List of top Questions asked in KEAM- 2018

Equation of line through \( (a,b) \) parallel to \( \frac{x}{a} + \frac{y}{b} = 1 \)

If \( (x,y) \) is equidistant from \( (a+b,b-a) \) and \( (a-b,a+b) \), then

If \( \int_{-1}^{1} f(x)dx = 4 \) and \( \int_{2}^{1} (3-f(x))dx = 7 \), then \( \int_{-1}^{2} f(x)dx \) is

The remainder when \( 2^{2000} \) is divided by 17 is

The coefficient of \( x^5 \) in the expansion of \( (x + 3)^8 \) is

\( \int \frac{x e^x}{(1+x)^2} \, dx = \)

The maximum value of \( 5\cos \theta + 3\cos \left(\theta + \frac{\pi}{3}\right) + 3 \) is

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

\( \frac{1}{9!} + \frac{1}{3!7!} + \frac{1}{5!5!} + \frac{1}{7!3!} + \frac{1}{9!} \) is equal to

\( \int_{-2}^{2} |x| dx \) is equal to

\( \int_{0}^{1} \frac{dx}{x^2+2x+2} \) is equal to

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

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

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

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

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

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

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

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

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

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