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.
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