List of top Mathematics Questions asked in MHT CET

The statement \( [(p \rightarrow q) \wedge \sim q] \rightarrow r \) is a tautology when \( r \) is equivalent to:

If \( A = \begin{bmatrix} 1 & 0 \\ 1/2 & 1 \end{bmatrix} \), then \( A^{50} \) is:

The value of \( \sqrt{3} \csc 20^\circ - \sec 20^\circ \) is:
If \( y = \sec(\tan^{-1} x) \), find \( \frac{dy}{dx} \), given that \( x = 1 \):
If \( p \land q \) is False and \( p \rightarrow q \) is False, then the truth values of \( p \) and \( q \) are:
The statement \( (p \wedge (\sim q)) \vee ((\sim p) \wedge q) \vee ((\sim p) \wedge (\sim q)) \) is equivalent to:
If \[ B = \begin{bmatrix} 3 & \alpha & -1 \\ 1 & 3 & 1 \\ -1 & 1 & 3 \end{bmatrix} \] is the adjoint of a 3x3 matrix \( A \) and \( |A| = 4 \), then \( \alpha \) is equal to:
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:
The number of all four-digit numbers which begin with 4 and end with either zero or five is
Find the value of \( (a + b) \cdot p + (b + c) \cdot q + (c + a) \cdot r \):
If \( y = (\sin x)^y \), then \( \frac{dy}{dx} \) is:
Evaluate \( \int_{0}^{\pi/4} \frac{\cos^2 x}{\cos^2 x + 4 \sin^2 x} \, dx \):
The order and degree of the differential equation \( \sqrt{\frac{dy}{dx}} - 4 \frac{dy}{dx} - 7x = 0 \) are respectively
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:
Let the following system of equations: $$ kx + y + z = 1, \quad x + ky + z = k, \quad x + y + kz = k^2 $$ have no solution. Find $|k|$:
The integral \( \int e^x \frac{2 + \sin 2x}{1 + \cos 2x} \, dx \) is equal to
If \( x = \frac{1 - t^2}{1 + t^2} \) and \( y = \frac{2t}{1 + t^2} \), then \( \frac{dy}{dx} \) is equal to:
If \( x \neq 0 \), then \[ \frac{\sin(\pi + x)\cos\left(\frac{\pi}{2} + x\right)\tan\left(\frac{3\pi}{2} - x\right)\cot(2\pi - x)}{\sin(2\pi - x)\cos(2\pi + x)\csc(-x)\sin\left(\frac{3\pi}{2} + x\right)} = \]
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:
Find the differential equation of the family of all circles, whose center lies on the x-axis and touches the y-axis at the origin.
If \( y = \log_e \left[ e^{3x} \left( \frac{x - 4}{x + 3} \right)^{3/2} \right] \), then find \( \frac{dy}{dx} \):
If the vector equation of the line \[ \frac{x - 2}{2} = \frac{2y - 5}{-3} = z + 1, \] is given by: \[ \vec{r} = \left(2\hat{i} + \frac{5}{2}\hat{j} - \hat{k}\right) + \lambda\left(2\hat{i} - \frac{3}{2}\hat{j} + p\hat{k}\right), \] then \( p \) is equal to:
If two numbers \( p \) and \( q \) are chosen randomly from the set \( \{1, 2, 3, 4\} \) with replacement, what is the probability that \( p^2 \geq 4q \)?

Let \( f(x) = \frac{2 - \sqrt{x + 4}}{\sin 2x}, \, x \neq 0 \). In order that \( f(x) \) is continuous at \( x = 0 \), \( f(0) \) is to be defined as:

The maximum value of \(\frac{\log(x)}{x}\) is: