Aptitude Archives - Page 28 of 80 -

Question: In how many different ways can the letters of the word ‘DETAIL’ be arranged in such a way that the vowels occupy only the odd positions?
[A].

[B].

[C].

[D].

Answer: Option C

Explanation:

There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.

Let us mark these positions as under:

(1) (2) (3) (4) (5) (6)

Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.

Number of ways of arranging the vowels = 3P3 = 3! = 6.

Also, the 3 consonants can be arranged at the remaining 3 positions.

Number of ways of these arrangements = 3P3 = 3! = 6.

Total number of ways = (6 x 6) = 36.

In how many different ways can the letters of the word ‘DETAIL’ be arranged in such a way that the vowels occupy only the odd positions? Read More »

Aptitude, Permutation And Combination

In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?

Aptitude, Permutation And Combination / admin

Question:
In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?

[A].

10080

[B].

4989600

[C].

120960

[D].

None of these

Answer: Option C

Explanation:

In the word ‘MATHEMATICS’, we treat the vowels AEAI as one letter.

Thus, we have MTHMTCS (AEAI).

Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.

Number of ways of arranging these letters =	8!	= 10080.
	(2!)(2!)

Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.

Number of ways of arranging these letters =	4!	= 12.
	2!

Required number of words = (10080 x 12) = 120960.

In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together? Read More »

Aptitude, Permutation And Combination

In how many different ways can the letters of the word ‘CORPORATION’ be arranged so that the vowels always come together?

Aptitude, Permutation And Combination / admin

Question: In how many different ways can the letters of the word ‘CORPORATION’ be arranged so that the vowels always come together?
[A].

810

[B].

1440

[C].

2880

[D].

50400

Answer: Option D

Explanation:

In the word ‘CORPORATION’, we treat the vowels OOAIO as one letter.

Thus, we have CRPRTN (OOAIO).

This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.

Number of ways arranging these letters =	7!	= 2520.
	2!

Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged

in	5!	= 20 ways.
	3!

Required number of ways = (2520 x 20) = 50400.

Video Explanation: https://youtu.be/o3fwMoB0duw

In how many different ways can the letters of the word ‘CORPORATION’ be arranged so that the vowels always come together? Read More »

Aptitude, Permutation And Combination

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

Aptitude, Permutation And Combination / admin

Question: 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].

360

[B].

480

[C].

720

[D].

5040

Answer: Option C

Explanation:

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.

Video Explanation: https://youtu.be/WCEF3iW3H2c

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

Aptitude, Permutation And Combination

In how many different ways can the letters of the word ‘OPTICAL’ be arranged so that the vowels always come together?

Aptitude, Permutation And Combination / admin

Question:
In how many different ways can the letters of the word ‘OPTICAL’ be arranged so that the vowels always come together?

[A].

120

[B].

720

[C].

4320

[D].

2160

Answer: Option B

Explanation:

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.

In how many different ways can the letters of the word ‘OPTICAL’ be arranged so that the vowels always come together? Read More »

Aptitude, Permutation And Combination

In how many ways can the letters of the word ‘LEADER’ be arranged?

Aptitude, Permutation And Combination / admin

Question: In how many ways can the letters of the word ‘LEADER’ be arranged?
[A].

[B].

144

[C].

360

[D].

720

Answer: Option C

Explanation:

The word ‘LEADER’ contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.

Required number of ways =	6!	= 360.
	(1!)(2!)(1!)(1!)(1!)

Video Explanation: https://youtu.be/2_2QukHfkYA

In how many ways can the letters of the word ‘LEADER’ be arranged? Read More »

Aptitude, Permutation And Combination

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?

Aptitude, Permutation And Combination / admin

Question: 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?
[A].

[B].

400

[C].

5040

[D].

2520

Answer: Option C

Explanation:

‘LOGARITHMS’ contains 10 different letters.