List of top Questions asked in KEAM- 2018

The solutions of \( x^{2/5} + 3x^{1/5} - 4 = 0 \) are

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

If the vectors \( \vec{a} = \hat{i} - \hat{j} + 2\hat{k}, \vec{b} = 2\hat{i} + 4\hat{j} + \hat{k} \) and \( \vec{c} = 2\lambda \hat{i} + 9\hat{j} + \mu \hat{k} \) are mutually orthogonal, then \( \lambda + \mu \) is equal to

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

Let \( \vec{a} = \hat{i}+\hat{j}+\hat{k}, \vec{b} = \hat{i}+3\hat{j}+5\hat{k}, \vec{c} = 7\hat{i}+9\hat{j}+11\hat{k} \). Then the area of parallelogram with diagonals \( \vec{a}+\vec{b} \) and \( \vec{b}+\vec{c} \) is

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

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

If the vectors \( 4\hat{i} + 11\hat{j} + m\hat{k},\ 7\hat{i} + 2\hat{j} + 6\hat{k} \) and \( \hat{i} + 5\hat{j} + 4\hat{k} \) are coplanar, then \( m \) is equal to

An ellipse of eccentricity \( \frac{2\sqrt{2}}{3} \) is inscribed in a circle. A point is chosen inside the circle at random. The probability that the point lies outside the ellipse is

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

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

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

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

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

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

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

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