List of top Questions asked in MHT CET- 2021

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 $P(2 \le X < 5) =$

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 $2\ \text{cm}$.

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

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

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

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 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

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

The value of $\int e^x \left(\frac{x - 1}{x^2}\right) dx =$

The value of $\int_{-\pi}^{\pi} \frac{x\sin x}{1+\cos^2 x}\,dx =$

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

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

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

If $A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1 \end{bmatrix}$, then the value of the determinant of $A^{-1}$ is

If the slope of one of the lines $ax^2 + 2hxy + by^2 = 0$ is twice that of the other, then $h^2 : ab$ is

The general solution of $\sin^{-1}\left(\frac{dy}{dx}\right) = x + y$ is

$\tan 3A \cdot \tan 2A \cdot \tan A =$

In $\triangle ABC$, with usual notations, $2ab \sin \frac{1}{2}(A+B-C) =$

If statements $p$ and $q$ are true and $r$ and $s$ are false, then truth values of $\sim ( p \rightarrow q ) \leftrightarrow ( r \wedge s )$ and $( \sim p \rightarrow q ) \wedge ( r \leftrightarrow s )$ are respectively

Bismuth has a half-life period of $5$ days. A sample originally has a mass of $1000\text{ mg}$, then the mass of Bismuth after $30$ days is

The equation of a circle that passes through the origin and cut off intercepts $-2$ and $3$ on the X-axis and Y-axis respectively is