List of top Questions asked in KEAM

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

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

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

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

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

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

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

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

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

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 \( P(X=1) \)?

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

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

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

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

The sum of odd integers from 1 to 2001 is

The foci of the hyperbola \( 16x^2 - 9y^2 - 64x + 18y - 90 = 0 \) are

If \( z_1 = 2 - i \) and \( z_2 = 1 + i \), then \( \left|\frac{z_1 + z_2 + 1}{z_1 - z_2 + i}\right| \) is

\( (\sqrt{3} + \sqrt{2})^4 - (\sqrt{3} - \sqrt{2})^4 = \)

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

Sum of last 30 coefficients in the binomial expansion of \( (1+x)^{59} \) is

Three players A, B and C play a game. The probability that A, B and C finish the game are respectively \( \frac{1}{2}, \frac{1}{3}, \frac{1}{4} \). The probability that the game is finished is