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Question Detail
How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together.
- 17280
- 4320
- 720
- 80
Answer: Option A
Explanation:
word SIGNATURE contains total 9 letters.
There are four vowels in this word, I, A, U and E
Make it as, SGNTR(IAUE), consider all vowels as 1 letter for now
So total letter are 6.
6 letters can be arranged in 6! ways = 720 ways
Vowels can be arranged in themselves in 4! ways = 24 ways
Required number of ways = 720*24 = 17280
1. Evaluate combination
100C100
- 10000
- 1000
- 10
- 1
Answer: Option D
Explanation:
nCn=1100C100=1
2. Evaluate permutation equation
59P3
- 195052
- 195053
- 195054
- 185054
Answer: Option C
Explanation:
nPr=n!(n−r)!59P3=59!(56)!=59∗58∗57∗56!(56)!=195054
3. In how many way the letter of the word "RUMOUR" can be arranged
- 2520
- 480
- 360
- 180
Answer: Option D
Explanation:
In above word, there are 2 "R" and 2 "U"
So Required number will be
=6!2!∗2!=6∗5∗4∗3∗2∗14=180
4. In a Cricket cup total 153 matches were played and every two teams played exactly one match with each other. So what were the total number of teams participating in Cricket Cup ?
- 15
- 16
- 17
- 18
- 19
Answer: Option D
Explanation:
Lets suppose there were x number os team in cricket cup then from the given statement we can calculate :
=>nC2=153 it given n = 18 and n = -17
As answer cannot be negative to 18 is the answer
5. How many words can be formed by using all letters of TIHAR
- 100
- 120
- 140
- 160
Answer: Option B
Explanation:
First thing to understand in this question is that it is a permutation question.
Total number of words = 5
Required number =
5P5=5!=5∗4∗3∗2∗1=120
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