Shubham has to make a telephone call to his friend Nisheeth. Unfortunately, he does not remember the 7 digit phone number. But he remembers that the first three digits are 635 or 674 , the number is odd and there is exactly one 9 in the number. The maximum number of trials that Shubham has to make to be successful is N then N - 3400 is equal to

The number of digits in the phone number is 7 , Place 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th Possible digits As given, in question, in the 1 st , 2 nd and 3 rd place possible inputs are either 6 , 3 and 5 or 6 , 7 and 4 . So, number of possible conditions = 2 . Now, if the 7 th place is occupied by an odd digit 1 or 3 or 5 or 7 and exactly one digit 9 is there in the number so, digit 9 can occupy 4 th , 5 th or 6 th place, and remaining places will be occupied by digits 0 to 8 , So, the number of such possible numbers = 3 × 4 × 9 × 9 = 972 Now, if the 7 th place can be occupied by the digit 9 , So, the 4 th, 5 th and 6 th place can be occupied by digits 0 to 8 . Hence, the number of such numbers = 9 × 9 × 9 = 729 . So the number of total possible numbers N = 2 972 + 729 = 3402 Hence, N - 3400 = 2 .

HARD

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IMPORTANT

Earn 100

Find the number of all rational numbers $\frac{m}{n}$ such that:

(i) $0 < \frac{m}{n} < 1$

(ii) $m$ and $n$ are relatively prime

(iii) $m \cdot n = 25!$

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Important Questions on Permutation and Combination

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 21

The number of five-digit numbers divisible by

3

that can be formed using the digits

0, 1, 2, 3, 4, 7

and

8,

if each digit is to be used at most one is

N

then

(\frac{N}{8})

is equal to

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 22

The side

A B, B C a n d C A

of a triangle

A B C

have

3, 4 a n d 5

interior points respectively on them. Find the number of triangles that can be constructed using these interior points as vertices.

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 23

Shubham has to make a telephone call to his friend Nisheeth. Unfortunately, he does not remember the

7

digit phone number. But he remembers that the first three digits are

635

674,

the number is odd and there is exactly one

9

in the number. The maximum number of trials that Shubham has to make to be successful is

N

then

(N - 3400)

is equal to

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 24

Seven different coins are to be divided amongst three persons. If no two of the persons receive the same number of coins but each receives atleast one coin & none is left over, then the number of ways in which the division may be made is

k,

then

(\frac{k}{10})

is equal to.

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 25

The number of ways in which five vowels of English alphabets and ten decimal digits can be placed in a row such that between any two vowels, odd number of digits are placed and both end places are occupied by vowels, is

20 (b!) (5!)

. Then evaluate

b

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 26

The number of integers which lie between

1

and

10^{6}

and which have the sum of the digits equal to

12

N

then

N - 6000

is equal to

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 27

The number of ways in which

8

non-identical apples can be distributed among

3

boys such that every boy should get atleast

1

apple & atmost

4

apples is

N

then

(\frac{N}{60})

is equal to

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-2>Q 28

in a hockey series between team

X

and

Y,

they decide to play till a team wins

' 10'

match. Then the number of ways in which a team

X

wins is

\frac{{}^{20}C_{m}}{2}

then

m

is equal to

Find the number of all rational numbers mn such that: (i) 0<mn<1 (ii) m and n are relatively prime (iii) m·n=25!

Important Questions on Permutation and Combination

Learn and Prepare for any exam you want !

Find the number of all rational numbers $\frac{m}{n}$ such that:

(i) $0 < \frac{m}{n} < 1$

(ii) $m$ and $n$ are relatively prime

(iii) $m \cdot n = 25!$