IIT JEE Mathematics - Revision Problem Set 6

1. A bag contains 50 chits containing 1 to 50 numbers. 5 tickets are drawn at random. They are arranged in an ascending order from x1 to x5. The probability that the middle number x3 is equal to 30 is

a. [²⁰C₂*³⁰C₂]/⁵⁰C₅
b. [²⁹C₂*²⁰C₂]/⁵⁰C₅
c. [¹⁹C₂*³¹C₂]/⁵⁰C₅
d. None are correct

2. Number of divisors of the form 4n+2 (n≥0) of the integer 240 is

a. 4
b. 8
c. 10
d. 3

3. If in a triangle ABC, Sin A, Sin B, and Sin C are in A.P., then

a. the altitudes re in A.P.
b. the altitudes are in H.P.
c. the medians are in G.P.
d. the medians are in A.P.

4. If f(x) = (x²-1)/(x²+1), for every real number x, then the minimum value of f

a. does not exist because f is unbounded.
b. is not attained even though f is is bounded
c. is equal to 1
d. is equal to -1

5. Seven white balls and three black balls are randomly placed in a row. the probability that no two black balls are placed adjacently equals

a. 1/2
b. 7/15
c. 2/15
d. 1/3






Problems 2 to 5 JEE 1998