List of top Questions asked in MHT CET- 2021

If $x^y \cdot y^x = 16$, then $\frac{dy}{dx}$ at $(2,2)$ is

If $A = \begin{bmatrix} 1 & 2 & 1 \\ -1 & 1 & 3 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 2 \\ -3 & 1 \\ 0 & 2 \end{bmatrix}$, then $(AB)^{-1} =$

With usual notations, in any $\Delta ABC$, if $a\cos B = b\cos A$, then the triangle is

The general solution of $\frac{dy}{dx} = \frac{x+y}{x-y}$ is

A fair coin is tossed 4 times. If $X$ is a random variable which indicates number of heads, then $P[X \lt 3] =$

A line drawn from a point $A(-2,-2,3)$ and parallel to the line $\frac{x}{-2} = \frac{y}{2} = \frac{z}{-1}$ meets the $YOZ$ plane in point $P$, then the coordinates of the point $P$ are

First bag contains 3 red and 5 black balls and second bag contains 6 red and 4 black balls. A ball is drawn from each bag. The probability that one ball is red and the other is black, is

$$\int \frac{\tan^4 \sqrt{x} \cdot \sec^2 \sqrt{x}}{\sqrt{x}} \, dx =$$

If the points $P(4,5,x)$, $Q(3,y,4)$ and $R(5,8,0)$ are collinear, then the value of $x+y$ is

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

The particular solution of the differential equation $\frac{dy}{dx} = \frac{y+1}{x^2-x}$, when $x=2$ and $y=1$ is

The line $\frac{x-2}{3} = \frac{y-1}{-5} = \frac{z+2}{2}$ lies in the plane $x + 3y - \alpha z + \beta = 0$, then value of $\alpha \beta$ is

The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is

If the vectors $2\hat{i} - \hat{j} - \hat{k}$, $\hat{i} + 2\hat{j} - 3\hat{k}$ and $3\hat{i} + \lambda\hat{j} + 5\hat{k}$ are coplanar, then the value of $\lambda$ is

A spherical raindrop evaporates at a rate proportional to its surface area. If its radius originally is $3\text{ mm}$ and $1\text{ hour}$ later has been reduced to $2\text{ mm}$, then the expression of radius $r$ of the raindrop at any time $t$ is (where $0 \le t \lt 3$)

If $2 \tan^{-1}(\cos x) = \tan^{-1}(2 \csc x)$, then the value of $x$ is

Given $p$ : A man is a judge, $q$ : A man is honest.
If $S_1$ : If a man is a judge, then he is honest
$S_2$ : If a man is a judge, then he is not honest
$S_3$ : A man is not a judge or he is honest
$S_4$ : A man is a judge and he is honest
Then

$$\lim_{x \to 2} (x - 1)^{\frac{1}{3x - 6}} =$$

The area bounded by the parabola $y^2 = x$ and the line $x + y = 2$ in the first quadrant is

For an invertible matrix $A$, if $A(\text{adj } A) = \begin{bmatrix} 20 & 0 \\ 0 & 20 \end{bmatrix}$, then $|A| =$

If $f(x) = x^2 + ax + b$ has minima at $x = 3$ whose value is $5$, then the values of $a$ and $b$ are respectively

$$\int_{\frac{\pi}{6}}^{\frac{\pi}{2}} \frac{\csc x \cdot \cot x}{1 + \csc^2 x} \, dx =$$

If $2 \cos \theta = x + \frac{1}{x}$, then $2 \cos 3\theta =$

The function $f(x) = \frac{\lambda \sin x + 6 \cos x}{2 \sin x + 3 \cos x}$ is increasing, if

Two circles centred at $(2,3)$ and $(4,5)$ intersect each other. If their radii are equal, then the equation of the common chord is