List of top Questions asked in MHT CET- 2021

If the sum of mean and variance of a binomial distribution for 5 trials is 1.8, then probability of a success is

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

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

If the variance of the numbers $2, 3, 11$ and $x$ is $\frac{49}{4}$, then the values of $x$ are

The co-factors of the elements of second column of $\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 2 & 1 \\ -1 & 3 & 4\end{array}\right]$ are

The Cartesian equation of the plane $\overline{\mathrm{r}}=(\hat{\mathrm{i}}-\hat{\mathrm{j}})+\lambda(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})+\mu(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$ is

$\cos^{-1}\left(\frac{4}{5}\right)+\cos^{-1}\left(\frac{12}{13}\right)=$

The differential equation of an ellipse whose major axis is twice its minor axis, is

The solution set for the system of linear inequations $x+y \ge 1 ; 7x+9y \le 63 ; y \le 5 ; x \le 6, x \ge 0$ and $y \ge 0$ is represented graphically in the figure. What is the correct option?

The general solution of the differential equation $\cos x \cdot \sin y dx + \sin x \cdot \cos y dy = 0$ is

$\int \sec^4 x \cdot \tan^4 x dx = \frac{\tan^m x}{m} + \frac{\tan^n x}{n} + c$ (where $c$ is constant of integration), then $m + n =$

$\vec{a}, \vec{b}$ and $\vec{c}$ are three vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ and $|\vec{a}| = 3, |\vec{b}| = 5, |\vec{c}| = 7$, then the angle between $\vec{a}$ and $\vec{b}$ is

The Cartesian equation of the line passing through the points A(2, 2, 1) and B(1, 3, 0) is

The x-intercept of a line passing through the points $\left(-\frac{1}{2}, 1\right)$ and $(1, 2)$ is :

If $[\vec{a} \vec{b} \vec{c}]=4$, then the volume (in cubic units) of the parallelopiped with $\vec{a}+2\vec{b}, \vec{b}+2\vec{c}$ and $\vec{c}+2\vec{a}$ as coterminal edges, is

If $\omega$ is complex cube root of unity and $(1+\omega)^7=A+B\omega$, then values of $A$ and $B$ are, respectively

If $\frac{n!}{2!(n-2)!}$ and $\frac{n!}{4!(n-4)!}$ are in the ratio $2:1$, then $n =$

The variance of the following probability distribution is,

If $a = \lim_{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{n^2}$ and $b = \lim_{n \rightarrow \infty} \frac{1^2+2^2+3^2+\ldots+n^2}{n^3}$, then

p : It rains today
q : I am going to school
r : I will meet my friend
s : I will go to watch a movie.
Then symbolic form of the statement "If it does not rain today or I won't go to school, then I will meet my friend and I will go to watch a movie" is

$\vec{a}, \vec{b}, \vec{c}$ are vectors such that $|\vec{a}| = 5, |\vec{b}| = 4, |\vec{c}| = 3$ and each is perpendicular to the sum of the other two, then $|\vec{a} + \vec{b} + \vec{c}|^2 = $

The surface area of a spherical balloon is increasing at the rate $2\ \text{cm}^2/\text{sec}$. Then rate of increase in the volume of the balloon is, when the radius of the balloon is $6\ \text{cm}$.

The p.m.f. of a random variable $X$ is $P(X = x) = \frac{1}{2^5} \binom{5}{x}, x = 0, 1, 2, 3, 4, 5$, then

If $m$ is order and $n$ is degree of the differential equation $y = x\frac{dy}{dx} + \sqrt{a^2 \left(\frac{dy}{dx}\right)^2 - b^2}$, then the value of $m + n$ is

Evaluate: $\sin^{-1}[\sin(-600^\circ)] + \cot^{-1}(-\sqrt{3})$