List of top Questions asked in KEAM

If \(f(x) = \begin{cases}     \cos x       & for\ x\geq0 \\       2x      &for\ x\lt0  \end{cases}\), then the value of \(\displaystyle\int^{\frac{\pi}{2}}_{-2}dx\) is equal to
The value of \(\displaystyle\int^{10}_{-10}\frac{x^{10}\sin x}{\sqrt{1+x^{10}}}dx\) is equal to
The value of \(\int^{2}_{-1}(x-2)|x|)dx\) is equal to
The area bounded by the curve y = x(2-x) and the line y=x is
The value of \(\displaystyle\int^{\frac{\pi}{2}}_{\frac{\pi}{6}}\frac{\cot x}{\sin x}dx \) is equal to
\(\int\frac{dx}{x^2-x}=\)
\(\int\sin^3xdx+\int\cos^2x\sin xdx=\)
\(\int(\tan^2(2x)-\cot^2(2x))dx=\)
\(\int\frac{1}{x^3}\sqrt{1-\frac{1}{x^2}}dx=\)
The feasible region for a L.P.P. is shown in the figure below. Let z = 50x+15y be the objective function, then the maximum value of z is
The feasible region for a L.P.P. is shown in the figure below
\(\int\frac{sin^{25}x}{cos^{27}x}dx\) is equal to
\(\int\frac{e^{\frac{1}{\sqrt t}}}{t\sqrt t}dt=\)
Let f(x)=cosx for \(0\leq x \leq\frac{\pi}{3}\). Then the value of c which satisfies the conclusion of the Mean Value Theorem for the function f on \([0,\frac{\pi}{3}]\) is equal to
If x+13y=40 is normal to the curve y=5x2+ax+β at the point (1, 3), then the value of αß is equal to
The function f(x)=x5e-x is increasing in the interval
The normal to the curve y=√x at the point (25, 5) intersects the y-axis at
If x and y are both non-negative and if x+y=π, then the maximum value of 5sinxsiny is equal to
The equation of tangent to the circle (x-5)2+y2 = 25 at (2, 4) is
Air is blown into a spherical balloon. If its diameter d is increasing at the rate of 3 cm/min, then the rate at which the volume of the balloon is increasing when d = 10 cm, is
\(\frac{d}{dx}(\frac{1}{x}\frac{d^2}{dx^2}(\frac{1}{x^3}))=\)
Let \(f(x) =   \begin{cases}     \tan x,       & if\ 0\leq x\leq \frac{\pi}{4} \\      ax+b,       & if\ \frac{\pi}{4}\lt x\lt \frac{\pi}{2}   \end{cases}\), If f(x) is differentiable at \(x=\frac{\pi}{4}\), then the values of a and b are respectively
If \(xsiny + ysinx = \pi\), then \(\frac{dy}{dx}\) at \(\)\((\frac{\pi}{2},\frac{\pi}{2})\)is equal to
If \(y=e^{3\log(2x+1)}\), then \(\frac{dy}{dx}=\)
If \(x=\sqrt{10^{\cos^{-1}\theta}}\ and\ y=\sqrt{10^{\sin^{-1}\theta}}\), then \(\frac{dy}{dx}\) is equal to
\(\displaystyle\lim_{x\rightarrow-2}\frac{3x^2+ax-2}{x^2-x-6}\) is a finite number, then the value of a is equal to