List of top Questions asked in MHT CET

If \( p \land q \) is False and \( p \rightarrow q \) is False, then the truth values of \( p \) and \( q \) are:
The inverse of the matrix \[ \begin{bmatrix} 1 & 0 & 0 \\ 3 & 3 & 3 \\ 5 & 2 & -1 \end{bmatrix} \] is:

The function \( f(x) = \tan^{-1} (\sin x + \cos x) \) is an increasing function in:

If \( A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{bmatrix} \), then \( A^{-1} \) is:
If \( f(x) = |x| - |1| \), then points where \( f(x) \) is not differentiable, is/are:
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:
If \( \sqrt{\frac{y}{x}} + 4\sqrt{\frac{x}{y}} = 4 \), then \( \frac{dy}{dx} \):
The value of \( \int \frac{x \sin^{-1} x}{\sqrt{1 - x^2}} dx \) is equal to:
The equation \( (\cos p - 1)x^2 + (\cos p)x + \sin p = 0 \), where \( x \) is a variable with real roots. Then the interval of \( p \) may be any one of the following:
If \( \mathbf{a} = \mathbf{i} + 2\mathbf{j} - 3\mathbf{k} \) and \( \mathbf{b} = 2\mathbf{i} - 3\mathbf{j} - 5\mathbf{k} \), then:

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

A student scores the following marks in five tests: 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is:
The equation of the plane passing through the point \( (1, 1, 1) \) and perpendicular to the planes \( 2x + y - 2z = 5 \) and \( 3x - 6y - 2z = 7 \) is:
If \( AX = B \), where \[ A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}, \quad X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}, \quad B = \begin{bmatrix} 4 \\ 0 \\ 2 \end{bmatrix}, \] then \( 2x + y - z \) is:
Find the area of the region bounded by the parabola $$ y^2 = 4ax \text{ and its latus rectum.} $$ 
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:
A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to the retail store. Then the probability that the store will receive at most one defective bulb is:
One of the principal solutions of \( \sqrt{3} \sec x = -2 \) is equal to:
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:
The particular solution of the differential equation \(e \frac{dy}{dx} = (x + 1)\), \(y(0) = 3\), is:
The negative of \( (p \land (\sim q)) \lor (\sim p) \) is equivalent to:
If the curve \(y^2 = 6x\) and \(9x^2 + by^2 = 16\) intersect each other at right angles, then the value of \(b\) is:
The maximum value of \(\frac{\log(x)}{x}\) is:

The general solution of
$$ \left(x\frac{dy}{dx} - y\right)\sin\frac{y}{x} = x^3 e^x $$ is: 
The integral \( \int \frac{\csc x}{\cos^2\left(1 + \log \tan \frac{x}{2}\right)} \, dx \) is equal to: