List of top Mathematics Questions

Match List-I with List-II

List-I (Definite integral)List-II (Value)
(A) \( \int_{0}^{1} \frac{2x}{1+x^2}\, dx \)(I) 2
(B) \( \int_{-1}^{1} \sin^3x \cos^4x\, dx \)(II) \(\log_e\!\left(\tfrac{3}{2}\right)\)
(C) \( \int_{0}^{\pi} \sin x\, dx \)(III) \(\log_e 2\)
(D) \( \int_{2}^{3} \frac{2}{x^2 - 1}\, dx \)(IV) 0


Choose the correct answer from the options given below:

$\int_{\pi/6}^{\pi/3} \frac{\tan x}{\tan x + \cot x} dx$ is equal to
The rate of change of area of a circle with respect to its circumference when radius is 4cm, is
The function f(x) = tanx - x

Match List-I with List-II

List-IList-II
(A) The minimum value of \( f(x) = (2x - 1)^2 + 3 \)(I) 4
(B) The maximum value of \( f(x) = -|x + 1| + 4 \)(II) 10
(C) The minimum value of \( f(x) = \sin(2x) + 6 \)(III) 3
(D) The maximum value of \( f(x) = -(x - 1)^2 + 10 \)(IV) 5


Choose the correct answer from the options given below:

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

Match List-I with List-II

List-IList-II
(A) \( f(x) = |x| \)(I) Not differentiable at \( x = -2 \) only
(B) \( f(x) = |x + 2| \)(II) Not differentiable at \( x = 0 \) only
(C) \( f(x) = |x^2 - 4| \)(III) Not differentiable at \( x = 2 \) only
(D) \( f(x) = |x - 2| \)(IV) Not differentiable at \( x = 2, -2 \) only


Choose the correct answer from the options given below:

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
Let A = [aij]2x3 and B = [bij]3x2, then |5AB| is equal to
If A and B are invertible matrices then which of the following statement is NOT correct?
If A and B are skew-symmetric matrices, then which one of the following is NOT true?
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
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 = \{1, 2, 3\}. Then, the number of relations containing (1, 2) and (1, 3), which are reflexive and symmetric but not transitive, is
Let f: R $\rightarrow$ R be defined as f(x) = 10x. Then (Where R is the set of real numbers)
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

The probability distribution of a random variable X is given by

X012
P(X)\(1 - 7a^2\)\(\tfrac{1}{2}a + \tfrac{1}{4}\)\(a^2\)


If \(a > 0\), then \(P(0 < X \leq 2)\) 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