List of top Questions asked in MHT CET- 2021

Two waves $Y_1 = 0.25 \sin(316t)$ and $Y_2 = 0.25 \sin(310t)$ are propagating in the same direction. The number of beats produced per second are

In an LCR series a.c. circuit, the voltage across each of the components L, C and R is 60 V. The voltage across the LC combination is

If $x = a\left(t - \frac{1}{t}\right)$ and $y = b\left(t + \frac{1}{t}\right)$, then $\frac{dy}{dx} =$

The area bounded by the parabola $y^2 = 4ax$ and its latus-rectum $x = a$ is

Equation of planes parallel to the plane $x - 2y + 2z + 4 = 0$ which are at a distance of one unit from the point $(1, 2, 3)$ are

Out of 7 consonants and 4 vowels, the number of words consisting of 3 consonants and 2 vowels are

If $f(x) = \csc^{-1} \left[ \frac{10}{6 \sin(2^x) - 8 \cos(2^x)} \right]$, then $f'(x) =$

If $y = \log \sqrt{\tan x}$, then the value of $\frac{dy}{dx}$ at $x = \frac{\pi}{4}$ is

In a triangle ABC, with usual notations $a = 2$, $b = 3$, $c = 5$, then $\frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} =$

Evaluate the limit: $\lim_{x \to 1} \left[ \frac{\sqrt{x} - 1}{\log x} \right] =$

If $f(x) = \frac{1 - \sin x + \cos x}{1 + \sin x + \cos x}$, for $x \neq \pi$ is continuous at $x = \pi$, then the value of $f(\pi)$ is

Negation of the statement : $3 + 6 > 8$ and $2 + 3 < 6$ is

Rooms in a hotel are numbered from 1 to 19. Rooms are allocated at random as guests arrive. The first guest to arrive is given a room which is a prime number. The probability that the second guest to arrive is given a room which is a prime number is

Given that the total of 16 values is 528 and the sum of the squares of deviation from 33 is 9158. The variance is

If the surrounding air is kept at 25$^\circ$C and a body cools from 80$^\circ$C to 50$^\circ$C in 30 minutes, then temperature of the body after one hour will be

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

If $z = x + iy$ satisfies the condition $|z + 1| = 1$, then $z$ lies on the

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

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

Evaluate the integral: $\int e^{(e^x + x)} dx$

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

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

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

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