List of top Questions asked in KEAM

If \( f(x) = x^6 + 6^x \), then \( f'(x) \) is equal to

Let \( f \) and \( g \) be differentiable functions such that \( f(3)=5, g(3)=7, f'(3)=13, g'(3)=6, f'(7)=2 \) and \( g'(7)=0 \). If \( h(x) = (f \circ g)(x) \), then \( h'(3) \) is

\( \lim_{x \to 0} \frac{\sqrt{1+2x} - 1}{x} \) is

\( \lim_{x \to 0} \frac{1 - \cos(mx)}{1 - \cos(nx)} \) is

The equations of the asymptotes of the hyperbola \( xy + 3x - 2y - 10 = 0 \) are

The minimum value of \( f(x) = \max\{x, 1+x, 2-x\} \) is

A quadratic equation \( ax^2 + bx + c = 0 \), with distinct coefficients is formed. If \( a,b,c \) are chosen from the numbers 2,3,5, then the probability that the equation has real roots is

If \( 5^{97} \) is divided by 52, the remainder obtained is

A password is set with 3 distinct letters from the word LOGARITHMS. How many such passwords can be formed?

\( \lim_{x \to \infty} \frac{3x^3 + 2x^2 - 7x + 9}{4x^3 + 9x - 2} \) is equal to

If the mean of a set of observations \( x_1, x_2, ..., x_{10} \) is 20, then the mean of \( x_1+4, x_2+8, x_3+12, ..., x_{10}+40 \) is

A letter is taken at random from the word "STATISTICS" and another letter is taken at random from the word "ASSISTANT". The probability that they are same letters is

If the sides of a triangle are 4, 5 and 6 cms. Then the area of triangle is ______ sq.cms.

If \( \sin \alpha \) and \( \cos \alpha \) are the roots of the equation \( ax^2 + bx + c = 0 \), then

In a group of 6 boys and 4 girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is

The mean deviation of the data \( 2, 9, 9, 3, 6, 9, 4 \) from the mean is

The number of diagonals of a polygon with 15 sides is

The mean and variance of a binomial distribution are 8 and 4 respectively. What is \( P(X=1) \)?

If the sum of the coefficients in the expansion of \( (a^2x^2 - 2ax + 1)^{51} \) is zero, then \( a \) is equal to

In a class, 40% of students study maths and science and 60% of students study maths. What is the probability of a student studying science given the student is already studying maths?

The eccentricity of the conic \( x^2 + 2y^2 - 2x + 3y + 2 = 0 \) is

If \( y = \frac{\sin^2 x}{1+\cot x} + \frac{\cos^2 x}{1+\tan x} \), then \( y'(x) \) is equal to

The sum of odd integers from 1 to 2001 is

The value of \( \sin \left(\frac{31\pi}{3}\right) \) is

If \( f(x) = \sqrt{\frac{x - \sin x}{x + \cos^2 x}} \), then \( \lim_{x \to \infty} f(x) \) is equal to