IIT JEE Mathematics Final Revision Set No. 9

1. the centre of a circle passing through the points (0,0), (1,0) and touching the circle x²+y² = 9 is

a. 3/2, 1/2
b. 1/2, 3/2
c. 1/2,1/2
d. 1/2, -√2)

2. If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is,

a. square
b. circle
c. straight line
d. two intersecting lines

3. India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0,1,and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is

a. 0.8750
b. 0.0875
c. 0.0625
d. 0.0250

4. Match the columns
z ≠ 0 is a complex numer

Column 1 ---- Column2
i) Re z = 0 ----- A. Re z² = 0
ii) Arg z = π/4 - B. Im z² = 0
----------------- C. Re z² = Im z²

5. Let the functions defined in column 1 have domain (-π/2, π/2)

Column 1 ---- Column2
i) x + sin x----- A. increasing
2. sec x -------- B. decreasing
------------------C. neither increasing nor decreasing