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In a colony, there are 55 members. Every member posts a greeting card to all the members. How many greeting cards were posted by them?

A.

2970

B.

990

C.

1980

D.

890

Answer with explanation

Answer: Option AExplanation

Explanation: First player can post greeting cards to the remaining 54 players in 54 ways. Second player can post greeting card to the 54 players. Similarly, it happens with the rest of the players. The total numbers of greeting cards posted are

54 + 54 + 54 …

54 (55times) = 54 x 55 = 2970.

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How many three letter words are formed using the letters of the word TIME?

A.

12

B.

16

C.

20

D.

24

Answer with explanation

Answer: Option DExplanation

Explanation:

The number of letters in the given word is four.

The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 * 3 * 2 = 24.

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In how many different ways can the letters of the word ‘LEADING’ be arranged in such a way that the vowels always come together?

A.

5040

B.

480

C.

720

D.

360

Answer with explanation

Answer: Option CExplanation

The word ‘LEADING’ has 7 different letters.

When the vowels EAI are always together, they can be supposed to form one letter.

Then, we have to arrange the letters LNDG (EAI).

Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.

The vowels (EAI) can be arranged among themselves in 3! = 6 ways.

Required number of ways = (120 x 6) = 720.

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