List of top Mathematics Questions asked in MHT CET

If \[ A = \{2, 4\}, \quad B = \{3, 4, 5\}, \quad \text{then} \quad (A \cap B) \times (A \cup B) = \]

The particular solution of the differential equation \[ \sin^2 y \frac{dx}{dy} + x = \cot y \quad \text{when} \quad x = 0 \quad \text{and} \quad y = \frac{3\pi}{4} \text{ is} \]

If \[ y = 3e^{5x} + 5e^{3x}, \quad \text{then} \quad \frac{d^2 y}{dx^2} - 8 \frac{dy}{dx} = \]

If \[ 2 + 4 + 6 + \cdots \text{ up to } n \text{ terms} = \frac{37}{36}, \] then \( n = \)

If \[ f(x) = |x - 2|, \quad x \in [0, 4], \quad \text{then the Rolle's theorem cannot be applied to the function because} \]

Evaluate the integral \[ \int_0^\infty \frac{dx}{(x^2 + 4)(x^2 + 9)} = \]

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

Evaluate the following product: \[ \tan 1^\circ \times \tan 2^\circ \times \tan 3^\circ \times \cdots \times \tan 89^\circ \]

If \[ x = \log t, \quad y + 1 = \frac{1}{t}, \] then \[ e^{-x} \frac{d^2 x}{dy^2} + \frac{dx}{dy} = \]

If \( \theta \) is a parameter, then the parametric equations of the circle \[ x^2 + y^2 - 6x + 4y - 3 = 0 \] are given by

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

If \[ | \mathbf{a} \times \mathbf{b} \times \mathbf{c} | = 4, \] then the volume of the parallelepiped with coterminous edges \[ \mathbf{a} + 2\mathbf{b}, \quad \mathbf{b} + 2\mathbf{c}, \quad \mathbf{c} + 2\mathbf{a} \] is

If the body cools from \( 135^\circ C \) to \( 80^\circ C \) at room temperature of \( 25^\circ C \) in 60 minutes, then the temperature of the body after 2 hours is

The displacement of a particle at the time \( t \) is given by \[ s = \sqrt{1 + t}, \quad \text{then its acceleration } a \text{ is proportional to} \]

If \[ y = \tan^{-1}(\sec x + \tan x), \quad \text{then} \quad \frac{dy}{dx} = \]

Evaluate the integral \[ \int_0^{\frac{\pi}{2}} \frac{\sin x \cos x}{1 + \sin^4 x} \, dx = \]

The statement pattern \[ [(p \vee q) \wedge \neg p] \wedge (\neg q) \] is

Two cards are drawn from a pack of well shuffled 52 playing cards one by one without replacement. Then the probability that both cards are queens is

If \[ \mathbf{a} = \frac{1}{\sqrt{10}} (3i + k), \quad \mathbf{b} = \frac{1}{7} (2i + 3j - 6k), \quad \text{then the value of} \] \[ (2\mathbf{a} - \mathbf{b}) \cdot \left[ (\mathbf{a} \times \mathbf{b}) \times (\mathbf{a} + 2\mathbf{b}) \right] \]

The maximum value of the function \[ y = e^{5 + \sqrt{3} \sin x + \cos x} \]

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

The solution of the differential equation \[ x^2 \frac{dy}{dx} = y^2 + xy \]

If \( Z = 7x + y \) subject to \[ 5x + y \geq 5, \quad x + y \geq 3, \quad x \geq 0, \quad y \geq 0, \quad \text{then the minimum value of } Z \text{ is} \]

Evaluate the integral \[ \int \frac{dx}{\sqrt{5 + 4x - x^2}} = \]

If \( \cos 2\theta = \sin \alpha \), then \( \theta = \)