May 28, 2018

Question 1

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

25200

52000

120

24400

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Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = (7C3*4C2) = 210. Number of groups, each having 3 consonants and 2 vowels = 210. Each group contains 5 letters. Number of ways of arranging 5 letters among themselves = 5! = 120 Required number of ways = (210 x 120) = 25200.

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Question 2

A committee of 5 persons is to be formed from 6 men and 4 women. In how many ways can this be done when at least 2 women are included ?

196

186

190

200

When at least 2 women are included. The committee may consist of 3 women, 2 men : It can be done in 4C3*6C2 ways or, 4 women, 1 man : It can be done in 4C4*6C1ways or, 2 women, 3 men : It can be done in 4C2*6C3 ways. Total number of ways of forming the committees = 4C2*6C3+4C3*6C2+4C4*6C1 = 6 x 20 + 4 x 15 + 1x 6 = 120 + 60 + 6 =186

Question 3

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

720

520

700

750

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) 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

Question 4

n how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?

360

The word 'OPTICAL' contains 7 different letters. When the vowels OIA are always together, they can be supposed to form one letter. Then, we have to arrange the letters PTCL (OIA). Now, 5 letters can be arranged in 5! = 120 ways. The vowels (OIA) can be arranged among themselves in 3! = 6 ways. Required number of ways = (120 x 6) = 720.

Question 5

A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?

1260

1400

1250

1600

A team of 6 members has to be selected from the 10 players. This can be done in 10C6 or 210 ways. Now, the captain can be selected from these 6 players in 6 ways. Therefore, total ways the selection can be made is 210×6= 1260

Question 6

How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

4050

3600

1200

5040

'LOGARITHMS' contains 10 different letters. Required number of words = Number of arrangements of 10 letters, taking 4 at a time. = 10P4 = 5040.

Question 7

12 people at a party shake hands once with everyone else in the room.How many handshakes took place?

72

66

76

64

There are 12 people, so this is our n value. So, 12C21 = 66

Question 8

In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

135

63

125

Required number of ways = = (7C5*3C2) = 63

Question 9

There are 7 non-collinear points. How many triangles can be drawn by joining these points?

10

30

35

60

A triangle is formed by joining any three non-collinear points in pairs. There are 7 non-collinear points The number of triangles formed = 7C3 = 35

Question 10

In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?53400

17610

11760

45000

43000

Required number of ways = = (8C5*10C6) = (8C3*10C4) = 11760

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good questions!!nice

please provide the solution to the above questions.

good questions!!nice

please provide the solution to the above questions.