List of top Questions asked in KEAM

Two cells each of $2V$ and internal resistance $0.1\,\Omega$ are connected in parallel combination. This combination is equivalent to a single cell with emf and internal resistance of

If a spherical conductor of $10\,cm$ radius contains $5 \times 10^6$ electrons, then the electric field on its surface (in $NC^{-1}$) is

In the equation $A = \dfrac{B}{CD^2}$, if $B, C$ and $D$ have the dimensions of inductive reactance, capacitive reactance and angular frequency respectively, then the dimensions of $A$ are:

The solution of the differential equation $(x + 2y)dx + (2x - y)dy = 0$ is

$\displaystyle \int \frac{\sin(\cot^{-1}x)}{1+x^2} \, dx$ is equal to:

The value of $\displaystyle \int_{0}^{1} x(1-x)^4 \, dx$ is equal to:

$\displaystyle \int \left(\frac{1}{(1+x)^2} - \frac{2}{(1+x)^3}\right)e^x \, dx$ is equal to:

$\displaystyle \int \sqrt{1 + \sin\left(\frac{x}{8}\right)} \, dx =$

Let $f(x) = 1 + x\log\left(x + \sqrt{x^2+1}\right) - \sqrt{x^2+1}, \; x \geq 0$. Then:

Let $X = \{a,b,c,d,e,f\}$ and $Y = \{7,8,9,10,11\}$ be two sets. Which one of the following is true?

If $y = e^{-x^2}$, then $\dfrac{d^2y}{dx^2} + 2x\dfrac{dy}{dx}$ is equal to:

Let $y = \dfrac{3x^3 - 2x^2 + x}{|x|}, \; x \ne 0$. Then $\dfrac{dy}{dx}$ at $x=-2$ is equal to:

Let $f$ and $g$ be differentiable real valued functions on $[0,\infty)$. If $f$ is increasing, $g$ is decreasing and $h(x)=f(g(x))$, then $h(2026)-h(2025)$ is

Let $f(x)$ and $g(x)$ be two differentiable functions such that $f'(x)=g(x)$ and $g'(x)=-f(x)$. Let $h(x)=(f(x))^2+(g(x))^2$ and $h(3)=100$. Then $h(100)$ is equal to

The value of $\lim_{x \to 0} \dfrac{\sqrt{1 - \cos(x^2)}}{1 - \cos x}$ is equal to:

If $(3 + 5x)e^{\frac{y}{x}} = x$, then $\dfrac{dy}{dx}$ is equal to:

Which one of the following is not true?

The domain of the function $f(x) = \dfrac{\log_2 (x - 5)}{x^2 + 3x - 4}$ is:

The perpendicular drawn from the origin to the straight line $\sqrt{3}x + y - 24 = 0$ makes an angle $\alpha$ with the positive direction of x-axis. Then $\alpha$ is equal to:

The variance for the data: $65, 70, 75$ is

If the function $f(x)=\begin{cases}\dfrac{2x^2+3x-5}{x-1}, & x \ne 1 \\ k, & x=1\end{cases}$ is continuous at $x=1$, then the value of $k$ is:

Let $A, B, C$ be all the three possible mutually exclusive events of a random experiment. Which one of the following is not permissible in terms of their probabilities?

The value of $\lim_{x \to 1} \dfrac{x - 1}{3\sqrt{x} - 1}$ is equal to:

The value of $\lim_{x \to 0} \dfrac{\sin^2 x}{1 - \cos x}$ is equal to:

The shortest distance between the lines $\vec{r} = -\hat{i} + t\hat{k}, \; t \in \mathbb{R}$ and $\vec{r} = -\hat{j} + s\hat{i}, \; s \in \mathbb{R}$ is: