List of top Mathematics Questions asked in KEAM

The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\cos^2 x}{1 + 2^{-x}} \, dx$ is equal to:

The integral $\int \tan^5 x \sec^2 x \, dx$ is equal to:

Given the Linear Programming Problem:
Maximize $z = 11x + 7y$ subject to the constraints: $x \leq 3$ , $y \leq 2$ , $x, y \geq 0$ .
Then the optimal solution of the problem is:

The degree of the differential equation $(y^m)^2 + (\sin y')^4 + y = 0$ is:

The general solution of $\frac{dy}{dx} + y = 5$ is:

The differential equation $\frac{dy}{dx} + x = A$ (where A is constant) represents:

Find the area of the smaller segment cut-off from the circle $x^2 + y^2 = 25$ by $x = 3$ :

Find the area bounded by the curves $y = 2x$ and $y = x^2$ :

Evaluate $\int_{-\pi/2}^{\pi/2} \sin^9 x \cos^2 x \, dx$ :

Evaluate $\int_0^1 \log \left( \frac{1}{x - 1} \right) \, dx$ :

Evaluate $\int \frac{e^{6 \log x} - e^{5 \log x}}{e^{4 \log x} - e^{3 \log x}} \, dx$ :

Evaluate $\int \frac{dx}{x^2 (x^4 + 1)^{3/4}}$ :

If

\int \frac{dx}{\sqrt{16 - 9x^2}} = A \sin^{-1}(Bx) + C, { where } C { is an arbitrary constant, then } A + B =

Evaluate $\int x e^{x^2} \, dx$ :

Evaluate $\int x \cos x \, dx$ :

The integral $\int \frac{dx}{1 + e^x}$ is:

The limit $\lim_{x \to 10} \frac{x - 10}{\sqrt{x + 6} - 4}$ is equal to:

The maximum value of $y = 12 - |x - 12|$ in the range $-11 \leq x \leq 11$ is:

The function $f(x) = 2x^3 + 9x^2 + 12x - 1$ is decreasing in the interval:

If $y = \frac{x^2}{x - 1}$ , then $\frac{dy}{dx}$ at $x = -1$ is:

If $y = \tan^{-1} \left( \frac{\cos x - \sin x}{\cos x + \sin x} \right)$ , $\frac{-\pi}{2}<x<\frac{\pi}{2}$ , then $\frac{dy}{dx}$ is:

If $f(x) = \sin^{-1}(\cos x)$ , then $\frac{d^2 y}{dx^2}$ at $x = \frac{\pi}{4}$ is:

If $f(x) = \cos x - \sin x$ , and $x \in \left( \frac{\pi}{4}, \frac{\pi}{2} \right)$ , then $f' \left( \frac{\pi}{3} \right)$ is equal to:

Let $f(x) = x - \lfloor x \rfloor$ , where $\lfloor \cdot \rfloor$ denotes the greatest integer function and $x \in (-1, 2)$ . The number of points at which the function is not continuous is:

If $f(x) = \left\{ \begin{array}{ll} mx + 1, & \text{when } x \leq \frac{\pi}{2} \\ \sin x + n, & \text{when } x > \frac{\pi}{2} \end{array} \right.$ is continuous at $x = \frac{\pi}{2}$ , then the values of $m$ and $n$ are: