List of top Mathematics Questions

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:
The statement \( [(p \rightarrow q) \wedge \sim q] \rightarrow r \) is a tautology when \( r \) is equivalent to:
If the statement \( p \leftrightarrow (q \rightarrow p) \) is false, then the true statement is:
Find the expected value and variance of \( X \) for the following p.m.f: \[ \begin{array}{|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \\ \hline P(X) & 0.2 & 0.3 & 0.1 & 0.15 & 0.25 \\ \hline \end{array} \]
The solution of the differential equation \( x \cos y \, dy = (x e^x \log x + e^x) \, dx \) is:
Integrate the function \( \int e^x \left( \frac{1 + \sin x}{1 + \cos x} \right) dx \):
The variance of the first 50 even natural numbers is:
The variance of the following probability distribution is:

\[ \begin{array}{|c|c|} \hline x & P(X) \\ \hline 0 & \frac{9}{16} \\ 1 & \frac{3}{8} \\ 2 & \frac{1}{16} \\ \hline \end{array} \]
The negative of \( (p \land (\sim q)) \lor (\sim p) \) is equivalent to:
The converse of \( ((\sim p) \land q) \Rightarrow r \) is:
If \( A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{bmatrix} \), then \( A^{-1} \) is:
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 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:
Find the area of the region bounded by the parabola $$ y^2 = 4ax \text{ and its latus rectum.} $$ 
The general solution of
$$ \left(x\frac{dy}{dx} - y\right)\sin\frac{y}{x} = x^3 e^x $$ is: 
Integrate the following function w.r.t. $x$: $\int \frac{e^{3x}}{e^{3x} + 1} \, dx$
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:
If \[ A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix} \] and \[ A^{-1} = \frac{1}{2} \begin{bmatrix} 1 & -1 & 1 \\ -8 & 6 & 2c \\ 5 & -3 & 1 \end{bmatrix}, \] then the values of \( a \) and \( c \) are respectively:
\( \sin^{-1}[\sin(-600^\circ)] + \cot^{-1}(-\sqrt{3}) = \)
If \( \sin^{-1} x + \cos^{-1} y = \frac{3\pi}{10} \), then the value of \( \cos^{-1} x + \sin^{-1} y \) is:
If \( y = (\sin x)^y \), then \( \frac{dy}{dx} \) is:
If \( f(x) = 2x^3 - 15x^2 - 144x - 7 \), then \( f(x) \) is strictly decreasing in:
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: