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Q:

Using numbers from 0 to 9 the number of 5 digit telephone numbers that can be formed is

A) 1,00,000	B) 59,049
C) 3439	D) 6561

Answer & Explanation Answer: C) 3439

Explanation:

The numbers 0,1,2,3,4,5,6,7,8,9 are 10 in number while preparing telephone numbers any number can be used any number of times.

This can be done in $10^{5}$ ways, but '0' is there

So, the numbers starting with '0' are to be excluded is $9^{4}$ numbers.

Total 5 digit telephone numbers = $10^{5} - 9^{4}$ = 3439

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Filed Under: Permutations and Combinations
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Q:

In how many ways the letters of the word 'DESIGN' can be arranged so that no consonant appears at either of the two ends?

A) 240	B) 72
C) 48	D) 36

Answer & Explanation Answer: C) 48

Explanation:

DESIGN = 6 letters

No consonants appear at either of the two ends.

= $2 x 4 P_{4}$ = 2 x 4 x 3 x 2 x 1= 48

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Q:

In How many ways can the letters of the word 'CAPITAL' be arranged in such a way that all the vowels always come together?

A) 360	B) 720
C) 120	D) 840

Answer & Explanation Answer: A) 360

Explanation:

CAPITAL = 7

Vowels = 3 (A, I, A)

Consonants = (C, P, T, L)

5 letters which can be arranged in $5 P_{5} = 5!$

Vowels A,I = $\frac{3!}{2!}$

No.of arrangements = 5! x $\frac{3!}{2!}$ =360

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Q:

The number of ways that 8 beads of different colours be strung as a necklace is

A) 2520	B) 2880
C) 4320	D) 5040

Answer & Explanation Answer: A) 2520

Explanation:

The number of ways of arranging n beads in a necklace is $\frac{(n - 1)!}{2} = \frac{(8 - 1)!}{2} = \frac{7!}{2}$ = 2520

(since n = 8)

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Q:

The number of ways that 7 teachers and 6 students can sit around a table so that no two students are together is

A) 7! x 7!	B) 7! x 6!
C) 6! x 6!	D) 7! x 5!

Answer & Explanation Answer: B) 7! x 6!

Explanation:

The students should sit in between two teachers. There are 7 gaps in between teachers when they sit in a roundtable. This can be done in $7 P_{6}$ ways. 7 teachers can sit in (7-1)! ways.

Required no.of ways is = $7 P_{6} . 6! = 7! . 6!$

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Filed Under: Permutations and Combinations
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Q:

Pointing to a Photograph, Arjun said, "She is the mother of my son's wife's daughter". How is Arjun related to the lady?

A) Uncle	B) Cousin
C) Daughter- in - law	D) None of these

Answer & Explanation Answer: C) Daughter- in - law

Explanation:

Arjun's son's wife's daughter ---- Arjun's son's daughter; Mother of daughter of Arjun's son - wife of Arjun's son.

So, Arjun is the father-in-law of the lady.

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Filed Under: Blood Relations

Q:

If 'A $ B' means 'A is brother of B', 'A @ B'means 'A is wife of B', 'A # B' means 'A is daughter of B' and 'A & B'means 'A is father of B', then which of the following expressions indicates the relationship 'K' is father-in-law of H'?

A) H @ J $ L # P & K	B) H @ J $ P & L # K
C) H @ J $ L # K & P	D) H @ P $ J & L # K

Answer & Explanation Answer: C) H @ J $ L # K & P

Explanation:

K is the father-in-law of H means H is the wife of the brother (say, J) of the daughter (say, L) of K and K is a male (brother or father of some person, say P) i.e H @ J $ L # K $ P or H @ J $ L # K & P.

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Q:

P's father is Q's Son. M is the paternal uncle of P and N is the brother of Q. How is N related to M?

A) Brother	B) Nephew
C) Cousin	D) None of these

Answer & Explanation Answer:

Explanation:

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Filed Under: Blood Relations

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