List of top Questions asked in MHT CET- 2021

If $|\vec{a}| = 4$, $|\vec{b}| = 5$, then the values of $k$ for which $\vec{a} + k\vec{b}$ is perpendicular to $\vec{a} - k\vec{b}$ are

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 function $$f(x) = \begin{array}{cc} 3ax + b, & \text{for } x < 1 \\ 11, & \text{for } x = 1 \\ 5ax - 2b, & \text{for } x > 1 \end{array}$$ is continuous at $x = 1$, then the values of $a$ and $b$ 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)} = $

$\int_{0}^{\pi / 2} \log\left(\frac{4+3\sin x}{4+3\cos x}\right) dx = $

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 $y = \log_{10} x + \log_x 10 + \log_x x + \log_{10} 10$, then $\frac{dy}{dx} = $

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

The negation of $p \wedge (q \rightarrow r)$ 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 square roots of the complex number $(-5 - 12i)$ are

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

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

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

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

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 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.

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

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 $\log 2 = 0.6912$)