List of top Questions asked in KEAM

The SI unit of surface tension is ________.

The dimensions of $\frac{mB}{kT}$ where $m$ is magnetic moment, $B$ is magnetic flux density, $k$ is Boltzmann constant and $T$ is temperature are ________.

Minimize $z=x+y$ subject to $2x+3y \ge 6, x \ge 0, y \ge 0$. The solution is ________.

The elimination of arbitrary constants $c_{1}, c_{2}, c_{3}, c_{4}$ from $y=(c_{1}+c_{2})\sin(2x+c_{3}) + c_{4}e^{5x}$ gives a differential equation of order ________.

The integrating factor of the differential equation $\frac{dy}{dx}-2y=2x-3$ is ________.

$\int_{-\pi/2}^{\pi/2}(x^{5}+x^{3}+x)\cos x dx = $ ________.

If $[x]$ is the greatest integer less than or equal to x, then $\int_{-3}^{3}[x]dx=$ ________.

$\int_{4}^{5}\frac{1}{x(1+x)}dx=$ ________.

$\int e^{x}[\frac{1}{1+x}-\frac{1}{(1+x)^{2}}]dx=$ ________.

$\int(\sin^{-1}\sqrt{x}+\cos^{-1}\sqrt{x})dx=$ ________.

$\int\frac{\cos \theta}{2-\sin^{2}\theta}d \theta=$ ________.

$\int\frac{\log(1+x)}{(1+x)}dx=$ ________.

$\int\frac{\sin 2x}{\sin x}dx=$ ________.

The maximum value of the function $f(x)=x\sqrt{4x-x^{2}}$ is ________.

The distance travelled by a moving particle is given by $s=t^{2}-6t+10$. The particle is at rest when $t=$ ________.

If $g(x)=x^{2}-x, x\in\mathbb{R},$ then $g(x)$ is increasing in ________.

The minimum of $f(x)=|x+2|$, $x\in\mathbb{R}$ occurs at ________.

If $y=(\tan x)^{x}$, then $\frac{1}{y}\frac{dy}{dx}=$ ________.

If $e^{y}+x^{2}y+xy^{2}=e^{1}$, then $\frac{dy}{dx}$ at (0,1) is equal to ________.

The function $f(x)=|x^{2}-3x+2|,x\in\mathbb{R}$ is not differentiable at ________.

Let \([a]\) denote the greatest integer less than or equal to \(a\). Then \[ \lim_{x\to 0^{+}} x\left( \left[\frac{1}{x}\right] + \left[\frac{2}{x}\right] \right) \] is equal to ________.

$\lim_{x\rightarrow0}\frac{x \cos^{2}x}{\sin x}$ is equal to ________.

$\lim_{x\rightarrow2}\frac{(x^{3}-8)\sin(x-2)}{x^{2}-4x+4}$ is equal to ________.

$\lim_{x\rightarrow0}\frac{\sin(\pi \sin^{2}x)}{x^{2}} = $ ________.

Four unbiased coins are tossed simultaneously. Probability of getting at most two heads is ________.