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Q:

How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?

A) 1000	B) 100
C) 500	D) 999

Answer & Explanation Answer: B) 100

Explanation:

1 million distinct 3 digit initials are needed.

Let the number of required alphabets in the language be ‘n’.

Therefore, using ‘n’ alphabets we can form n * n * n = $n^{3}$ distinct 3 digit initials.

Note distinct initials is different from initials where the digits are different.

For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.

This $n^{3}$ different initials = 1 million

i.e. $n^{3} = 10^{6}$ (1 million = $10^{6}$ )

=> n = $10^{2}$ = 100

Hence, the language needs to have a minimum of 100 alphabets to achieve the objective.

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Filed Under: Permutations and Combinations

Q:

When four fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3?

A) 620	B) 671
C) 625	D) 567

Answer & Explanation Answer: B) 671

Explanation:

When 4 dice are rolled simultaneously, there will be a total of 6 x 6 x 6 x 6 = 1296 outcomes.

The number of outcomes in which none of the 4 dice show 3 will be 5 x 5 x 5 x 5 = 625 outcomes.

Therefore, the number of outcomes in which at least one die will show 3 = 1296 – 625 = 671

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Filed Under: Permutations and Combinations

Q:

There are 5 novels and 4 biographies. In how many ways can 4 novels and 2 biographies can be arranged on a shelf ?

A) 26100	B) 21600
C) 24000	D) 36000

Answer & Explanation Answer: B) 21600

Explanation:

4 novels can be selected out of 5 in $5 C_{4}$ ways.

2 biographies can be selected out of 4 in $4 C_{2}$ ways.

Number of ways of arranging novels and biographies = $5 C_{4} * 4 C_{2}$ = 30

After selecting any 6 books (4 novels and 2 biographies) in one of the 30 ways, they can be arranged on the shelf in 6! = 720 ways.

By the Counting Principle, the total number of arrangements = 30 x 720 = 21600

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Filed Under: Permutations and Combinations

Q:

What is the SI on Rs.7500/- at the rate of 10% per annum for 5 years?

A) 3750	B) 2750
C) 1750	D) 750

Answer & Explanation Answer: A) 3750

Explanation:

S.I=PNR/100

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Filed Under: Simple Interest
Exam Prep: Bank Exams
Job Role: Bank PO

Q:

What is the SI on Rs.2500/- at the rate of 12% per annum for 8 years?

A) 2200	B) 2300
C) 2400	D) 2500

Answer & Explanation Answer: C) 2400

Explanation:

S.I=PNR/100

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Filed Under: Compound Interest
Exam Prep: Bank Exams
Job Role: Bank PO

Q:

If $n C_{10} = n C_{12}$ then,find n.

A) 10	B) 12
C) 22	D) 24

Answer & Explanation Answer: C) 22

Explanation:

Using, ${}^{n}C_{r} = {}^{n}C_{n - r}$ we get

n – 10 = 12

or, n = 12 + 10 = 22

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Filed Under: Permutations and Combinations

Q:

Payments of $2000 and $1000 were originally scheduled to be paid one year and five years, respectively, from today. They are to be replaced by a $1500 payment due four years from today, and another payment due two years from today. The replacement stream must be economically equivalent to the scheduled stream. What is the unknown payment, if money can earn 7% compounded semiannually?

A) 1548	B) 1348
C) 1648	D) 1748

Answer & Explanation Answer: C) 1648

Explanation:

FV1 = Future value of $2000, 1 year later
= PV (1+ i)^n

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Filed Under: Compound Interest
Exam Prep: Bank Exams
Job Role: Bank PO

Q:

The Indian Cricket team consists of 16 players. It includes 2 wicket keepers and 5 bowlers. In how many ways can a cricket eleven be selected if we have to select 1 wicket keeper and atleast 4 bowlers?

A) 1024	B) 1900
C) 2000	D) 1092

Answer & Explanation Answer: D) 1092

Explanation:

We are to choose 11 players including 1 wicket keeper and 4 bowlers or, 1 wicket keeper and 5 bowlers.

Number of ways of selecting 1 wicket keeper, 4 bowlers and 6 other players in $2 C_{1} * 5 C_{4} * 9 C_{6}$ = 840

Number of ways of selecting 1 wicket keeper, 5 bowlers and 5 other players in $2 C_{1} * 5 C_{5} * 9 C_{5}$ =252

Total number of ways of selecting the team = 840 + 252 = 1092

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Filed Under: Permutations and Combinations

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