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Q:

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) 4050	B) 3600
C) 1200	D) 5040

Answer & Explanation Answer: D) 5040

Explanation:

'LOGARITHMS' contains 10 different letters.

Required number of words = Number of arrangements of 10 letters, taking 4 at a time.

= $10 P_{4}$

= 5040.

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Q:

A Map is an Array,which contains the addresses of the free space in swap device that are allocatable resources,and the number of the resource unit available there.

A) TRUE

B) FALSE

Answer & Explanation Answer: A) TRUE

Explanation:

The given statement is clearly true.

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Subject: Operating Systems
Exam Prep: GRE

Q:

In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

A) 54	B) 64
C) 63	D) 36

Answer & Explanation Answer: C) 63

Explanation:

Required number of ways = $(7 C_{5} \times 3 C_{2}) = 63$

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Q:

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) 36	B) 25
C) 42	D) 120

Answer & Explanation Answer: A) 36

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 = $3 P_{3}$ = 3! = 6.

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

Number of ways of these arrangements = $3 P_{3}$ = 3! = 6.

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

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Q:

A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

A) 48	B) 64
C) 63	D) 45

Answer & Explanation Answer: B) 64

Explanation:

We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).

Required number of ways= $(3 C_{1} * 6 C_{2}) + (3 C_{2} * 6 C_{1}) + 3 C_{3}$ = (45 + 18 + 1) =64

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Q:

In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

A) 11670	B) 12000
C) 11760	D) 20050

Answer & Explanation Answer: C) 11760

Explanation:

Required number of ways= $(8 C_{5} \times 10 C_{6})$ = ( $8 C_{3} \times 10 C_{4}$ )= 11760.

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Q:

The PS command prints the process status for only some of the running processes.

A) TRUE

B) FALSE

Answer & Explanation Answer: B) FALSE

Explanation:

The PS command prints the process status for some or all of the running processes

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Subject: Operating Systems
Exam Prep: GATE

Q:

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

A) 209	B) 290
C) 200	D) 208

Answer & Explanation Answer: A) 209

Explanation:

We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).

Required number of ways = $(6 C_{1} * 4 C_{3}) + (6 C_{2} * 4 C_{2}) + (6 C_{3} * 4 C_{1}) + 6 C_{4}$

= $(6 C_{1} * 4 C_{1}) + (6 C_{2} * 4 C_{2}) + (6 C_{3} * 4 C_{1}) + 6 C_{2}$ = 209.

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