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Q:

There are 4 books on fairy tales, 5 novels and 3 plays. In how many ways can you arrange these so that books on fairy tales are together, novels are together and plays are together and in the order, books on fairytales, novels and plays ?

A) 12400	B) 17820
C) 17280	D) 12460

Answer & Explanation Answer: C) 17280

Explanation:

There are 4 books on fairy tales and they have to be put together. They can be arranged in 4! ways.

Similarly, there are 5 novels.They can be arranged in 5! ways.

And there are 3 plays.They can be arranged in 3! ways.

So, by the counting principle all of them together can be arranged in 4!´5!´3! ways = 17280

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Filed Under: Permutations and Combinations

Q:

In how many ways can an animal trainer arrange 5 lions and 4 tigers in a row so that no two lions are together?

A) 2800	B) 2880
C) 2600	D) 3980

Answer & Explanation Answer: B) 2880

Explanation:

They have to be arranged in the following way :

L T L T L T L T L

The 5 lions should be arranged in the 5 places marked ‘L’.

This can be done in 5! ways.

The 4 tigers should be in the 4 places marked ‘T’.

This can be done in 4! ways.

Therefore, the lions and the tigers can be arranged in 5!´ 4! ways = 2880 ways.

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Filed Under: Permutations and Combinations

Q:

Consider the word ROTOR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5-letter palindromes.

A) 17756	B) 17576
C) 12657	D) 12666

Answer & Explanation Answer: B) 17576

Explanation:

The first letter from the right can be chosen in 26 ways because there are 26 alphabets.

Having chosen this, the second letter can be chosen in 26 ways

The first two letters can chosen in 26 x 26 = 676 ways

Having chosen the first two letters, the third letter can be chosen in 26 ways.

All the three letters can be chosen in 676 x 26 =17576 ways.

It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.

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Filed Under: Permutations and Combinations

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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Filed Under: Permutations and Combinations

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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Filed Under: Permutations and Combinations

Q:

Other things being equal, would an investor prefer an interest rate of 10.5% compounded monthly or 11% compounded annually for a two-year investment?

A) 1232	B) 1243
C) 1254	D) 1262

Answer & Explanation Answer: A) 1232

Explanation:

i=j/m

FV= PV(1+ i)^n

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

Q:

if $\log_{10} 5 + \log (5 x + 1) = \log_{10} (x + 5) + 1, t h e n x i s e q u a l t o$

A) 1	B) 3
C) 5	D) 10

Answer & Explanation Answer: B) 3

Explanation:

$\log_{10} 5 + \log (5 x + 1) = \log_{10} (x + 5) + 1$

$\log_{10} [5 (5 x + 1)] = \log_{10} [10 (x + 5)]$

$5 (5 x + 1) = 10 (x + 5)$

5x+1=2x+10

3x=9

x=3

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Filed Under: Logarithms
Exam Prep: Bank Exams
Job Role: Bank PO

Q:

A sum of money amounts to Rs.6690 after 3 years and to Rs.10,035 after 6 years on compound interest.find the sum.

A) 4360	B) 4460
C) 4560	D) 4660

Answer & Explanation Answer: B) 4460

Explanation:

Let the sum be Rs.P.then
P(1+R/100)^3=6690…(i) and P(1+R/100)^6=10035…(ii)
On dividing,we get (1+R/100)^3=10025/6690=3/2.
Substituting this value in (i),we get:
P*(3/2)=6690 or P=(6690*2/3)=4460
Hence,the sum is rs.4460.

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

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