List of top Questions asked in MHT CET- 2021

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

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

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

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 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

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

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

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

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 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

If $|\vec{u}| = 2$ and $\vec{u}$ makes angles of $60^\circ$ and $120^\circ$ with the axes $OX$ and $OY$ at the origin, then $\vec{u} =$

A spherical snow ball is forming so that its volume is increasing at the rate of $8\ \text{cm}^3/\text{sec}$. Find the rate of increase of its radius when the radius is $2\ \text{cm}$.

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

If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ with $|\vec{a}| = 3$, $|\vec{b}| = 5$ and $|\vec{c}| = 7$, then the angle between $\vec{a}$ and $\vec{b}$ 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 $P(2 \le X < 5) =$

Area of the triangle formed by the lines $y^2 - 9xy + 18x^2 = 0$ and $y = 9$ is

For two events $A$ and $B$, $P(A \cup B) = \frac{5}{6}$, $P(A) = \frac{1}{6}$, $P(B) = \frac{2}{3}$, then $A$ and $B$ are

The point on the curve $y^2 = 2(x - 3)$ at which the normal is parallel to the line $y - 2x + 1 = 0$ is

The value of $\lim_{x \to 0} \frac{\cos(mx) - \cos(nx)}{x^2}$ is

The area bounded between the curve $x^2 = y$ and the line $y = 4x$ is

The area of the parallelogram whose diagonals are represented by the vectors $\vec{a} = 3\hat{i} - \hat{j} - 2\hat{k}$ and $\vec{b} = -\hat{i} + 3\hat{j} - 3\hat{k}$ is

A rectangle of maximum area is inscribed in an ellipse $\frac{x^2}{25} + \frac{y^2}{16} = 1$, then its dimensions are

The position vector of the point of intersection of the medians of a triangle, whose vertices are $A(1, 2, 3)$, $B(1, 0, 3)$ and $C(4, 1, -3)$ is

The Cartesian equation of a line is $3x + 1 = 6y - 2 = 1 - z$, then its vector equation is

Solution of the differential equation $y' = \frac{x^2+y^2}{xy}$, where $y(1) = -2$ is given by