List of top Questions asked in KEAM

Let a=2-3i be a root of the equation z2-4z+k=0 , where k is a real number. If β is the other root, then the value of α2 +β2 is
If \(\frac{z}{i}=11-13i\), then \(z+\bar z\) is equal to
Let z1, z2 and z3 be three distinct points in the complex plane such that the segment joining z1 and z2 is perpendicular to the segment joining z1 and z2. If |z1-z2|=5 and|z1-z3|=12 then|z2-z3| is equal to
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
The function \(f\ \R\rightarrow\R\) given by f(x)=7-3x is
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