List of top Mathematics Questions asked in KEAM

A relation R on (0, 1, 2) is given by R = {(0,0), (1, 1), (0, 1), (2, 2), (1, 2)). Then the relation R is
Let \(f:[-4,2] \rightarrow \R\) be given by \(f(x) = \sqrt{16-x^2}\). Then the range of the function f is
The function \(f\ \R\rightarrow\R\) given by f(x)=7-3x is
Let A and B be subsets of the universal set U. If n(A) = 24 , n (A∩B)=8 and n(U) = 63, then n( A'∪B') 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 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 general solution of the differential equation y-xy' = x2 + y2 is
The integrating factor of the differential equation xy'+2y-7x3=0 is
The value of \(\displaystyle\int_{0}^{\sqrt3}\frac{6}{9+x^2}dx\) is equal to
\(\int\frac{4x^9}{x^{10}-10}dx=\)
\(\int\frac{1}{(1+cot^2x)sin^2x}dx=\)
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 \(\displaystyle\int_{0}^{2}\frac{x^2}{(x^3+1)^2}dx\) is equal to
\(\int\sin2x\ cosx\ dx=\)
\(\int\frac{1}{e^{2x}-1}dx=\)
\(\int\frac{\cos(\tan x)}{\cos^2x}dx=\)
\(\int(5-4x)e^{-x}dx=\)
\(\int x^5e^{1-x^6}dx=\)
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
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
If the tangent line to the graph of a function f at the point x=3 has x-intercept \(\frac{5}{2}\) and y-intercept-10, then f'(3) is equal to
If h(x)=4x3-5x+7 is the derivative of f(x), then \(\lim\limits_{t\rightarrow0}\frac{f(1+t)-f(1)}{t}\) is equal to