List of top Questions asked in KEAM- 2017

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

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

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

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

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

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

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

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

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

If the points \( (1, 0), (0, 1) \) and \( (x, 8) \) are collinear, then the value of \( x \) 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 expression \( \tan\left(\frac{\pi}{4} + \frac{\theta}{2}\right) + \tan\left(\frac{\pi}{4} - \frac{\theta}{2}\right) \) is equal to:

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

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

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

If \( \frac{|x-3|}{x-3} > 0 \), then:

If \( \int_{0}^{x} f(t)dt = x^2 + e^x (x > 0) \), then \( f(1) \) is equal to:

The mode of the data 8, 11, 9, 8, 11, 9, 7, 8, 7, 3, 2, 8 is:

The set of all real numbers satisfying the inequality \( x - 2 < 1 \) is:

If the mean of six numbers is 41, then the sum of these numbers is:

The integral \( \int \frac{x+1}{x^{1/2}} \, dx \) is equal to:

The number of words that can be formed by using all the letters of the word PROBLEM only once is: