List of top Mathematics Questions asked in KEAM

The modulus of \((\frac{1+i}{1-i})^{75}-(\frac{1-i}{1+i})^{75}\)is
If \(|\bar{a}|=\sqrt{14},|\bar{b}|=\sqrt{10},|\bar{a}-\bar{b}|=\sqrt{24}\ and\ \theta\) is angle between \(\bar{a}\ and\ \bar{b}\), then \(\cos\theta=\)
The normal to the curve y=√x at the point (25, 5) intersects the y-axis at
Three fair dice are rolled simultaneously. Let a, b, c be the numbers on the top of the dice. Then the probability that min(a, b, c) =6 is
Air is blown into a spherical balloon. If its diameter d is increasing at the rate of 3 cm/min, then the rate at which the volume of the balloon is increasing when d = 10 cm, is
The 11th term of the geometric series \(\displaystyle\sum^{20}_{r=0}2\times(-2)^r\) is equal to
The number of arrangements containing all the seven letter of the word ALRIGHT that begins with LG is
The sum of the first 24 terms of the series 9+13+17+...... 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
A particular solution of the differential equation \(\frac{dy}{dx}=xy^2\) with y(0)=1 is
The general solution of the differential equation \((x^2y^2+y)dx-(x-2x^3y)dy=0\) is
The value of \(\displaystyle\int^{\frac{\pi}{16}}_{0}\cos6x\cos2xdx\) is equal to
The value of \(\displaystyle\int^{\frac{\pi}{2}}_{\frac{\pi}{6}}\frac{\cot x}{\sin x}dx \) is equal to
The area bounded by the curve y = x(2-x) and the line y=x is
\(\int\frac{dx}{x^2-x}=\)
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
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
\(\int\sin^3xdx+\int\cos^2x\sin xdx=\)
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
\(\int\frac{sin^{25}x}{cos^{27}x}dx\) is equal to
\(\int\frac{1}{x^3}\sqrt{1-\frac{1}{x^2}}dx=\)
\(\int\frac{e^{\frac{1}{\sqrt t}}}{t\sqrt t}dt=\)
\(\int(\tan^2(2x)-\cot^2(2x))dx=\)