List of top Mathematics Questions asked in KEAM

The area of the region bounded by y = 5x, x-axis and x = 4 is (in square units)
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
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
\(\int\sin2x\ cosx\ dx=\)
\(\int\frac{1}{(1+cot^2x)sin^2x}dx=\)
The area of the region bounded by the curves y = x2 and y = √x is (in square units)
\(\int\frac{4x^9}{x^{10}-10}dx=\)
\(\int x^5e^{1-x^6}dx=\)
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
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
\(\int\frac{1}{e^{2x}-1}dx=\)
\(\int\frac{\cos(\tan x)}{\cos^2x}dx=\)
\(\int(5-4x)e^{-x}dx=\)
Let f(x) = x2 logx, x > 0. Then the minimum value of f is
If \(f(x) =   \begin{cases}  e^x, & \text{if}\ x\leq1 \\  mx+6, & \text{if}\ x\gt1 \end{cases}\) be differentiable at x=1. Then the value of m is
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
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
The slope of tangent line to the curve 4x2+2xy+y2=12 at the point (1, 2) is
\(\lim\limits_{t\rightarrow0}\frac{tan^2(\frac{\pi}{3}+t)-3}{t}\) is equal to
Let f(x)=√x+5 for 1≤x≤9. Then the value of c whose existence is guaranteed by the Mean Value Theorem is
If \(f(x) =   \begin{cases}  3x+2, & \text{if}\ x\lt-2 \\  x^2-3x-1, & \text{if}\ x\geq-2 \end{cases}\). Then \(\lim\limits_{x\rightarrow2^-}f(x)\) and \(\lim\limits_{x\rightarrow2^+}f(x)\) are respectively
\(\lim\limits_{t\rightarrow-3}\frac{x^2+16x+39}{2x^2+7x+3}\) is equal to