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11.
A polygon has 44 diagonals the number of its sides is
  • A.
    9
  • C.
    11
  • B.
    10
  • D.
    12
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Answer : [C]
Explanation :
 
Let there be n sides of the polygon. Then it has n vertices. The total number of straight lines obtained by joining n verticals by taking 2 at a time is nC2. These nC2 lines also include n sides of polygon. Therefore, the number of diagonals formed is nC2-n.
 
Thus nC2 - n = 44  
 
 
 
n(n-1)
2
 - n = 44    
 
 
 
n2 - 3n
2
 = 44    
 
 
    n2- 3n = 88  
 
 
    n2- 3n - 88 = 0  
 
 
    (n - 11) (n + 8) = 0  
 
 
    n = 11    
 
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12.
Letters of the word DIRECTOR are arranged in such a way that all the vowels come together. Find out the total no. of ways for making such arrangement.
  • A.
    4320
  • C.
    2160
  • B.
    2720
  • D.
    1120
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Answer : [C]
Explanation :
 
Taping all vowels (IEO) as a single letter (Since they come together) there are six letters with two Rs
 
Hence no. of arrangements =
6!
2!
 x 3! = 2160  
 
[3 vowels can be arranged in 3! Ways among themselves, hence multiplied with 3!.]
 
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13.
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
  • A.
    210
  • C.
    25200
  • E.
    None of these
  • B.
    1050
  • D.
    21400
  • Answer & Explanation
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Answer : [C]
Explanation :
 
Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = (7C3 x 4C2)
 
 
7 x 6 x 5
3 x 2 x 1
x
4 x 3
2 x 1
   = 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 ! = (5 x 4 x 3 x 2 x 1) = 120.
 
 
  Required number of words = (210 x 120) = 25200.  
 
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14.
In how many different ways can the letters of the word 'JUDGE' be arranged in such a way that the vowels always come together?
  • A.
    48
  • C.
    124
  • E.
    None of these
  • B.
    120
  • D.
    160
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Answer : [A]
Explanation :
 
The word 'JUDGE' has 5 different letters.
 
When the vowels UE are always together, they can be supposed to form one letter.
 
Then, we have to arrange the letters JDG (UE)
 
Now, 4 letters can be arranged in 4! = 24 ways.
 
The vowels (UE) can be arranged among themselves in 2! = 2 ways.
 
 
  Required number of ways = (24 x 2) = 48  
 
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15.
8 men entered a lounge simultaneously. If each person shook hands with the other, then find the total no. of hand shakes.
  • A.
    16
  • C.
    56
  • B.
    36
  • D.
    28
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Answer : [D]
Explanation :
 
Applying the given rule, we have required no. of hand shakes =
8(8 - 1)
2
 = 28
 
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