IIT JEE Mathematics - Revision Problem Set 3

1. One Indian couple (wife and husband) and four Americal couples are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

a. 1/2 b. 1/3 c. 1/5 d. 1/8 e.2/5

2. The number of values of x in the interval [0,5π] satisfying the equation 3 sin²x 7 sin x+2 = 0 is
a. 0
b. 5
c. 6
d. 10

3. Which of the following n umber(s) is/(are) rational?
a. sin 15°
b. cos 15°
c. sin 15° cos 15°
d. sin 15° cos 75°

4. If the vertices P,Q,R of a triangle are rational points, which of the following points of the triangle PQR is(are) always rational point(s)?

a. centroid
b. incentre
c. circumcentre
d. orthocentre.

5. The number of values of x where the function f(x) = cos x + cos [(√2)x] attains its maximum is

a. 0
b. 1
c. 2
d. infinite

Questions 2 to 5 are from JEE 1998 paper