List of top Mathematics Questions asked in KEAM

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
The equation of the circle touching the x-axis at (5, 0) and the line y = 10 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
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
\(\int\frac{dx}{x^2-x}=\)
\(\int\sin^3xdx+\int\cos^2x\sin xdx=\)
\(\int(\tan^2(2x)-\cot^2(2x))dx=\)
\(\int\frac{1}{x^3}\sqrt{1-\frac{1}{x^2}}dx=\)
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