List of top Questions asked in MHT CET- 2021

If $|\bar{a}| = 3, |\bar{b}| = 4, |\bar{a} - \bar{b}| = 5$, then $|\bar{a} + \bar{b}| =$

A body at an unknown temperature is placed in a room which is held at a constant temperature of $30^{\circ}F$. If after 10 minutes the temperature of the body is $0^{\circ}F$ and after 20 minutes the temperature of the body is $15^{\circ}F$, then the expression for the temperature of the body at any time $t$ is

If $y = \operatorname{cosec}^{-1} \left[ \frac{\sqrt{x}+1}{\sqrt{x}-1} \right] + \cos^{-1} \left[ \frac{\sqrt{x}-1}{\sqrt{x}+1} \right]$, then $\frac{dy}{dx} =$

If the function $$f(x) = \begin{cases} 1 + \sin\frac{\pi}{2}, & -\infty < x \le 1 \\ ax + b, & 1 < x < 3 \\ 6 \tan\frac{x\pi}{12}, & 3 \le x < 6 \end{cases}$$ is continuous in $(-\infty, 6)$, then the values of $a$ and $b$ are respectively.

If $A^{-1} = \frac{-1}{2} \begin{bmatrix} 1 & -4 \\ -1 & 2 \end{bmatrix}$, then $2A + I_2 = \dots$ where $I_2$ is a unit matrix of order 2.

If $\int \frac{x^3}{\sqrt{1+x^2}} dx = a(1+x^2)^{\frac{3}{2}} + b\sqrt{1+x^2} + c$, then $a+b =$, (where $c$ is constant of integration)

If $f(x) = |x-1| + |x-2| + |x-3|, \forall x \in [1,4]$, then $\int_1^4 f(x) dx =$

The equation of the circle whose centre lies on the line $x-4y=1$ and which passes through the points $(3,7)$ and $(5,5)$ is

If the polar co-ordinates of a point are $\left(\sqrt{2}, \frac{\pi}{4}\right)$, then its Cartesian co-ordinates are

The shaded figure given below is the solution set for the linear inequations. Choose the correct option.

$\int_0^{\frac{\pi}{2}} \frac{\sin x-\cos x}{1-\sin x \cos x} d x=$

The equation of the plane passing through $(-2,2,2)$ and $(2,-2,-2)$ and perpendicular to the plane $9x-13y-3z=0$ is

The complex number with argument $\frac{5\pi}{6}$ at a distance of 2 units from the origin is

If $\bar{a}=3\hat{i}-5\hat{j}, \bar{b}=6\hat{i}+3\hat{j}$ are two vectors and $\bar{c}$ is a vector such that $\bar{c}=\bar{a}\times\bar{b}$, then $|\bar{a}|:|\bar{b}|:|\bar{c}|$ is

If vectors $\bar{a}=2\hat{i}+2\hat{j}+3\hat{k}$, $\bar{b}=-\hat{i}+2\hat{j}+\hat{k}$ and $\bar{c}=3\hat{i}+\hat{j}+2\hat{k}$ are such that $\bar{a}+\lambda\bar{b}$ is perpendicular to $\bar{c}$, then $\lambda =$

If $F(\alpha)=\begin{bmatrix}\cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1\end{bmatrix}$, where $\alpha \in R$, then $[F(\alpha)]^{-1} =$

The Cartesian equation of the plane passing through the point $A(7, 8, 6)$ and parallel to the XY plane is

In a quadrilateral PQRS, M and N are mid-points of the sides PQ and RS respectively. If $\overline{PS} + \overline{QR} = t\overline{MN}$, then $t =$

A coin is tossed and a die is thrown. The probability that the outcome will be head or a number greater than 4 or both, is

Negation of the statement $\forall x \in R, x^2+1=0$ is

The differential equation of family of circles whose centres lie on X-axis is

The area of the region bounded by the curve $y^2 = 4x$ and the line $y = x$ is

If $\frac{\cos(A+B)}{\cos(A-B)} = \frac{\sin(C+D)}{\sin(C-D)}$, then $\tan A \tan B \tan C =$

The general solution of the differential equation $y(1+\log x)\left(\frac{dx}{dy}\right) - x\log x = 0$ is

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs selected at random from the lot and sent to retain store, then the probability that the store will receive at most one defective bulb is