List of top Mathematics Questions

The probability distribution of a random variable X is given by
\begin{tabular}{|c|c|c|c|} \hline X & 0 & 1 & 2 \\ \hline P(X) & $1 - 7a^2$ & $\frac{1}{2}a + \frac{1}{4}$ & $a^2$ \\ \hline \end{tabular}
If a > 0, then P(0 $<$ x $\le$ 2) is equal to
The solution of the differential equation $\log_e(\frac{dy}{dx}) = 3x + 4y$ is given by
Which of the following are linear first order differential equations?
(A) $\frac{dy}{dx} + P(x)y = Q(x)$
(B) $\frac{dx}{dy} + P(y)x = Q(y)$
(C) $(x - y)\frac{dy}{dx} = x + 2y$
(D) $(1 + x^2)\frac{dy}{dx} + 2xy = 2$
Choose the correct answer from the options given below:
The area (in sq. units) of the region bounded by the parabola y2 = 4x and the line x = 1 is
The integral I = $\int \frac{e^{5\log_e x} - e^{4\log_e x}}{e^{3\log_e x} - e^{2\log_e x}} dx$ is equal to
$\int_{1}^{4} |x - 2| dx$ is equal to
If the maximum value of the function f(x) = $\frac{\log_e x}{x}$, x > 0 occurs at x = a, then a2f''(a) is equal to
The interval, on which the function f(x) = x2e-x is increasing, is equal to
If y = 3e2x + 2e3x, then $\frac{d^2y}{dx^2} + 6y$ is equal to
If A = $\begin{bmatrix} 0 & 0 & \sqrt{3} \\ 0 & \sqrt{3} & 0 \\ \sqrt{3} & 0 & 0 \end{bmatrix}$, then |adj A| is equal to
If A is a square matrix and I is the identity matrix of same order such that A2 = I, then (A - I)3 + (A + I)3 - 3A is equal to
If A = $\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$ and B = $\begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix}$ then the matrix AB is equal to
Let A = [aij]n x n be a matrix. Then Match List-I with List-II
List-I
(A) AT = A
(B) AT = -A
(C) |A| = 0
(D) |A| $\neq$ 0
List-II
(I) A is a singular matrix
(II) A is a non-singular matrix
(III) A is a skew symmetric matrix
(IV) A is a symmetric matrix
Choose the correct answer from the options given below:
The general solution of the differential equation \( x\,dy + \left(y - e^x\right) dx = 0 \) is:
The general solution of the differential equation \( x\,dy + \left(y - e^x\right) dx = 0 \) is:
The vertices of a closed convex polygon representing the feasible region of the LPP with objective function \(z = 5x + 3y\) are \((0,0)\), \((3,1)\), \((1,3)\) and \((0,2)\). The maximum value of \(z\) is:
Corner points of a feasible bounded region are \((0, 10)\), \((4, 2)\), \((3, 7)\) and \((10, 6)\). Maximum value 50 of objective function \(z = ax + by\) occurs at two points \((0, 10)\) and \((10, 6)\). The value of \(a\) and \(b\) are:
If A and B are square matrices of order 3 such that \(|A| = -1\), \(|B| = 3\) then \(|3AB|\) is:
If \(B\) is a non-singular \(4 \times 4\) matrix and \(A\) is its adjoint such that \(|A| = 125\), then \(|B|\) is:
The derivative of \(\sin\left(\tan^{-1} e^{2x}\right)\) with respect to \(x\) is:
The minimum value of \(\left(x^2 + \frac{250}{x}\right)\) is:
An amount becomes 5 times its original value in 25 years. What is the rate of simple interest per annum?
PQ and RS are common tangents to two circles intersecting at A and B. A and B, when produced on both sides, meet the tangents PQ and RS at X and Y, respectively. If \(AB = 3\) cm and \(XY = 5\) cm, then PQ is:
In a circle of radius 13 cm, a chord is at a distance of 12 cm from the center of the circle. Find the length (in cm) of the chord.
The absolute maximum value of $y = x^{3} - 3x + 2$, for $0 \leq x \leq 2$, is: