHT CET- 2021

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

A perfect gas of volume 10 litre is compressed isothermally to a volume of 1 litre. The rms speed of the molecules will

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

If $\int_2^e \left[ \frac{1}{\log x} - \frac{1}{(\log x)^2} \right] dx = a + \frac{b}{\log 2}$, then

If $\cos x = \frac{24}{25}$ and $x$ lies in first quadrant, then $\sin \frac{x}{2} + \cos \frac{x}{2} =$

Two unbiased dice are thrown. Then the probability that neither a doublet nor a total of 10 will appear is

Let $A=[a, b, c, d], B=[1,2,3]$. Relation $R_1, R_2, R_3, R_4$ are as follows :
$R_1=[(a, 1), (b, 2), (c, 1), (d, 2)]$
$R_2=[(a, 1), (b, 1), (c, 1), (d, 1)]$
$R_3=[(a, 2), (b, 3), (c, 2), (d, 2)]$
$R_4=[(a, 1), (b, 2), (a, 2), (d, 3)]$, then

The population of a city increases at a rate proportional to the population at that time. If the population of the city increase from 20 lakhs to 40 lakhs in 30 years, then after another 15 years the population is

The joint equation of pair of lines through the origin and making an equilateral triangle with the line $y=3$ is

If $A^{-1} = \left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$ and $B^{-1} = \left[\begin{array}{cc}1 & 0 \\ -3 & 1\end{array}\right]$, then $(AB)^{-1} =$

Negation of $(p \land q) \rightarrow (\sim p \lor r)$ is

If $A^{-1}=\left[\begin{array}{ccc}3 & 2 & 6 \\ 1 & 1 & 2 \\ 2 & 5 & 5\end{array}\right]$, then $A=$

If $\vec{r} = -4\hat{i} - 6\hat{j} - 2\hat{k}$ is a linear combination of the vectors $\vec{a} = -\hat{i} + 4\hat{j} + 3\hat{k}$ and $\vec{b} = -8\hat{i} - \hat{j} + 3\hat{k}$, then

The area bounded by the parabola $y = x^2$ and the line $y = x$ is

If $y = \sin^{-1}\left[\cos \sqrt{\frac{1+x}{2}}\right] + x^x$, then $\frac{dy}{dx}$ at $x=1$ is

Water is being poured at the rate of $36\ \text{m}^3/\text{min}$ into a cylindrical vessel, whose circular base is of radius $3\ \text{m}$. Then the water level in the cylinder is rising at the rate of

The general solution of $\left(x \frac{dy}{dx} - y\right) \sin \frac{y}{x} = x^3 e^x$ is

If the equation $3x^2 - kxy - 3y^2 = 0$ represents the bisectors of angles between the lines $x^2 - 3xy - 4y^2 = 0$, then value of $k$ is

If area of the parallelogram with $\vec{a}$ and $\vec{b}$ as two adjacent sides is 20 square units, then the area of the parallelogram having $3\vec{a}+\vec{b}$ and $2\vec{a}+3\vec{b}$ as two adjacent sides in square units is

If $y = \sqrt{e^{\sqrt{x}}}$, then $\frac{dy}{dx} =$

The equation of tangent to the circle $x^2+y^2=64$ at the point $P\left(\frac{2\pi}{3}\right)$ is

If $2 f(x) - 3 f\left(\frac{1}{x}\right) = x$, then $\int_1^e f(x) dx =$

If $f(x) = \frac{4^{x - \pi} + 4^{\pi - x} - 2}{(x - \pi)^2}$, for $x \ne \pi$, is continuous at $x = \pi$, then $f(\pi)$ is

The principal solutions of $\sqrt{3} \sec x + 2 = 0$ are

$\int \operatorname{cosec}(x-a) \operatorname{cosec} x dx = $