List of top Questions asked in MHT CET- 2020

Evaluate \( \int_0^{\frac{\pi}{2}} \left( e^{\sin x} - e^{\cos x} \right) \, dx \)

If \( y = \tan^{-1} \left( \frac{\sin 2x}{1 + \cos 2x} \right) \), then \[ \frac{dy}{dx} = \]

If the radius of a circular blot of oil is increasing at the rate of $2$ cm/min, then the rate of change of its area when its radius is $3$ cm is

If the line \( 6x - y - 4 = 0 \) touches the curve \( y^2 = ax^3 + b \) at the point (1, 2), then \( a + b = \)

If \( \dfrac{d^2y}{dx^2} = \sin x + e^x \), \( y(0) = 3 \) and \( \left.\dfrac{dy}{dx}\right|_{x=0} = 4 \), then the equation of the curve is

An urn contains 4 red and 5 white balls. Two balls are drawn one after the other without replacement. Find the probability that both the balls are red.

If \[ \int \sqrt{x - 1} \left( \frac{x^2 + 1}{x^2} \right) dx = \frac{2}{3} (x - 1)^k + c, \quad \text{then the value of } k \text{ is} \]

Evaluate \[ \int \frac{5^x}{\sqrt{5^{-2x}} - 5^{2x}}\,dx \]

Evaluate the integral: \[ \int_{-5}^{5} \frac{e^x + e^{-x}}{e^x - e^{-x}} \, dx. \]

Out of 100 people selected at random, 10 have common cold. If five persons are selected at random from the group, then the probability that at most one person will have common cold is

The general solution of the differential equation \[ \sec^2 x \tan y\,dx + \sec^2 y \tan x\,dy = 0 \] is

The equation of normal to the curve \( y = \sin \left( \frac{\pi x}{4} \right) \) at the point (2, 5) is

If \( f(x) = 2x^2 + bx + c \), \( f(0) = 3 \) and \( f(2) = 1 \), then \( (f \circ f)(1) = \)

If $x^2+y^2=t+\dfrac{1}{t}$ and $x^4+y^4=t^2+\dfrac{1}{t^2}$, then $\dfrac{dy}{dx}=$

The area bounded by the parabola \( x^2 = 4y \), the lines \( y = 2 \), \( y = 4 \) and the Y-axis is

The general solution of \( \tan 3x = 1 \) is

If \[ A = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix} \] then

For a sequence if \( S_n = \dfrac{5^n - 2^n}{2^n} \), then its fourth term is

If \[ \sec x + \tan x = 3, \quad x \in \left( 0, \frac{\pi}{2} \right), \] then \( \sin x = \)

If \( y = \tan^{-1} \left( \frac{x - \sqrt{1 - x^2}}{x + \sqrt{1 - x^2}} \right) \), then \( \frac{dy}{dx} \) is

If \[ A = \begin{pmatrix} 2 & 5 \\ 0 & 1 \\ 3 & 0 \end{pmatrix}, \quad A^{-1} = \begin{pmatrix} 3 & -1 \\ -6 & 6 \\ -5 & 2 \end{pmatrix} \] then the values of \( \alpha \) and \( \beta \) are, respectively

Water at \(100^\circ\text{C}\) cools in 15 minutes to \(75^\circ\text{C}\) in a room temperature of \(25^\circ\text{C}\). Then the temperature of water after 30 minutes is

If \[ A = \begin{bmatrix} 2 & -1 \\ -1 & 2 \end{bmatrix}, \] such that \[ A^2 - 4A + 3I = 0, \] then \( A^{-1} \) is

The coordinates of the point where the line $\dfrac{x-1}{2}=\dfrac{y-2}{-3}=\dfrac{z+3}{4}$ meets the plane $2x+4y-z=1$ are

If the lines \[ \frac{x - 1}{5} = \frac{y + 1}{3} = \frac{3 - z}{\lambda} \quad \text{and} \quad \frac{x + 1}{4} = \frac{1 - 3y}{15} = \frac{z + 1}{1} \] are perpendicular to each other, then \( \lambda = \)