List of top Mathematics Questions asked in KEAM

The function f(x)=x⁵e^-x is increasing in the interval

The normal to the curve y=√x at the point (25, 5) intersects the y-axis at

If x and y are both non-negative and if x+y=π, then the maximum value of 5sinxsiny is equal to

The equation of tangent to the circle (x-5)²+y² = 25 at (2, 4) 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

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 \(y=e^{3\log(2x+1)}\), then \(\frac{dy}{dx}=\)

If \(x=\sqrt{10^{\cos^{-1}\theta}}\ and\ y=\sqrt{10^{\sin^{-1}\theta}}\), then \(\frac{dy}{dx}\) is equal to

Let \(f(x) =   \begin{cases}     3x+6,       & if\ x\geq c \\       x^2-3x-1,       & if\ x\lt c   \end{cases}\), where x∈R and c is a constant. The values of c for which f is continuous on R are

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

There are 4 red, 3 blue and 3 yellow marbles in an urn. If three marbles are drawn simultaneously, then the probability that the number of yellow marbles will be less than 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

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

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

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 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

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 plane through the point (1, 5, 3) and having a normal vector \(\hat n=2\hat i-2\hat j-\hat k\) is