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Q:

There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?

A) 18! x 19!	B) 2 x 19!
C) 2 x 18!	D) 18! x 18!

Answer & Explanation Answer: C) 2 x 18!

Explanation:

fix one person and the brothers B1 P B2 = 2 ways to do so.
other 17 people= 17!

Each person out of 18 can be fixed between the two=18, thus, 2 x 17! x 18=2 x 18!

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Filed Under: Permutations and Combinations

Q:

Parenthesis is never required in Postfix or Prefix expressions

A) TRUE

B) FALSE

Answer & Explanation Answer: A) TRUE

Explanation:

Parenthesis is not required because the order of the operators in the postfix /prefix expressions determines the actual order of operations in evaluating the expression

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Subject: Database
Job Role: Database Administration

Q:

There are fourteen juniors and twenty-three seniors in the Service Club. The club is to send four representatives to the State Conference. If the members of the club decide to send two juniors and two seniors, how many different groupings are possible ?

A) 23024	B) 24023
C) 23023	D) 25690

Answer & Explanation Answer: C) 23023

Explanation:

Choose 2 juniors and 2 seniors.

$14 C_{2} * 23 C_{2} = 23023$

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Q:

The time complexity of sequential search is

A) O(n)	B) O(2n)
C) O(n^2)	D) None

Answer & Explanation Answer: A) O(n)

Explanation:

The time complexity of sequential search is O(n)

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Job Role: Database Administration

Q:

A coach must choose five starters from a team of 12 players. How many different ways can the coach choose the starters ?

A) 569	B) 729
C) 625	D) 769

Answer & Explanation Answer: B) 729

Explanation:

Choose 5 starters from a team of 12 players. Order is not important.

$12 C_{5}$ = 729

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Q:

It is necessary to sort a file before searching a particular item

A) True	B) False
C) May or may not be true	D) None of the above

Answer & Explanation Answer: C) May or may not be true

Explanation:

If less work is involved in searching a element than to sort and then extract, then we don’t go for sort

If frequent use of the file is required for the purpose of retrieving specific element, it is more efficient to sort the file.

Thus it depends on situation

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Job Role: Database Administration

Q:

A standard deck of playing cards has 13 spades. How many ways can these 13 spades be arranged?

A) 13!	B) 13^2
C) 13^13	D) 2!

Answer & Explanation Answer: A) 13!

Explanation:

The solution to this problem involves calculating a factorial. Since we want to know how 13 cards can be arranged, we need to compute the value for 13 factorial.

13! = (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) = 6,227,020,800

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Q:

Eight first class and six second class petty officers are on the board of the 56 club. In how many ways can the members elect, from the board, a president, a vice-president, a secretary, and a treasurer if the president and secretary must be first class petty officers and the vice-president and treasurer must be second class petty officers?

A) 1500	B) 1860
C) 1680	D) 1640

Answer & Explanation Answer: C) 1680

Explanation:

Since two of the eight first class petty officers are to fill two different offices, we write $8 P_{2} =$ 56

Then, two of the six second class petty officers are to fill two different offices; thus, we write $6 P_{2}$ =30

The principle of choice holds in this case; therefore, the members have 56 x 30 = 1680 ways to select the required office holders

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