Past IIT JEE Problems - Questions - Collection 1 (For JEE 2010)

1. The value of (tan x)/tan 3x, wherver defined never lies between 1/3 and 3. State whether the statement is true or false.

2. Determine a positive integer n≤5, such that
∫₀¹ e^x(x-1)ⁿdx = 16 - 6e

3. Three circles touch one another externally. The tangents at their points of contact meet at a point whose distance from a point of contact is 4. Find the ratio of the product of the radii to the sum of th radii of the circles.

4. A lot contains 50 defective and 50 nondefective bulbs. Two bulbs are drawn at random, one at a time, with replacement. The events A,B, and C are defined as follows:

A = {the first bulb is defective}
B = {the second bulb is nondefective}
C = {the two bulbs are both defective or both nondefective}

Are A,B and C are pairwise independent?

5. Determine all values of α for which the point (α, α²) lies inside the triange formed by the lines

2x + 3y -1 = 0
x +2y - 3 = 0
5x - 6y - 1 = 0


(Source : 1992 JEE paper)