List of top Questions asked in KEAM

Of the given numbers,
(1) 25300
(2) 5.600
(3) 0.07200
the number of significant figures for

The value of $\int_{0}^{\frac{\pi}{2}}\frac{\cos^{11}x}{\cos^{11}x+\sin^{11}x}dx$ is equal to} \textit{Note: The original exam paper contained a typographical error ($c\hat{D}$ instead of $dx$). It has been corrected here to permit a valid solution.

The solution of the differential equation $(y+x^{2})dx=xdy, x>0$ is a curve which passes through the point (1,0). The equation of the curve is

Consider the Linear Programming Problem: Maximize $Z=x+2y$ Subject to $2x+3y\le12, x\ge0, y\ge0$. The optimal value is} \textit{Note: A stray '0.' from the original document has been removed for clarity.

The order and the degree of the differential equation $2\frac{dy}{dx}-3x=\left(2y-x\frac{dy}{dx}\right)^{-3}$ respectively, are

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

The value of $\int_{0}^{\pi}\frac{\sin x}{1+\sin x}dx$ is equal to} \textit{Note: The upper limit in the integral from the original paper contains a typo ($x$ instead of $\pi$). It has been corrected here to yield the valid options provided.

$\int\frac{2+3x}{2\sqrt{1+x}}dx$ is equal to} \textit{Note: The original exam paper contained a typographical error in the denominator ($1+c$ instead of $1+x$). It has been corrected here to match the given solutions.

$\int\frac{x\cos x-\sin x}{x^{2}}dx$ is equal to

$\int x(1+2\log x)dx$ is equal to

If $f(x)=2x^{3}-3x^{2}-\lambda x+1, x\in[0,3]$ attains a local minimum at $x=2$, then the value of $\lambda$ is equal to

$\int e^{-x}(1+(1-x)\log x)dx$ is equal to

Let $f(x)=x^{2}-10x+16$, $x\in\mathbb{R}.$ If $f^{\prime}(c)$ is equal to slope of the straight line joining the points (2,0) and (8,0), then the value of $c$ is

The function $f(x)=2x^{3}-15x^{2}+36x-24$ is strictly decreasing in the interval is

$\int\frac{\tan x+\cot x}{1+\tan^{2}x}dx$ is equal to

The distance $s$ in meters travelled by a particle in $t$ seconds is given by $s=e^{t}(4\cos 3t+5\sin 3t)$. Then the velocity of the particle at time $t$ is given by

If $f(x)=\frac{|x|}{x^{2}}$ then $f^{\prime}(2)$ is equal to

If $f(x)=\tan^{-1}\left(\frac{3\cos x-5\sin x}{5\cos x+3\sin x}\right)$ , then the value $f^{\prime}(1)$ is

If $f^{\prime}(5)=\frac{3}{5}$ then the value of $\lim_{h\rightarrow 0}\frac{f(5+10h)-f(5)}{h}$ is equal to

If $f(x)=\frac{1}{2x-4}$ then the point(s) of discontinuity of $f(f(x))$ is/are

If $f(x)=(2x+3)e^{5x}$, then $f^{\prime\prime}(1)-10f^{\prime}(1)$ is equal to

Let $f(x)=\begin{cases}ax+3 & x<1\\ \frac{4x}{a} & x\ge 1\end{cases}$. If $\lim_{x\rightarrow 1}f(x)$ exists, then the possible values of $a$ are

The domain of the function $f(x)=\sqrt{\frac{x+1}{2-x}}$ is

The value of $\lim_{x\rightarrow 2^{+}}\frac{[x]-2}{x-2}$ is

The value of $\lim_{x\rightarrow 0}\frac{\sqrt{1+3x}-\sqrt{1-3x}}{x}$ is