List of top Mathematics Questions asked in KEAM

For any two positive rational numbers m and n, a binary operation * is defined by \(m*n=\frac{m+n}{3}\), then \(\frac{7}{2}*\frac{5}{2}\) is equal to
Let f(x) = [x], x ∈ R, where [x] denotes the greatest integer ≤ x. Then the images of the elements -4.6 and 2.7 are respectively
Let f(x) = x2 and \(g(x) = \sqrt{9+x}\). Then the value of \((f^\circ g-g^\circ f)(4)\) is equal to
The constraints of a linear programming problem are x+2y≤10 and 6x+3y≤18. Which of the following points lie in the feasible region?
The general solution of the differential equation 4xy+12x+(2x2+3)y' = 0 is
The integrating factor of the differential equation xy'+2y-7x3=0 is
The general solution of the differential equation y-xy' = x2 + y2 is
The area of the region bounded by y = 5x, x-axis and x = 4 is (in square units)
The value of \(\displaystyle\int_{\frac{\pi}{8}}^{\frac{3\pi}{8}}\frac{sin^4x}{sin^4x+cos^4x}dx\) is equal to
The value of \(\displaystyle\int_{0}^{2}\frac{x^2}{(x^3+1)^2}dx\) is equal to
The area of the region bounded by the curves y = x2 and y = √x is (in square units)
The value of \(\displaystyle\int_{-5}^{5}(4-|x|dx)dx\) is equal to
The value of \(\displaystyle\int_{0}^{\sqrt3}\frac{6}{9+x^2}dx\) is equal to
\(\int\frac{4x^9}{x^{10}-10}dx=\)
\(\int\frac{1}{(1+cot^2x)sin^2x}dx=\)
\(\int\sin2x\ cosx\ dx=\)
\(\int\frac{1}{e^{2x}-1}dx=\)
\(\int\frac{\cos(\tan x)}{\cos^2x}dx=\)
\(\int(5-4x)e^{-x}dx=\)
\(\int x^5e^{1-x^6}dx=\)
A cube is expanding in such a way that its edge is increasing at a rate of 2 inches per second. If its edge is 5 inches long, then the rate of change of its volume is
Let f(x) = x2 logx, x > 0. Then the minimum value of f is
The derivative of a function f is given by \(f'(x)=\frac{x-5}{\sqrt{x^2+4}}\). Then the interval in which f is increasing, is
Let f(x)=√x+5 for 1≤x≤9. Then the value of c whose existence is guaranteed by the Mean Value Theorem is
The slope of tangent line to the curve 4x2+2xy+y2=12 at the point (1, 2) is