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Q:

If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM ?

A) 32	B) 24
C) 72	D) 36

Answer & Explanation Answer: A) 32

Explanation:

The 5 letter word can be rearranged in 5!=120 Ways without any of the letters repeating.

The first 24 of these words will start with A.

Then the 25th word will start will CA _ _ _.
The remaining 3 letters can be rearranged in 3!=6 Ways. i.e. 6 words exist that start with CA.

The next word starts with CH and then A, i.e., CHA _ _.
The first of the words will be CHAMS. The next word will be CHASM.

Therefore, the rank of CHASM will be 24+6+2= 32

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Filed Under: Permutations and Combinations

Q:

When Dr. Ram arrives in his dispensary, he finds 12 patients waiting to see him. If he can see only one patients at a time,find the number of ways, he can schedule his patients if 3 leave in disgust before Dr. Ram gets around to seeing them.

A) 479001600	B) 79833600
C) 34879012	D) 67800983

Answer & Explanation Answer: B) 79833600

Explanation:

There are 12 - 3 = 9 patients.They can be seen in $12 P_{9}$ = 79833600 ways

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Filed Under: Permutations and Combinations

Q:

When John arrives in New York,he has eight stops to see, but he has time only to visit six of them.In how many different ways can he arrange his schedule in New York?

A) 20610	B) 24000
C) 20160	D) 21000

Answer & Explanation Answer: C) 20160

Explanation:

He can arrange his schedule in $8 P_{6}$ = 20160 ways

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Q:

Compute the sum of 4 digit numbers which can be formed with the four digits 1,3,5,7, if each digit is used only once in each arrangement.

A) 105555	B) 106665
C) 106656	D) 108333

Answer & Explanation Answer: C) 106656

Explanation:

The number of arrangements of 4 different digits taken 4 at a time is given by $4 P_{4}$ = 4! = 24.All the four digits will occur equal number of times at each of the position,namely ones,tens,hundreds,thousands.

Thus,each digit will occur 24/4 = 6 times in each of the position.The sum of digits in one's position will be 6 x (1+3+5+7) = 96.Similar is the case in ten's,hundred's and thousand's places.

Therefore,the sum will be 96 + 96 x 10 + 96 x 100 + 96 x 100 = 106656

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Q:

If each side of a square is increased by 25%, find the percentage change in its area.

A) 56.25%	B) 36.25%
C) 16.25%	D) 12.25%

Answer & Explanation Answer: A) 56.25%

Explanation:

Let each side of the square be a. Then, area = . $a^{2}$
New side = $\frac{125 a}{100} = \frac{5 a}{4}$ . New area = ${(\frac{5 a}{4})}^{2}$ = $(\frac{25 a^{2}}{16})$

Increase in area = $\frac{25 a^{2}}{16} - a^{2} = \frac{9 a^{2}}{16}$
Increase% = $[\frac{9 a^{2}}{16} * \frac{1}{a^{2}} * 100]$ % = 56.25%.

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

Q:

In how many different ways can 3 students be associated with 4 chartered accountants,assuming that each chartered accountant can take at most one student?

A) 12	B) 36
C) 24	D) 16

Answer & Explanation Answer: C) 24

Explanation:

Number of permutations = $4 P_{3}$ = 24

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Q:

First,second and third prizes are to be awarded at an engineering fair in which 13 exhibits have been entered.In how many different ways can the prizes be awarded?

A) 1736	B) 1716
C) 1216	D) 1346

Answer & Explanation Answer: B) 1716

Explanation:

$13 P_{3}$ = 13!/10! = 1716

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Q:

The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

A) 20%	B) 30%
C) 40%	D) 50%

Answer & Explanation Answer: D) 50%

Explanation:

Let original length = x and original breadth = y.

Original area = xy.

New length = x/2 and New breadth=3y

New area = $\frac{3}{2} x y$

Therefore, Increase in area = New area-original area = $\frac{3}{2} x y - x y = \frac{1}{2} x y$

Therefore, Increase % = $\frac{i n c r e a s e i n a r e a}{o r i g i n a l a r e a} * 100 = (\frac{\frac{1}{2} x y}{x y}) * 100 = 50$ %

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

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