List of top Questions asked in MHT CET- 2021

If $y = \tan^{-1}\left[\frac{\log\left(\frac{e}{x^2}\right)}{\log(ex^2)}\right] + \tan^{-1}\left[\frac{3 + 2\log x}{1 - 6\log x}\right]$, then $\frac{d^2y}{dx^2} = $

If the vectors $\vec{a} = 2\hat{i} + p\hat{j} + 4\hat{k}$ and $\vec{b} = 6\hat{i} - 9\hat{j} + q\hat{k}$ are collinear, then $p$ and $q$ are

If $\mathrm{P(A)} = \frac{3}{10}$, $\mathrm{P(B)} = \frac{2}{5}$, and $\mathrm{P(A \cup B)} = \frac{3}{5}$, then $\mathrm{P(A / B) \times P(B / A)} = $

The order of the differential equation whose solution is $y = a \cos x + b \sin x + c e^{-x}$ is

If $\vec{a} = \hat{i} + \hat{j} + \hat{k}$, $\vec{c} = \hat{j} - \hat{k}$, $\vec{a} \times \vec{b} = \vec{c}$ and $\vec{a} \cdot \vec{b} = 1$, then $\vec{b} = $

The general solution of the differential equation $(2y - 1) \, dx - (2x + 3) \, dy = 0$ is

Equation of the plane passing through the point $(1, 2, 3)$ and parallel to the plane $2x + 3y - 4z = 0$ is

The square roots of the complex number $(-5 - 12i)$ are

The negation of $p \wedge (q \rightarrow r)$ is

The arithmetic mean of marks in Mathematics for four divisions A, B, C and D were 80, 75, 70 and 72 respectively. Their standard deviations were 12, 6, 8 and 10 respectively. Then, which division has more uniformity.

$f(x) = \log|\sin x|$, where $x \in (0, \pi)$ is strictly increasing on

The velocity of a particle at time $t$ is given by the relation $v = 6t - \frac{t^2}{6}$. If its displacement $S$ is zero at $t = 0$, then the distance travelled in $3\ \text{sec}$ is

The length of perpendicular drawn from the point $2\hat{i} - \hat{j} + 5\hat{k}$ to the line $\vec{r} = (11\hat{i} - 2\hat{j} - 8\hat{k}) + \lambda(10\hat{i} - 4\hat{j} - 11\hat{k})$ is

If the angle between two lines is $\frac{\pi}{4}$ and the slope of one of the lines is $\frac{1}{2}$, then the slope of the other line is

If $u = \cos^3 x$ and $v = \sin^3 x$, then $\left(\frac{dv}{du}\right)_{x = \frac{\pi}{4}}$ is equal to

The particular solution of the differential equation $\frac{dy}{dx} = \frac{x+y+1}{x+y-1}$ when $x = \frac{2}{3}$ and $y = \frac{1}{3}$ is

If the lines $\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4}$ and $\frac{x-2}{1} = \frac{y+m}{2} = \frac{z-2}{1}$ intersect each other, then the value of $m$ is

If the probability distribution function of a random variable $X$ is given as

Then $F(0)$ is equal to

If $a\sin\theta = b\cos\theta$, where $a, b \neq 0$, then $a\cos 2\theta + b\sin 2\theta = $

If $\vec{a} = 4\hat{i} + 13\hat{j} - 18\hat{k}$, $\vec{b} = \hat{i} - 2\hat{j} + 3\hat{k}$, and $\vec{c} = 2\hat{i} + 3\hat{j} - 4\hat{k}$ are three vectors such that $\vec{a} = x\vec{b} + y\vec{c}$, then $x + y = $

If the population grows at the rate of $8\%$ per year, then the time taken for the population to be doubled is (Given $\log 2 = 0.6912$)

If $f(x) = \frac{x}{2x+1}$ and $g(x) = \frac{x}{x+1}$, then $(f \circ g)(x) = $

The maximum area of the rectangle that can be inscribed in a circle of radius $r$ is

If the lines represented by $ax^2 - bxy - y^2 = 0$ make angles $\alpha$ and $\beta$ with the positive direction of the $X$-axis, then $\tan(\alpha + \beta) = $

The difference between the maximum values of $^{6}\mathrm{C}_r$ and $^{n}\mathrm{C}_r$ is 16, then $n = $