List of top Mathematics Questions asked in KEAM

The distance between \( (2, 1, 0) \) and \( 2x + y + 2z + 5 = 0 \) is:

The equation of the hyperbola with vertices \( (0, \pm 15) \) and foci \( (0, \pm 20) \) is:

\( \int_{2016}^{2017} \frac{\sqrt{x}}{\sqrt{x} + \sqrt{4033 - x}} \, dx \) is equal to:

If the vectors \( 2\hat{i} + 2\hat{j} + 6\hat{k} \), \( 2\hat{i} + \lambda\hat{j} + 6\hat{k} \), \( 2\hat{i} - 3\hat{j} + \hat{k} \) are coplanar, then the value of \( \lambda \) is:

The area bounded by the curves \( y = -x^2 + 3 \) and \( y = 0 \) is:

The equation \( 5x^2 + y^2 + y = 8 \) represents:

The center of the ellipse \( 4x^2 + y^2 - 8x + 4y - 8 = 0 \) is:

The area of the circle \( x^2 - 2x + y^2 - 10y + k = 0 \) is \( 25\pi \). The value of \( k \) is equal to:

The order of the differential equation \( \left(\frac{d^3y}{dx^3}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^5 = 0 \) is:

The value of \( \cos\left(\frac{\pi}{4} + x\right) + \cos\left(\frac{\pi}{4} - x\right) \) is:

The coefficient of \( x^5 \) in the expansion of \( (1+x^2)^5(1+x)^4 \) is:

The coefficient of \( x^4 \) in the expansion of \( (1-2x)^5 \) is equal to:

The equation of the line passing through \( (-3, 5) \) and perpendicular to the line through the points \( (1, 0) \) and \( (-4, 1) \) is:

Area of the triangle with vertices \( (-2, 2), (1, 5) \) and \( (6, -1) \) is:

\textbf \( \int_{0}^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \) is equal to:}

If the points \( (1, 0), (0, 1) \) and \( (x, 8) \) are collinear, then the value of \( x \) is equal to:

Let \( f(x+y) = f(x)f(y) \) for all \( x \) and \( y \). If \( f(0)=1, f(3)=3 \) and \( f'(0)=11 \), then \( f'(3) \) is equal to:

The minimum value of the function \( \max\{x, x^2\} \) is equal to:

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

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

The expression \( \tan\left(\frac{\pi}{4} + \frac{\theta}{2}\right) + \tan\left(\frac{\pi}{4} - \frac{\theta}{2}\right) \) is equal to:

In a flight 50 people speak Hindi, 20 speak English and 10 speak both English and Hindi. The number of people who speak at least one of the two languages is:

The integral \( \int \frac{dx}{e^x + e^{-x} + 2} \) is equal to:

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

The limit \( \lim_{x\to0} \frac{\sqrt{2+x} - \sqrt{2-x}}{x} \) is equal to: