List of top Questions asked in MHT CET- 2020

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

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

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

For a sequence if \( S_n = \dfrac{5^n - 2^n}{2^n} \), then its fourth term 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 \( y = \tan^{-1} \left( \frac{\sin 2x}{1 + \cos 2x} \right) \), then \[ \frac{dy}{dx} = \]

If the equation \[ kxy + 5x + 3y + 2 = 0 \text{ represents a pair of lines, then } k = \]

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

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

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

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

A fair coin is tossed 2 times. A person receives \( X^3 \) if he gets \( X \) number of heads. His expected gain 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

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

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

The logical expression \( [p \wedge (q \vee r)] \vee [\neg r \wedge \neg q \wedge p] \) is equivalent to

The particular solution of the differential equation \[ y \frac{dx}{dy} = x \log x \quad \text{at} \quad x = e \text{ and } y = 1 \] is

Evaluate \[ \int \frac{\log x - 1}{1 + (\log x)^2} \, dx \]

The population \( P(t) \) of a certain mouse species at time \( t \) satisfies the differential equation \[ \frac{dP(t)}{dt} = 0.5P(t) - 450. \quad \text{If} \, P(0) = 850, \, \text{then the time at which the population becomes zero is} \]

If $\displaystyle \int_{1}^{k} (3x^2 + 2x + 1)\,dx = 11$, then $k =$

The cumulative distribution function of a continuous random variable \( X \) is given by \( F(X = x) = \dfrac{\sqrt{x}}{2} \). Then \( P(X>1) \) is

The derivative of $\sin^{-1}\!\left(\dfrac{\sqrt{1+x}+\sqrt{1-x}}{2}\right)$ with respect to $\cos^{-1}x$ is

The integrating factor of the differential equation \[ \frac{dy}{dx} + \frac{1}{x}y = x^3 - 3 \] is

If the points \( (1, 1, \lambda) \) and \( (-3, 0, 1) \) are equidistant from the plane \( 3x + 4y - 12z + 13 = 0 \), then the integer value of \( \lambda \) is

Degree of the differential equation \[ \frac{dy}{dx} e^x + \left( \frac{dy}{dx} \right)^3 = x \]