List of top Questions asked in MHT CET- 2021

The general solution of the differential equation $x + y \frac{d y}{d x} = \sec(x^2 + y^2)$ is

If $A = \begin{bmatrix} 3 & 2 & 4 \\ 1 & 2 & 1 \\ 3 & 2 & 6 \end{bmatrix}$ and $A_{ij}$ are cofactors of the elements $a_{ij}$ of $A$, then $a_{11}A_{11} + a_{12}A_{12} + a_{13}A_{13}$ is equal to

$\lim_{x \to \infty} \left( \sqrt{x^2 + 5x - 7} - x \right) =$

The general solution of the differential equation $\frac{d y}{d x}=\frac{x+y+1}{x+y-1}$ is given by

If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect, then the value of $k$ is

If inverse of $\begin{bmatrix} 1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6 \end{bmatrix}$ does not exist, then $x =$

The logical expression $p \wedge(\sim p \vee \sim q) \equiv$

The parametric equations of a line passing through the points $A(3,4,-7)$ and $B(1,-1,6)$ are

If $\bar{\mathrm{e}}_1$, $\bar{\mathrm{e}}_2$ and $\bar{\mathrm{e}}_1+\bar{\mathrm{e}}_2$ are unit vectors, then the angle between $\bar{\mathrm{e}}_1$ and $\bar{\mathrm{e}}_2$ is

The Cartesian equation of the plane passing through the point $(0,7,-7)$ and containing the line $\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$ is

If $\bar{\mathrm{a}}$, $\bar{\mathrm{b}}$, $\bar{\mathrm{c}}$ are three vectors which are perpendicular to $\bar{\mathrm{b}} + \bar{\mathrm{c}}$, $\bar{\mathrm{c}} + \bar{\mathrm{a}}$ and $\bar{\mathrm{a}} + \bar{\mathrm{b}}$ respectively, such that $|\bar{a}| = 2$, $|\bar{b}| = 3$, $|\bar{c}| = 4$, then $|\bar{a} + \bar{b} + \bar{c}| =$

A particle is moving on a straight line. The distance S travelled in time t is given by $S = a t^2 + b t + 6$. If the particle comes to rest after 4 seconds at a distance of 16 m from the starting point, then the acceleration of the particle is

If $y=\log \tan \left(\frac{x}{2}\right)+\sin ^{-1}(\cos x)$, then $\frac{d y}{d x}=$

The negation of a statement '$x \in A \cap B \rightarrow (x \in A \text{ and } x \in B)$' is

A differential equation for the temperature 'T' of a hot body as a function of time, when it is placed in a bath which is held at a constant temperature of $32^\circ\text{F}$, is given by (where k is a constant of proportionality)

The joint equation of the pair of lines through the origin and making an equilateral triangle with the line $x = 3$ is

A random variable X has the following probability distribution

then F(4) =

$\int_0^{\pi / 4} \log (1+\tan x) \text{d}x=$

If 1 is added to first 10 natural numbers, then variance of the numbers so obtained is

The shaded part of the given figure indicates the feasible region. Then the constraints are

If the acute angle between the lines given by $ax^2 + 2hxy + by^2 = 0$ is $\frac{\pi}{4}$, then $4h^2 =$

A wire of length 20 units is divided into two parts such that the product of one part and cube of the other part is maximum, then product of these parts is

If the volume of a tetrahedron whose conterminous edges are $\vec{\mathrm{a}}+\vec{\mathrm{b}}$, $\vec{\mathrm{b}}+\vec{\mathrm{c}}$, $\vec{\mathrm{c}}+\vec{\mathrm{a}}$ is 24 cubic units, then the volume of parallelopiped whose coterminous edges are $\vec{\mathrm{a}}$, $\vec{\mathrm{b}}$, $\vec{\mathrm{c}}$ is

$\int \tan^{-1}(\sec x + \tan x) dx =$

Identify reductant in following reaction: $\text{C}_2\text{O}_4^{2-} + \text{MnO}_4^- + \text{H}^+ \longrightarrow \text{Mn}^{2+} + \text{CO}_2 + \text{H}_2\text{O}$