# JEE (Advanced) 2013 Paper-2

Instructions

A box $$B_1$$ contains 1 white ball, 3 red balls and 2 black balls. Another box $$B_2$$, contains 2 white balls, 3 red balls and 4 black balls. A third box $$B_3$$ contains 3 white balls, 4 red balls and 5 black balls.

Question 51

Question 52

## If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the otherball is red, the probability that these 2 balls are drawnfrom box $$B_2$$ is

Instructions

Let $$f : [0, 1] \rightarrow R$$ (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0) = f(1) = 0 and satisfies $$f"(x) - 2f'(x) + f(x) \geq e^x, x \in [0, 1]$$.

Question 53

Question 54

## If the function $$e^{-x} f(x)$$ assumes its minimum in the interval [0, 1] at $$x = \frac{1}{4}$$ which of the following is true ?

Instructions

Let PQ be a focal chord of the parabola $$y^2 = 4ax$$. The tangents to the parabola at P and Q meet at a point lying on the line $$y = 2x + a, a > 0.$$

Question 55

Question 56

## If chord PQ subtends an angle $$\theta$$ at the vertex of $$y^2 = 4ax$$, then $$\tan \theta =$$

Instructions

For the following questions answer them individually

Question 57

Question 58

Question 59

Question 60