1. Three numbers are chosen at random without replacement from {1,2,... 10}. The probabality that the minimum of the chosen numbers is 3, or their maximum is 7, is _________.

2. A spherical rain drop evaporates at a rate proportional to its surface area at any instant t. The differential equation giving the rate of change of the radius of the rain drop is _______________ .

3. Let a,b and c be three vectors having magnitudes 1,1, and 2 respectively. If a ×(a×c)+b = 0, then the acute angle between a and c is________ .

4. Two vertices of an equilateral triangle are (-1,0) and (1,0), and its third vertex lies above the x-axis. The equation of its circumcircle is ______________ .

5. The equation √(x+1) - √(x-1) = √(4x-1) has

a. no solution

b. one solution

c. two solution

d. more than two solutions

questions 1 to 5 are from 1997 JEE cancelled paper.

## Wednesday, December 23, 2009

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