List of top Mathematics Questions asked in KEAM

\(\int\frac{e^{\frac{1}{\sqrt t}}}{t\sqrt t}dt=\)
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
If x and y are both non-negative and if x+y=π, then the maximum value of 5sinxsiny is equal to
If x+13y=40 is normal to the curve y=5x2+ax+β at the point (1, 3), then the value of αß is equal to
The equation of tangent to the circle (x-5)2+y2 = 25 at (2, 4) is
\(\frac{d}{dx}(\frac{1}{x}\frac{d^2}{dx^2}(\frac{1}{x^3}))=\)
The function f(x)=x5e-x is increasing in the interval
Let \(f(x) =   \begin{cases}     \tan x,       & if\ 0\leq x\leq \frac{\pi}{4} \\      ax+b,       & if\ \frac{\pi}{4}\lt x\lt \frac{\pi}{2}   \end{cases}\), If f(x) is differentiable at \(x=\frac{\pi}{4}\), then the values of a and b are respectively
If \(xsiny + ysinx = \pi\), then \(\frac{dy}{dx}\) at \(\)\((\frac{\pi}{2},\frac{\pi}{2})\)is equal to
If \(x=\sqrt{10^{\cos^{-1}\theta}}\ and\ y=\sqrt{10^{\sin^{-1}\theta}}\), then \(\frac{dy}{dx}\) is equal to
The coefficient of variation (C.V.) and the mean of a distribution are respectively 75 and 44. Then the standard deviation of the distribution is
\(\displaystyle\lim_{t\rightarrow0}(\frac{(2t-3)(1-2)}{t}-\frac{3(t+2)}{t})\ is\ equal\ to\)
If \(f(x) =   \begin{cases}     x^2\sin(\frac{\pi}{6}x)       & for\ x\leq-3 \\      x\cos(\frac{\pi}{3}x)       & for\ x\gt-3   \end{cases}\), then the value of \(\displaystyle\lim_{x\rightarrow3}f(x)\ is\ equal\ to\)
\(\displaystyle\lim_{x\rightarrow0}\frac{\log(1+x)+1-e^x}{4x^2-9x} \ is\ equal\ to\)
In a box there are four marbles and each of them is marked with distinct number from the set {1, 2, 5, 10}. If one marble is randomly selected four times with replacement and the number on it noted, then the probability that the sum of numbers equals 18 is
If A and B are two events such that P(A)=0.5, P(B)=0.4 and P(A\(\cap\)B)=0.2, then P(A|(A\(\cup\)B)) is equal to
The distance from the point (2, 2, 2) to the plane 2x-y+3z = 5 is equal to
A fair coin is tossed twice. Given that the first toss resulted in head, then the probability that the second toss also, would result in head is
There are 37 men and 33 women at a party. If a prize is given to one person chosen at random, then the probability that the prize goes to a woman is
The angle between the planes x=√3 and z = √2 is equal to
Let L1 be the line joining (0, 0, 0) and (1, 2, 3) and L2 be the line joining (2, 3, 4) and (3, 4, 5). The point of intersection of L1 and L2 is
The equation of the plane through the point (1, 5, 3) and having a normal vector \(\hat n=2\hat i-2\hat j-\hat k\) is
The equation of the plane passing through the point (-1,-2,-3) and perpendicular to the x-axis is
The equation of the line through the point (1, 1, 1) and parallel to the line joining the points (-2, 2, 0) and (-1, 1, 1) is
If \(\theta\) is angle between the lines \(\frac{x}{1}=\frac{y+1}{2}=\frac{z-1}{3}\) and \(\frac{x+1}{3}=\frac{y}{2}=\frac{z}{1}\), then \(\cos\theta=\)