List of top Mathematics Questions

The integral I = $\int e^x (\frac{x-1}{3x^2}) dx$ is equal to

The area (in sq. units) of the region bounded by the curve \( y = x^5 \), the x-axis and the ordinates x = -1 and x = 1 is equal to

Let AX = B be a system of three linear equations in three variables. Then the system has
(A) a unique solution if |A| = 0
(B) a unique solution if |A| $\neq$ 0
(C) no solutions if |A| = 0 and (adj A) B $\neq$ 0
(D) infinitely many solutions if |A| = 0 and (adj A)B = 0
Choose the correct answer from the options given below:

The function f(x) = tanx - x

If the function f(x) = $\begin{cases}\frac{k\cos x}{\pi - 2x} & ; x \neq \frac{\pi}{2} \\ 3 & ; x = \frac{\pi}{2} \end{cases}$ is continuous at x = $\frac{\pi}{2}$, then k is equal to

The rate of change of area of a circle with respect to its circumference when radius is 4cm, is

Let \( y=\sin(\cos(x^2)) \). Find \( \frac{dy}{dx} \) at \( x=\frac{\sqrt{\pi}}{2} \).

Let A = $\begin{bmatrix 1 & 2 & 1 \\ 1 & 3 & 2 \\ 2 & 4 & 1 \end{bmatrix}$ and Mij, Aij respectively denote the minor, co-factor of an element aij of matrix A, then which of the following are true?}
(A) M22 = -1
(B) A23 = 0
(C) A32 = 3
(D) M23 = 1
(E) M32 = -3
Choose the correct answer from the options given below:

for $|x| < 1$, sin(tan-1x) equal to

Let A = $\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$ and I = $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$. If AT + A = I, then

If A and B are skew-symmetric matrices, then which one of the following is NOT true?

If A and B are invertible matrices then which of the following statement is NOT correct?

Let A = [aij]2x3 and B = [bij]3x2, then |5AB| is equal to

The solution of the differential equation $\log_e(\frac{dy}{dx}) = 3x + 4y$ is given by

Consider the LPP: Minimize Z = x + 2y subject to 2x + y $\ge$ 3, x + 2y $\ge$ 6, x, y $\ge$ 0. The optimal feasible solution occurs at

The corner points of the feasible region associated with the LPP: Maximise Z = px + qy, p, q > 0 subject to 2x + y $\le$ 10, x + 3y $\le$ 15, x,y $\ge$ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). If optimum value occurs at both (3, 4) and (0, 5), then

Let f: R $\rightarrow$ R be defined as f(x) = 10x. Then (Where R is the set of real numbers)

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

Let A = \{1, 2, 3\}. Then, the number of relations containing (1, 2) and (1, 3), which are reflexive and symmetric but not transitive, is

The area (in sq. units) of the region bounded by the parabola y2 = 4x and the line x = 1 is