List of top Questions asked in KEAM- 2018

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

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

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

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

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

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

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

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

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

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 \( A \)

Find plane at distance 5 from origin perpendicular to \(2\hat{i}+\hat{j}+2\hat{k}\)

\( \int \frac{(\sin x + \cos x)(2 - \sin 2x)}{\sin^2 2x} \, dx \)

\( \lim_{x\to0} \frac{1+x-e^x}{x^2} \)

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

The differential equation whose general solution is \( y = e^x(A\cos x + B\sin x) \) is

Equation of circle with centre \( (2,2) \) passing through \( (4,5) \)

Let \( f:\mathbb{N}\to\mathbb{N} \) be such that \( f(1)=2 \) and \( f(x+y)=f(x)f(y) \). If \( \sum_{k=1}^{n} f(a+k)=16(2^n-1) \), then \( a \) is

If \( ^{56}P_{r+6} : \, ^{54}P_{r+3} = 30800 : 1 \), then \( r \) is equal to

If \( |\vec{a}|=13, |\vec{b}|=5 \) and \( \vec{a}\cdot\vec{b}=30 \), then \( |\vec{a}\times\vec{b}| \) is

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