List of top Questions asked in MHT CET- 2021

If $3\hat{j}$, $4\hat{k}$ and $3\hat{j} + 4\hat{k}$ are the position vectors of the vertices $A, B, C$ respectively of $\Delta ABC$, then the position vector of the point in which the bisector of $\angle A$ meets $BC$ is

10 is divided into two parts such that the sum of double of the first and square of the other is minimum, then the numbers are respectively

The combined equation of a pair of lines passing through the origin and inclined at $60^\circ$ and $30^\circ$ respectively with X-axis is

Range of the function $f(x) = 3 + 2^x + 4^x$ is

If two lines represented by $ax^2 + 2hxy + by^2 = 0$ make angles $\alpha$ and $\beta$ with the positive direction of X-axis, then $\tan(\alpha + \beta) =$

If $A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & -1 & 0 \\ 3 & 3 & -4\end{array}\right]$, $B=\left[\begin{array}{l}1 \\ 1 \\ 2\end{array}\right]$ and $X=\left[\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right]$ such that $AX = B$, then the value of $x_1 + x_2 + x_3 =$

The vector equation of the line passing through $\text{P}(1,2,3)$ and $\text{Q}(2,3,4)$ is

If $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$, $\vec{b} = -\hat{i} + 2\hat{j} + \hat{k}$, $\vec{c} = 3\hat{i} + \hat{j}$ and $\vec{a} + \lambda \vec{b}$ is perpendicular to $\vec{c}$, then the value of $\lambda =$

If $\tan^{-1} \left[ \frac{\sqrt{1+x^2} - \sqrt{1-x^2}}{\sqrt{1+x^2} + \sqrt{1-x^2}} \right] = \alpha$, then the value of $\sin 2\alpha$ is

The general solution of the differential equation $\frac{dy}{dx} = 2^{y - x}$ is

If $x = -2$ and $x = 4$ are the extreme points of the function $y = x^3 - \alpha x^2 - \beta x + 5$, then the values of $\alpha$ and $\beta$ are respectively

The coordinates of the foot of the perpendicular drawn from the origin to the plane $2x + y - 2z = 18$ are

If $\mathrm{A}=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$, then $\mathrm{A}(\text{adj }\mathrm{A}) =$

A random variable X has the following probability distribution

Then P ( 3 < x $\le$ 6 ) =

If a circle passes through the points $(0,0)$, $(x, 0)$ and $(0, y)$, then the coordinates of its centre are

If $A=\left[\begin{array}{rr}2 & 3 \\ 5 & -2\end{array}\right]$ and $A^{-1}=K A$, then $K$ is

Evaluate the integral: $\int \frac{10^{x/2}}{\sqrt{10^{-x} - 10^x}} dx$

The maximum value of the objective function $z = 2x + 3y$ subject to the constraints $x + y \le 5$, $2x + y \ge 4$ and $x \ge 0, y \ge 0$ is

The particular solution of differential equation $(x + y) dy + (x - y) dx = 0$ at $x = y = 1$ is

If $3 \sin \theta = 2 \sin 3 \theta$ and $0 < \theta < \pi$, then $\sin \theta =$

Evaluate the integral: $\int_0^{\pi / 2} \frac{\cos x}{3 \cos x + \sin x} dx$

Function $f(x) = e^{-1/x}$ is strictly increasing for all $x$ where

The general solution of the differential equation $\frac{dx}{dt} = \frac{x \log x}{t}$ is

The distance between the parallel lines $\frac{x-2}{3}=\frac{y-4}{5}=\frac{z-1}{2}$ and $\frac{x-1}{3}=\frac{y+2}{5}=\frac{z+3}{2}$ is

The general solution of the differential equation $\frac{dy}{dx} + \frac{y^2+y+1}{x^2+x+1} = 0$ is