IIT JEE Mathematics Final Revision Set No. 10

1. What normal to the curve y = x² forms the shortest chord?

2. The value of integral dx/[1+tan³x] from 0 to π/2 is
a. 0
b. 1
c. π/4
d. π/2

3. ABCD is rhombus. Its diagonals AC and BD intersect at the point M and satisfy BD = 2AC. If the points D and M represent the complex numbers 1 + i and 2 - i respectively, then A represents the complex number ___________ or __________ .

4. If K = sin (π/18)sin (5π/18)sin (7π/18), the numerical value of K is __________ .

5. If A and B are g.t.zero and A+B = π/3, the the maximum value of tan A tan B is ______.

Questions 2 to 5 are from IIT JEE paper 1993
Q 1 is from 1992 paper.