List of top Questions asked in MHT CET

The general solution of
$$ \left(x\frac{dy}{dx} - y\right)\sin\frac{y}{x} = x^3 e^x $$ is:

Marks of 5 students of a group are $ 8, 12, 13, 15, 22 $. Find the variance.

If $ X $ is a random variable such that $ P(X = -2) = P(X = -1) = P(X = 2) = P(X = 1) = \frac{1}{6} $, and $ P(X = 0) = \frac{1}{3} $, then the mean of $ X $ is

A committee of 11 members is to be formed out of 8 males and 5 females. If $ m $ is the number of ways the committee is formed with at least 6 males and $ n $ is the number of ways with at least 3 females, then:

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

The point on the line $ 4x - y - 2 = 0 $ which is equidistant from the points $ (-5, 6) $ and $ (3, 2) $ is

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

The value of the integral $ \int_0^1 \frac{\sqrt{1 - x}}{\sqrt{1 + x}} \, dx $ is:

If $ p \land q $ is False and $ p \rightarrow q $ is False, then the truth values of $ p $ and $ q $ are:

The value of $ \sqrt{3} \csc 20^\circ - \sec 20^\circ $ is:

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

If $ y = \sec(\tan^{-1} x) $, find $ \frac{dy}{dx} $, given that $ x = 1 $:

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 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:

If $ y = (\sin x)^y $, then $ \frac{dy}{dx} $ is:

Find the value of $ (a + b) \cdot p + (b + c) \cdot q + (c + a) \cdot r $:

The number of all four-digit numbers which begin with 4 and end with either zero or five 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 $|k|$:

If $ x \neq 0 $, then \[ \frac{\sin(\pi + x)\cos\left(\frac{\pi}{2} + x\right)\tan\left(\frac{3\pi}{2} - x\right)\cot(2\pi - x)}{\sin(2\pi - x)\cos(2\pi + x)\csc(-x)\sin\left(\frac{3\pi}{2} + x\right)} = \]

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: