List of top Questions asked in MHT CET

If \( \sin x + \sin^2 x = 1 \), then \( \cos^8 x + 2 \cos^6 x + \cos^4 x \) is

The integral \[ \int_0^{\frac{\pi}{2}} \log \left( \frac{\sqrt{1 - \cos 2x}}{\sqrt{1 + \cos 2x}} \right) dx \] is

The differential equation of the circles having their centres on the line $y = 8$ and touching the $x$-axis is

The distance of the point $(1,2,-1)$ from the plane $x-2y+4z+10=0$ is

If \( \mathbf{a} = 2\hat{i} - \hat{j} + \hat{k} \), \( \mathbf{b} = \hat{i} + 2\hat{j} - 3\hat{k} \), and \( \mathbf{c} = 2\hat{i} + 3\hat{j} + 5\hat{k} \) are coplanar, then \( \lambda \) is the root of the equation

If \( \sin(x + y) + \cos(x + y) = \sin \left[ \cos^{-1} \left( \frac{1}{3} \right) \right] \), then \[ \frac{dy}{dx} = \]

The value of \( \int_{2}^{3} \frac{x}{x^2 - 1} \, dx \) is

The equation of a line passing through the point \( (2, 4, 6) \) and parallel to the line \[ 3x + 4 = 4y - 1 = 1 - 4z \] is

In a box containing 100 bulbs, 10 are defective. The probability that out of 20 bulbs selected at random, none is defective is

Evaluate \( \sin 690^\circ \times \sec 240^\circ \)

Evaluate \[ \sec 2\theta - \tan 2\theta = \]

The area bounded by the circle \(x^2 + y^2 = 16\) and the lines \(x = 0\) and \(x = 2\) is

Evaluate \( \int_{-2}^{1} \left[ x + 1 \right] \, dx \), where \( [x] \) is the greatest integer function not greater than \( x \)

Evaluate $\displaystyle \int_{0}^{1} x(1-x)^5 \, dx$

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

Evaluate the integral: \[ \int \left[ \frac{1 - \log x}{1 + (\log x)^2} \right]^2 dx \]

If \[ f(x) = \begin{cases} 6\beta - 3x, & \text{if } -4 \leq x<-2,
4x + 1, & \text{if } -2 \leq x \leq 2, \end{cases} \] is continuous on \( [-4, 2] \), then \( \alpha + \beta = \)

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

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

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

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

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

If \[ \sqrt{\frac{x}{y}} + \sqrt{\frac{y}{x}} = 4, \quad \text{then} \quad \frac{dy}{dx} = \]

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

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