List of top Questions asked in KEAM

If \(z=\frac{(3+i)(7-i)^2}{3-i}\), then the value of |z| 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
The end points of the major axis of an ellipse are (2, 4) and (2,-8). If the distance between foci of this ellipse is 4, then the equation of the ellipse is
If the solution set of the inequality \(|a+3x|\leq6\ is\ [\frac{-8}{3},\frac{4}{3}]\), then the value of a is
If 11Pr=7920 and 11Cr = 330, then the value of r is equal to
In a reaction 3A → Products, the concentration of A decreases from 0.4molL-1 to 0.1molL-1 in 20 minutes at 300K. The rate of decrease in [A] during this interval (in molL-1min-1) at 300K is
Let L1 be the line joining (0, 0, 0) and (1, 2, 3) and L2 be the line joining (2, 3, 4) and (3, 4, 5). The point of intersection of L1 and L2 is
Which of the following aryl chlorides on warming with water forms the corresponding phenol?
Given below are the velocity-time graph of five particles, A, B, C, D and E. The correct graph from the following v-t plot in which the velocity if the particle is a function of t2 is
A tuning fork produces 4 beats per second with both 26.0 cm and 25.2 cm of stretched sonometer wire. Frequency of the fork is
If n(A∪B)=97, n(A∩B) = 23 and n(A-B)=39, then n(B) is equal to
If \(f(x) =   \begin{cases}     x^2\sin(\frac{\pi}{6}x)       & for\ x\leq-3 \\      x\cos(\frac{\pi}{3}x)       & for\ x\gt-3   \end{cases}\), then the value of \(\displaystyle\lim_{x\rightarrow3}f(x)\ is\ equal\ to\)
Consider the linear programming problem:
Maximize   z=10x+5y
subject to the constraints
2x+3y≤120
2x + y ≤ 60
x,y≥0.
Then the coordinates of the corner points of the feasible region are
The integrating factor of the differential equation 4xdy-e-2y dy + dx = 0 is
The general solution of the differential equation \((x^2y^2+y)dx-(x-2x^3y)dy=0\) is
A particular solution of the differential equation \(\frac{dy}{dx}=xy^2\) with y(0)=1 is
The value of \(\displaystyle\int^{\frac{\pi}{16}}_{0}\cos6x\cos2xdx\) is equal to
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
\(\int\frac{dx}{x^2-x}=\)
\(\int\sin^3xdx+\int\cos^2x\sin xdx=\)
\(\int(\tan^2(2x)-\cot^2(2x))dx=\)