List of top Questions asked in MHT CET

\( \int_{\pi/11}^{9\pi/22} \frac{dx}{1 + \sqrt{\tan x}} \) is equal to:
The tangent at the point \( (x_1, y_1) \) on the curve \( y = x^3 + 3x^2 + 5 \) passes through the origin. Then \( (x_1, y_1) \) does NOT lie on the curve:
The value of \( \int \frac{x \sin^{-1} x}{\sqrt{1 - x^2}} dx \) is equal to:

The value of : \( \int \frac{x + 1}{x(1 + xe^x)} dx \).

The order and degree of the differential equation \( \sqrt{\frac{dy}{dx}} - 4 \frac{dy}{dx} - 7x = 0 \) are respectively
Let \( \vec{a} = \hat{i} + \hat{j} + \hat{k}, \, \vec{b} = \hat{i} + 3\hat{j} + 5\hat{k} \) and \( \vec{c} = 7\hat{i} + 9\hat{j} + 11\hat{k} \). Then the area of a parallelogram having diagonals \( \vec{a} + \vec{b} \) and \( \vec{b} + \vec{c} \) is:
The integral \( \int \frac{\csc x}{\cos^2\left(1 + \log \tan \frac{x}{2}\right)} \, dx \) is equal to:
The value of \( \sqrt{3} \csc 20^\circ - \sec 20^\circ \) is:
The statement \( (p \wedge (\sim q)) \vee ((\sim p) \wedge q) \vee ((\sim p) \wedge (\sim q)) \) is equivalent to:
The distribution function \( F(X) \) of a discrete random variable \( X \) is given. Then \( P[X = 4] + P[X = 5] \):
\[ \begin{array}{|c|c|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline F(X = x) & 0.2 & 0.37 & 0.48 & 0.62 & 0.85 & 1 \\ \hline \end{array} \]
If the lines \( \frac{x-k}{2} = \frac{y+1}{3} = \frac{z-1}{4} \) and \( \frac{x-3}{1} = \frac{y - 9/2}{2} = z/1 \) intersect, then the value of \( k \) is:
A vector parallel to the line of intersection of the planes \[ \overrightarrow{r} \cdot (3\hat{i} - \hat{j} + \hat{k}) = 1 \quad \text{and} \quad \overrightarrow{r} \cdot (\hat{i} + 4\hat{j} - 2\hat{k}) = 2 \] is:
The surface area of a spherical balloon is increasing at the rate of \( 2 \, \text{cm}^2/\text{sec} \). Then the rate of increase in the volume of the balloon, when the radius of the balloon is \( 6 \, \text{cm} \), is:
If \( f(x) = 2x^3 - 15x^2 - 144x - 7 \), then \( f(x) \) is strictly decreasing in:
If \( y = (\sin x)^y \), then \( \frac{dy}{dx} \) is:
If \( \sin^{-1} x + \cos^{-1} y = \frac{3\pi}{10} \), then the value of \( \cos^{-1} x + \sin^{-1} y \) is:
\( \sin^{-1}[\sin(-600^\circ)] + \cot^{-1}(-\sqrt{3}) = \)
If \[ A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix} \] and \[ A^{-1} = \frac{1}{2} \begin{bmatrix} 1 & -1 & 1 \\ -8 & 6 & 2c \\ 5 & -3 & 1 \end{bmatrix}, \] then the values of \( a \) and \( c \) are respectively:
The p.m.f. of a random variable \( X \) is: \[ P(X) = \frac{2x}{n(n+1)}, \quad x = 1, 2, 3, \ldots, n \] \[ P(X) = 0, \quad \text{Otherwise.} \] Then \( E(X) \) is:
One of the principal solutions of \( \sqrt{3} \sec x = -2 \) is equal to:
Integrate the following function w.r.t. $x$: $\int \frac{e^{3x}}{e^{3x} + 1} \, dx$
The general solution of
$$ \left(x\frac{dy}{dx} - y\right)\sin\frac{y}{x} = x^3 e^x $$ is: 
The converse of \( ((\sim p) \land q) \Rightarrow r \) is:
The negative of \( (p \land (\sim q)) \lor (\sim p) \) is equivalent to:
The variance of the following probability distribution is:

\[ \begin{array}{|c|c|} \hline x & P(X) \\ \hline 0 & \frac{9}{16} \\ 1 & \frac{3}{8} \\ 2 & \frac{1}{16} \\ \hline \end{array} \]