List of top Questions asked in KEAM- 2018

If \( |\vec{a}-\vec{b}| = |\vec{a}| = |\vec{b}| = 1 \), then the angle between \( \vec{a} \) and \( \vec{b} \) is

Let \( a \) and \( b \) be 2 consecutive integers selected from the first 20 natural numbers. The probability that \( \sqrt{a^2 + b^2 + a^2b^2} \) is an odd positive integer is

A Poisson variate \( X \) satisfies \( P(X=1) = P(X=2) \). \( P(X=6) \) is equal to

\( \frac{\sqrt{3}}{\sin(20^\circ) - \frac{1}{\cos(20^\circ)}} = \)

The standard deviation of the data \( 6, 5, 9, 13, 12, 8, 10 \) is

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

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

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

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

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

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

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

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

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

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

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

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

The number of diagonals of a polygon with 15 sides 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

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