List of top Mathematics Questions asked in KEAM

\( \int_{0}^{\pi/2} \frac{2\sin x}{2\sin x + 2\cos x} dx \)

\( \lim_{x\to\infty} \left(\sqrt{x^2+1} - \sqrt{x^2-1}\right) \)

If \( f \) is differentiable and \( \lim_{h\to0} \frac{f(1+h)-f(1)}{h}=5 \), find \( f'(1) \)

Point equidistant from \( (2,0,3), (0,3,2), (0,0,1) \)

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

If the points \( (2a,a), (a,2a), (a,a) \) form a triangle of area 18, find centroid

If \( x^2 + y^2 + 2gx + 2fy + 1 = 0 \) represents a pair of straight lines, then \( f^2 + g^2 \) is equal to

If \( \theta \) is the angle between the pair of straight lines \( x^2 - 5xy + 4y^2 + 3x - 4 = 0 \), then \( \tan^2\theta \) is equal to

The area of a triangle is 5 sq. units. Two of its vertices are (2,1) and (3,-2). The third vertex lies on \( y = x + 3 \). The coordinates of the third vertex can be

The area of the triangle in the complex plane formed by \( z, iz \) and \( z + iz \) is

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

The area of the triangle formed by the points \( (a,b+c), (b,c+a), (c,a+b) \) is

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

Let \( f:\mathbb{R} \to \mathbb{R} \) be a differentiable function. If \( f \) is even, then \( f'(0) \) is equal to

The coordinate of the point dividing internally the line joining the points \( (4,-2) \) and \( (8,6) \) in the ratio \( 7:5 \) is

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

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

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

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

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

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

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

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