Ok, so a lot of confusion regarding how to go about all of these questions. Question 55-56 would require some context so I'll paste the link as well as the questions.

QUESTION 42. A fair coin is tossed until a head comes up for the 1st

time. The probability of this happening on an odd-numbered toss is

(a) 1/2

(b) 1/3

(c) 2/3

(d) 3/4

Answer: (c)

QUESTION 43. An experiment has 10 equally likely outcomes. Let A and

B be two non-empty events of the experiment. If A consists of 4 outcomes,

then the number of outcomes B must have so that A and B are independent,

is

(a) 4

(b) 3 or 9

(c) 6

(d) 5 or 10

Answer: (d)

QUESTION 44. Consider the system of equations

x + y = 0

x + y = 0

; ; and are i.i.d random variable. Each of them takes value 1 and 0

with equal probability.

Statement A: The probability that the system of equations has a unique

solution is 3/8.

Statement B: The probability that the system of equations has at least one

solution is 1.

(a) Both the statements are correct

(b) Both the statements are false

(c) Statement A is correct but B is false

(d) Statement B is correct but A is false

Q 48. A rectangle has its lower left hand corner at the origin and

its upper right hand corner on the graph of f(x) = x^2 + (1/x^2). For which x

is the area of the rectangle minimized?

(a) x= 0

(b) x = Infinity

(c) x = (1/3)^1/4

(d) x = 2^1/3

For 55 and 56:

http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/2012-option-a.pdf