List of top Questions asked in KEAM- 2018

If \( 3\hat{i} + 2\hat{j} - 5\hat{k} = x(2\hat{i} - \hat{j} + \hat{k}) + y(\hat{i} + 3\hat{j} - 2\hat{k}) + z(-2\hat{i} + \hat{j} - 3\hat{k}) \), then

Two dice of different colours are thrown at a time. The probability that the sum is either 7 or 11 is

The order and degree of the differential equation \( (y'')^2 + (y''')^3 - (y')^4 + y^5 = 0 \) is

If \( \sin\theta - \cos\theta = 1 \), then the value of \( \sin^3\theta - \cos^3\theta \) is

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

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

If the equations \( x^2 + ax + 1 = 0 \) and \( x^2 - x - a = 0 \) have a real common root, then the value of \( b \) is

If \( |\vec{a}|=3, |\vec{b}|=1, |\vec{c}|=4 \) and \( \vec{a}+\vec{b}+\vec{c}=0 \), then the value of \( \vec{a}\cdot\vec{b} + \vec{b}\cdot\vec{c} + \vec{c}\cdot\vec{a} \) is

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

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

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

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

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

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

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

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

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

In AP, \( a_k=5k+1 \). Find sum of first 100 terms

If \( f(x)=\begin{vmatrix} \frac{1}{2x} & \frac{1}{x-1} & \frac{1}{x} \\ 3x(x-1) & (x-1)(x-2) & x(x-1) \end{vmatrix} \), then \( f(50) \) is