List of top Questions asked in MHT CET

A circular coil of radius $R$ has $N$ turns of a wire. The coefficient of self-induction of the coil will be ($\mu_0 = $ permeability of free space)

A logic gate which gives output 'HIGH' only when its two input terminals are at different logic levels with respect to each other is

A sound wave is travelling with a frequency of $50\ \text{Hz}$. The phase difference between the two points in the path of a wave is $\frac{\pi}{3}$. The distance between those two points is (Velocity of sound in air $= 330\ \text{m/s}$)

If $\vec{a}$, $\vec{b}$, $\vec{c}$ are mutually perpendicular vectors having magnitudes $1$, $2$, $3$ respectively, then $[\vec{a} + \vec{b} + \vec{c} \quad \vec{b} - \vec{a} \quad \vec{c}] =$

A random variable $X \sim B(n, p)$. If the values of the mean and variance of $X$ are $18$ and $12$ respectively, then $n =$

The equation of the perpendicular bisector of the line segment joining $A(-2, 3)$ and $B(6, -5)$ is

The shortest distance between lines $\vec{r} = (2\hat{i} - \hat{j}) + \lambda(2\hat{i} + \hat{j} - 3\hat{k})$ and $\vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(2\hat{i} + \hat{j} - 5\hat{k})$ is

If $y = \tan^{-1}\left(\sqrt{\frac{1 + \sin x}{1 - \sin x}}\right)$, where $0 \le x < \frac{\pi}{2}$, then $\frac{dy}{dx}$ at $x = \frac{\pi}{6}$ is

If the variance of the data $2, 4, 5, 6, 8, 17$ is $23.33$, then the variance of $4, 8, 10, 12, 16, 34$ will be

The indefinite integral $\int \frac{\sec^8 x}{\csc x}\,dx$ is equal to

The domain of the function $f(x) = \sqrt{x - 1 + \sqrt{6 - x}}$ is

The integral $\int \sin^{-1}\left(\frac{2x}{1 + x^2}\right)\,dx$ for $|x| < 1$ is equal to

The differential equation of all family of lines $y = mx + \frac{4}{m}$ obtained by eliminating the arbitrary constant $m$ is

The value of $\int_0^1 \tan^{-1}\left(\frac{2x - 1}{1 + x - x^2}\right)\,dx$ is

If $x = \frac{1 - t^2}{1 + t^2}$ and $y = \frac{2at}{1 + t^2}$, then $\frac{dy}{dx} =$

$\tan^{-1}\left(\tan \frac{5\pi}{6}\right) + \cos^{-1}\left(\cos \frac{13\pi}{6}\right) =$

If in $\Delta ABC$, with usual notations, the angles are in A.P., then $\frac{a}{c}\sin(2C) + \frac{c}{a}\sin(2A) =$

The sum of three numbers is 6. Thrice the third number when added to the first number gives 7. On adding three times first number to the sum of second and third number we get 12. The product of these numbers is

The expression $[(p \wedge \sim q) \vee q] \vee (\sim p \wedge q)$ is equivalent to

A coin is tossed three times. If $X$ denotes the absolute difference between the number of heads and the number of tails, then $P(X = 1) =$

If a plane meets the axes $X$, $Y$, $Z$ in $A$, $B$, $C$ respectively such that centroid of $\Delta ABC$ is $(1, 2, 3)$, then the equation of the plane is

The maximum value of $z = 10x + 25y$ subject to $0 \le x \le 3$, $0 \le y \le 3$, $x + y \le 5$ occurs at the point

The plane $\frac{x}{2} + \frac{y}{3} + \frac{z}{4} = 1$ cuts the $X$-axis at $A$, $Y$-axis at $B$ and $Z$-axis at $C$, then the area of $\Delta ABC$ is

A random variable $X$ has the following probability distribution:
{|c|c|c|c|c|c|c|} $X = x$ & 1 & 2 & 3 & 4 & 5 & 6 $P(X = x)$ & $k$ & $3k$ & $5k$ & $7k$ & $8k$ & $k$ Then $P(2 \le X < 5) =$

If $A = \begin{bmatrix} k & 2 \\ -2 & -k \end{bmatrix}$, then $A^{-1}$ does not exist if $k =$