List of top Mathematics Questions asked in KEAM

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
The three vertices of a triangle are (0, 0), (3, 1) and (1, 3). If this triangle is inscribed in a circle, then the equation of the circle 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
Let \(t_n=\frac{1}{n}\displaystyle\sum^{n}_{k=1}\left(\frac{k}{n} \right)^2\)for n=1,2,3…. Then t10 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
Let (3+x)10 = a0+a1(1+x)+a2(1+x)2+..... a10(1+x)10, where a1, a2, ... a10 are constants. Then the value of a0+a1+a2+.... a10 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 value of \(\displaystyle\int^{\frac{\pi}{16}}_{0}\cos6x\cos2xdx\) is equal to
The general solution of the differential equation \((x^2y^2+y)dx-(x-2x^3y)dy=0\) is
The value of \(\displaystyle\int^{10}_{-10}\frac{x^{10}\sin x}{\sqrt{1+x^{10}}}dx\) is equal to
\(\int\frac{dx}{x^2-x}=\)
The area bounded by the curve y = x(2-x) and the line y=x is
\(\int\sin^3xdx+\int\cos^2x\sin xdx=\)
The value of \(\int^{2}_{-1}(x-2)|x|)dx\) is equal to
The value of \(\displaystyle\int^{\frac{\pi}{2}}_{\frac{\pi}{6}}\frac{\cot x}{\sin x}dx \) 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
The feasible region for a L.P.P. is shown in the figure below. Let z = 50x+15y be the objective function, then the maximum value of z is
The feasible region for a L.P.P. is shown in the figure below
\(\int\frac{sin^{25}x}{cos^{27}x}dx\) is equal to
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
\(\int(\tan^2(2x)-\cot^2(2x))dx=\)