List of top Questions asked in MHT CET- 2021

A mass '$m_1$' is suspended from a spring of negligible mass. A spring is pulled slightly in downward direction and released, mass performs S.H.M. of period '$T_1$'. If the mass is increased by '$m_2$', the time period becomes '$T_2$'. The ratio $\frac{m_2}{m_1}$ is

An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half the quantity of ice melts in 20 minutes, $x_0$ is the initial quantity of ice. If after 40 minutes the amount of ice left is $Kx_0$, then K =

If the lines $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ are tangents to a circle, then the radius of the circle is

If $\int_0^{\frac{\pi}{2}} \frac{dx}{5+4\sin x} = A \tan^{-1} B$, then A + B =

If $X \sim B(4, p)$ and $P(X = 0) = \frac{16}{81}$, then $P(X = 4) =$

$\int \frac{x+\sin x}{1+\cos x} d x=$

If $4 \sin ^{-1} x+6 \cos ^{-1} x=3 \pi$, where $-1 \leq x \leq 1$, then $x =$

If $x = a \cos \theta$, $y = b \sin \theta$, then $\left[\frac{d^2 y}{d x^2}\right] = $

If the line $\frac{x+1}{2}=\frac{y-m}{3}=\frac{z-4}{6}$ lies in the plane $3x-14y+6z+49=0$, then the value of $m$ is

If $h(x)=\sqrt{4 f(x)+3 g(x)}$, $f(1)=4$, $g(1)=3$, $f^{\prime}(1)=3$, $g^{\prime}(1)=4$, then $h^{\prime}(1)=$

If $x \in \left(0, \frac{\pi}{2}\right)$ and $x$ satisfies the equation $\sin x \cos x = \frac{1}{4}$, then the values of $x$ are

The domain of the function $f(x) = \frac{1}{\sqrt{x + |x|}}$ is

The value of $\sin 18^{\circ}$ is

All the letters of the word 'ABRACADABRA' are arranged in different possible ways. Then the number of such arrangements in which the vowels are together is

The equation of the tangent to the curve $y = 4x e^x$ at $\left(-1, -\frac{4}{e}\right)$ is

If $\int \frac{1+x^2}{1+x^4} d x=\frac{1}{\sqrt{2}} \tan ^{-1}\left[\frac{f(x)}{\sqrt{2}}\right]+c$, then $f(x)=$

The slope of the line through the origin which makes an angle of $30^\circ$ with the positive direction of Y-axis measured anticlockwise is :

With usual notations if the angles of a triangle are in the ratio 1 : 2 : 3, then their corresponding sides are in the ratio

The differential equation of all circles which pass through the origin and whose centre lie on Y-axis is

$(2\hat{\mathrm{i}} + 6\hat{\mathrm{j}} + 27\hat{\mathrm{k}}) \times (\hat{\mathrm{i}} + \lambda\hat{\mathrm{j}} + \mu\hat{\mathrm{k}}) = \vec{0}$, then $\lambda$ and $\mu$ are respectively

The angle between a line with direction ratios 2, 2, 1 and a line joining $(3, 1, 4)$ and $(7, 2, 12)$ is

If $f(x) = [x]$, for $x \in (-1, 2)$, then $f$ is discontinuous at (where $[x]$ represents floor function)

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 area of the region bounded by the parabola $x^2 = y$ and the line $y = x$ is