1. lim h→0 [ln(1+2h)-2 ln(1+h)]/h² = ______________________.
2. An ellipse has OB as a semi-minor axis. F,F' are its foci, and the angle FBF' is a right angle. Then the eccentricity of the elliplse if _______________ .
3. If cos (x-y), cos x and cos (x+y) are in HP, then cos x sec (y/2) = _____________________.
4. Let x be the arithmetic mean and y, z be the two geometric means between any two positive numbers.
Then (y3+z³)/xyz + __________________ .
5.Consider the following statements S and R.
S: Both sin x and cos x are decreasing functions in the interval (π/2, π)
R: If a differentiable function decreases in an interval (a,b), then its derivative also decreases in (a,b).
Which of the folowing is true.
a. Both S and R are correct, but R is not a correct explanation for S.
b. Both S and R are wrong.
c. S is correct and R is the correct explanation for S.
d. S is correct and R is wrong.
Questions 1 to 4 are from cancelled paper 1997 JEE
Questions 5 is from IIT JEE 2000