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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 \begin{aligned}
\frac{30!}{28!}
\end{aligned}
- 970
- 870
- 770
- 670
Answer: Option B
Explanation:
\begin{aligned}
= \frac{30!}{28!} \\
= \frac{30 * 29 * 28!}{28!} \\
= 30 * 29 = 870
\end{aligned}
2. 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
\begin{aligned}
= \frac{6!}{2!*2!} \\
= \frac{6*5*4*3*2*1}{4} \\
= 180
\end{aligned}
3. A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw
- 64
- 128
- 132
- 222
Answer: Option A
Explanation:
From 2 white balls, 3 black balls and 4 red balls, 3 balls are to be selected such that
at least one black ball should be there.
Hence we have 3 choices
All three are black
Two are black and one is non black
One is black and two are non black
Total number of ways
= 3C3 + (3C2 x 6C1) + (3C1 x 6C2) [because 6 are non black]
\begin{aligned}
= 1 + \left[3 \times 6 \right] + \left[3 \times \left(\dfrac{6 \times 5}{2 \times 1}\right) \right]
= 1 + 18 + 45
= 64
\end{aligned}
4. Evaluate permutation
\begin{aligned}
^5{P}_5
\end{aligned}
- 120
- 110
- 98
- 24
Answer: Option A
Explanation:
\begin{aligned}
^n{P}_n = n! \\
^5{P}_5 = 5*4*3*2*1 \\
= 120
\end{aligned}
5. In how many ways can the letters of the word "CORPORATION" be arranged so that vowels always come together.
- 5760
- 50400
- 2880
- None of above
Answer: Option B
Explanation:
Vowels in the word "CORPORATION" are O,O,A,I,O
Lets make it as CRPRTN(OOAIO)
This has 7 lettes, where R is twice so value = 7!/2!
= 2520
Vowel O is 3 times, so vowels can be arranged = 5!/3!
= 20
Total number of words = 2520 * 20 = 50400
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