List of top Questions asked in KEAM- 2016

If $f\left(\frac{x + 1}{2x - 1}\right) = 2x,\ x \in \mathbb{N}$, then the value of $f(2)$ is equal to:

Let $f(x) = x^3$ and $g(x) = 3^x$. The values of $a$ such that $g(f(a)) = f(g(a))$ are:

If $A \setminus B = \{a, b\}$, $B \setminus A = \{c, d\}$ and $A \cap B = \{e, f\}$, then the set $B$ is equal to:

The domain of the function $f(x) = \begin{cases} \frac{x^2 - 9}{x - 3}, & \text{if } x \neq 3 \\ 6, & \text{if } x = 3 \end{cases}$ is:

The area bounded by the lines $y - 2x = 2$, $y = 4$ and the y-axis is equal to (in square units):

If $*$ is the operation defined by $a * b = a^b$ for $a, b \in \mathbb{N}$, then $(2 * 3) * 2$ is equal to:

The differential equation representing the family of curves $y^2 = a(ax + b)$ where $a$ and $b$ are arbitrary constants, is of:

The solution of the differential equation $\frac{x \frac{dy}{dx} - y}{\sqrt{x^2 - y^2}} = 10x^2$ is:

The general solution of the differential equation $(x + y + 3)\frac{dy}{dx} = 1$ is:

The general solution of the differential equation $x \, dy - y \, dx = y^2 \, dx$ is:

$\int_{0}^{\pi/2} \log\left( \frac{\cos x}{\sin x} \right)\, dx$ is equal to:

$\int \frac{1}{8 \sin^2 x + 1}\, dx$ is equal to:

The area of the region bounded by $y^2 = 16 - x^2, y = 0, x = 0$ in the first quadrant is (in square units):

The value of $\int_{-1}^{2} 4x^2 |x|\, dx$ is equal to:

The value of $\int_{2}^{4} (x-2)(x-3)(x-4)\, dx$ is equal to:

$\int \frac{1}{\sin x \cos x}\, dx$ is equal to:

$\int \frac{2x + \sin 2x}{1 + \cos 2x}\, dx$ is equal to:

$\int \left( \frac{x-a}{x} - \frac{x}{x+a} \right)\, dx$ is equal to:

$\int \frac{1}{7} \sin\left(\frac{x}{7} + 10\right)\, dx$ is equal to:

$\int (\sec x)^m (\tan^3 x + \tan x) dx$ is equal to:

$\int x^4 e^{x^5} \cos\left(e^{x^5}\right)\, dx$ is equal to:

The equation of the tangent to the curve $y = x^3 - 6x + 5$ at $(2, 1)$ is:

Let $f(x) = 2x^3 - 5x^2 - 4x + 3,\ \frac{1}{2} \leq x \leq 3$. The point at which the tangent to the curve is parallel to the x-axis is:

If $y = 8x^3 - 60x^2 + 144x + 27$ is a strictly decreasing function in the interval:

If $y = f(x)$ is continuous on $[0, 6]$, differentiable on $(0, 6)$, $f(0) = -2$ and $f(6) = 16$, then at some point between $x = 0$ and $x = 6$, $f'(x)$ must be equal to: