Monday, August 24, 2009

IIT JEE Mathematics - Revision Problem Set 2 - Past JEE Questions

1. Find the equation of the normal to the curve

y = (1+x)y + sin-1(sin2) at x = 0.

2. Find the coordinates of the point at which the circles x²+y²-4x-2y = -4 and x²+y²-12x-8y = -36 touch each other.

3. In a triangle ABC, D and E are points on BC and AC respectively, such that BD = 2DC ad AE = 3EC. Let P be the point of intersection of AD and BE. Find BP/PE. (The original problem said using vector methods).

4. Determine te smallest positive value of x (in degrees) for which
tan (x+100°) = tan (x+50°) tan(x)tan(x-50°).

5. Numbers are selected at random, one at a time, from the two-digit numbers 00,01,02...,99 with replacement. An event E occurs if and only if the product of the two digits of a selected number is 18. If four numbers are selected, find the probability that the event E occurs at least 3 times.

Saturday, August 22, 2009

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 ex(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)