IIt JEE Mathematics Final Revision Set Number 11

1. The product of n positive numbers is unity. Then their sum is

a. never less than n.
b. is equal to n - (1/n)
c. is equal to n + (1/n)
d. is less than n(n+1)/2

2. The area of a triangle is 5. Two of its vertices are (3,-2) and (2,1). The third vertex is lying on y = x+3. The possible coordinates of the third vertex are

a. (3/2, -3/2)
b. (-3/2, 3/2)
c. (7/2, 13/2)
d. (-1/4, 11/4)


3. If cos (θ-α), cos θ, and cos (θ+α) are in HP, then cos θ sec(α/2) is equal to

a. -1/2
b. 2
c. 1/2
d. √2

4. The dimensions of the base of the rectangular box of greatest volume that can be constructed from 200 square cm of cardboard if the box is to be three times as long as it is wide are:

a. 4 and 12
b. 10/3 and 10
c. 5 and 15
d. 3 and 9

5. If d = a×(b×c) + b×(c×a) + c×(a×b) (a,b,c are vectors), then

a. d is a vector with magnitude one.
b. d is a vector which is equal to a+b+c
c. d = 0
d. a,b,c are coplanar