List of top Mathematics Questions asked in KEAM

\(\int\frac{1}{x^3}\sqrt{1-\frac{1}{x^2}}dx=\)
\(\frac{d}{dx}(\frac{1}{x}\frac{d^2}{dx^2}(\frac{1}{x^3}))=\)
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 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
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
\(\displaystyle\lim_{t\rightarrow0}(\frac{(2t-3)(1-2)}{t}-\frac{3(t+2)}{t})\ is\ equal\ to\)
\(\displaystyle\lim_{x\rightarrow0}\frac{\log(1+x)+1-e^x}{4x^2-9x} \ is\ equal\ to\)
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 \(f(x) =   \begin{cases}     x^2\sin(\frac{\pi}{6}x)       & for\ x\leq-3 \\      x\cos(\frac{\pi}{3}x)       & for\ x\gt-3   \end{cases}\), then the value of \(\displaystyle\lim_{x\rightarrow3}f(x)\ is\ equal\ to\)
The angle between the planes x=√3 and z = √2 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
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
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
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 \(\cos\theta=\)
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
The equation of the plane passing through the point (-1,-2,-3) and perpendicular to the x-axis is
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
If the points (1, 0, 0), (0, 3, 0) and (0, 0, 2) lie on a plane, then the unit normal vector \(\hat n\) to the plane is
Let \(\bar{a}=\hat{i}+2\hat{j}-3\hat{k}\) and \(\bar{a}+\bar{b}=4\hat{i}-2\hat{j}+\lambda\hat{k}\). If \(\bar{a}\cdot\bar{b}=4\), then the value of \(\lambda\) is equal to
If \(|\bar a|=10\ and\ |\bar b|=5\), then the value of \((\bar a+2\bar b)\cdot(\bar a-2\bar b)\) is equal to