Question: A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?
Options:
(A) 190 metres
(B) 160 metres
(C) 180 metres
(D) 120 metres
(E) 200 metres
Answer: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s
Time taken to cross, t = 18 s
Distance Covered, d = vt = (400/36)× 18 = 200 m
Distance covered is equal to the length of the train = 200 m
The answer is (E).

Question: X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?
Options:
(A) 5
(B) 4
(C) 6
(D) 7
(E) 8
Answer: Work done by X in 1 day = 1/18
Work done by Y in 1 day = 1/15
Work done by Y in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which X can finish the remaining work = (1/3) / (1/18) = 6
The answer is (C).

Question: A bag contains nine black balls, three red balls and four red balls. In how many ways can two balls be drawn from the bag?
Options:
(A) ¹⁶C₂
(B) ⁹C₂
(C) ³C₂
(D) ¹²C₂
(E) ¹⁴C₂
Answer: Total number of balls = 9 + 3 + 4
Two balls can be drawn from 16 balls in ¹⁶C₂ ways.
The answer is (A).

Question: When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 4 times, what is the probability that it will land twice on heads and twice tails?
Options:
(A) 1/8
(B) 1/4
(C) 1/16
(D) 1/32
(E) 1/2
Answer:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
Must be twice on heads and twice on tails
1/2*1/2*1/2*1/2 = 1/16
The answer is (C).