List of top Questions asked in KEAM

The integrating factor of the differential equation \(3xy'-y=1+\log x\), \(x>0\) is

The general solution of the differential equation \(xy'+y=x^{2}\), \(x>0\) is

The area of the region bounded by $y=|x|$, $y=0$, $x=3$ and $x=-3$ is (in square units)

The value of $\int_{-10}^{10}(0.0002x^{3}-0.3x+20)dx$ is equal to

$\int_{-3}^{3}|x+2|dx=$

The area enclosed by the curve $x=3\cos\theta$, $y=2\sin\theta$, $0\le\theta\le\pi$, is (in square units)

The order and degree of the differential equation $\frac{d^{2}y}{dx^{2}}+\sqrt{x^{2}+\left(\frac{dy}{dx}\right)^{3/2}}=0$ are respectively

$\int\sec^{2}(5x-1)dx=$

$\int e^{x}\sec x(1+\tan x)dx=$

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

$\int_{0}^{\frac{\pi}{2}}\frac{1}{1+\cot^{4}x}dx=$

$\int\frac{1}{x^{2}-25}dx=$

$\int 3x^{2}(x^{3}+1)^{10}dx=$

The local minimum value of the function $f(x)=x^{2}-x$, $x\in\mathbb{R}$, is

$\int\frac{2x+\sin 2x}{1+\cos 2x}dx=$

The equation of normal to the curve $y=\frac{2}{x^{2}}$ at the point on the curve where $x=1$, is

The function given by $f(x)=x^{3}e^{x}$ is increasing on the interval

The function $f$ given by $f(x)=(x^{2}-3)e^{x}$ is decreasing on the interval

The equation of the tangent to $y=-2x^{2}+3$ at $x=1$ is

If $y=2+\sqrt{u}$ and $u=x^{3}+1$, then $\frac{dy}{dx}=$

Let $f(x)=\sqrt{x}$, $4\le x\le16$. If the point $c\in(4,16)$ is such that the tangent line to the graph of $f$ at $x=c$ is parallel to the chord joining $(16,4)$ and $(4,2)$, then the value of $c$ is

If $y=(\cos x)^{2x}$, then $\frac{dy}{dx}$ is equal to

$\lim_{x\to0}\frac{x^{100}\sin 7x}{(\sin x)^{101}}$ is equal to

Given $F(x)=(f(g(x)))^{2}$, $g(1)=2$, $g'(1)=3$, $f(2)=4$ and $f'(2)=5$. Then the value of $F'(1)$ is equal to

If $x^{3}+2xy+\frac{1}{3}y^{3}=\frac{11}{3}$ then $\frac{dy}{dx}$ at $(2,-1)$ is