q: In a race with 30 runners where 6 trophies will be given to the top 6 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?
Options:
(A) 6^6 ways
(B) 8^9 ways
(C) 7^8 ways
(D) 8^7 ways
(E) 8^6 ways
a: Stream of consciousness: 6 people can be prized with distinct prizes in 6^6 ways The answer is (A).

question: There are 10person among whom 2are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to?
Options:
(A) 4!*2!
(B) 7!*2!
(C) 6!*1!
(D) 2!*1!
(E) 5!*1!
answer: Stream of consciousness: Total number of ways = 7!*2!. The answer is (B).

q: The average of first 15 natural numbers is?
Options:
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
a: Stream of consciousness: Sum of 15 natural no. = 240/2 = 120
Average = 120/15 = 8 The answer is (B).

question: A 28 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
(A) 12
(B) 8
(C) 88
(D) 77
(E) 14
answer: Stream of consciousness: 1: 2/5 = 5: 2
2/7 * 28 = 8 The answer is (B).

q: If 12 men can reap 120 acres of land in 36 days, how many acres of land can 44 men reap in 54 days?
Options:
(A) 820 acres
(B) 660 acres
(C) 620 acres
(D) 720 acres
(E) 920 acres
a: Stream of consciousness: 12 men 120 acres 36 days
44 men ? 54 days
120 * 44/12 * 54/36
10 * 44 * 3/2
44 * 15 = 660 The answer is (B).

q: A 21 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
(A) 12
(B) 6
(C) 88
(D) 77
(E) 14
a:
Stream of consciousness: 1: 2/5 = 5: 2
2/7 * 21 = 6 The answer is (B).