Reasoning: Fix the third coin as H. The remaining 19 coins have 2^19 outcomes.
Ans: (A)
Question: Twenty coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
Options:
(A) 2^19
(B) 2^10
(C) 3 * 2^8
(D) 3 * 2^9
(E) 3 * 2^10
Rationale: 16 m/s = 16 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 16 * 18/5 * 15/4 km = 216 km.
The answer: (E)
Question: If a man can cover 16 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
(A) 180km
(B) 190km
(C) 200km
(D) 210km
(E) 216km
Reasoning: 17m - n = p
Add n to both sides:
17m = n + p
Add m to both sides:
18m = n + p + m
Now, divide both sides by 3
6m = (n + p + m)/3 = the average of n, p, and m
Ans: (C)
Question: If 17m n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
Options:
(A) 2m 1
(B) 4m
(C) 6m
(D) m/5
(E) 6m/5
Rationale: When the vowels are always together, then treat all the vowels as a single letter and then all the letters can be arranged in 6! ways and also all three vowels can be arranged in 3! ways. Hence, required no. of arrangements = 6! 3! = 4320.
The answer: (E)
Question: In how many different ways can be letters of the word SOFTWARE be arranged in such a way that the vowels always come together?
Options:
(A) 13440
(B) 1440
(C) 360
(D) 120
(E) None of these
Reasoning: Clearly, the required number would be such that it leaves a remainder of 1 when divided by 2, 3 or 4 and no remainder when divided by 5.
Ans: (A)
Question: I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?
Options:
(A) 5
(B) 7
(C) 23
(D) 4
(E) 2
Reasoning: Dividend Rs 20 = (9/100*20) = 9/5
12 is an income on Rs 100
Rs 9/5 is an income Rs (100/12*9/5) = Rs 15
Ans: (E)
Question: A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
Options:
(A) 12
(B) 10
(C) 14
(D) 25
(E) 15