List of top Mathematics Questions asked in MHT CET

Evaluate \( i^2 + i^3 + \dots + i^{4000} \):
The solution of the differential equation \( x \cos y \, dy = (x e^x \log x + e^x) \, dx \) is:
If \( X \) is a random variable with the probability mass function (p.m.f.) as follows: \[ P(X = x) = \begin{cases} \frac{5}{16}, & x = 0, \\ \frac{kx}{48}, & x = 1, \\ \frac{1}{4}, & x = 2, \\ \frac{1}{4}, & x = 3, \end{cases} \] then find \( E(X) \):

Given, the function \( f(x) = \frac{a^x + a^{-x}}{2} \) (\( a > 2 \)), then \( f(x+y) + f(x-y) \) is equal to

If \( f(x) = 3x + 6 \), \( g(x) = 4x + k \), and \( f \circ g(x) = g \circ f(x) \), then find \( k \):
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:
The inverse of the matrix \[ \begin{bmatrix} 1 & 0 & 0 \\ 3 & 3 & 3 \\ 5 & 2 & -1 \end{bmatrix} \] is:
If \( p \land q \) is False and \( p \rightarrow q \) is False, then the truth values of \( p \) and \( q \) are:
Evaluate \( \int_{0}^{\pi/4} \frac{\cos^2 x}{\cos^2 x + 4 \sin^2 x} \, dx \):

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

Evaluate \( \sin \left( \tan^{-1}\frac{4}{5} + \tan^{-1}\frac{4}{3} + \tan^{-1}\frac{1}{9} - \tan^{-1}\frac{1}{7} \right) \):
The solution of the differential equation \( \sqrt{1 - y^2} \, dx + x \, dy - \sin^{-1} y \, dy = 0 \) is:
If \( f(x) \) is differentiable at \( x = 1 \) and \[ \lim_{h \to 0} \frac{1}{h} f(1 + h) = 5, \] then \( f'(1) \) is equal to:
The Boolean expression \( (\sim(p \land q)) \lor q \) is equivalent to:
If \( \sqrt{\frac{y}{x}} + 4\sqrt{\frac{x}{y}} = 4 \), then \( \frac{dy}{dx} \):

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

The integral \( \int e^x \frac{2 + \sin 2x}{1 + \cos 2x} \, dx \) is equal to

Let \( F(\alpha) = \begin{bmatrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \end{bmatrix} \), where \( \alpha \in \mathbb{R} \). Then \( [F(\alpha)]^{-1} \) is equal to:

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

The range of  the function  \( f(x) = \sin^{-1}(x - \sqrt{x}) \) is equal to?

If \( x \neq 0 \), then \[ \frac{\sin(\pi + x)\cos\left(\frac{\pi}{2} + x\right)\tan\left(\frac{3\pi}{2} - x\right)\cot(2\pi - x)}{\sin(2\pi - x)\cos(2\pi + x)\csc(-x)\sin\left(\frac{3\pi}{2} + x\right)} = \]
The number of ways of distributing \( 500 \) dissimilar boxes equally among \( 50 \) persons is

Define \( f(x) = \begin{cases} x^2 + bx + c, & x< 1 \\ x, & x \geq 1 \end{cases} \). If f(x) is differentiable at x=1, then b−c is equal to

The value of \( \int \frac{x \sin^{-1} x}{\sqrt{1 - x^2}} dx \) is equal to: