List of top Mathematics Questions asked in KEAM

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

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

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

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 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

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

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

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

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

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

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

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

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

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?

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

The value of \( \frac{2(\cos 75^\circ + i \sin 75^\circ)}{0.2(\cos 30^\circ + i \sin 30^\circ)} \) is

If determinant of matrix is zero, then system is

If set \( S \) has 10 elements and \( A=\{(x,y):x,y\in S, x\ne y\} \), number of elements in \( A \)

The real part of \( (i - \sqrt{3})^{13} \) is