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This mock test of Test:- Permutations And Combinations - 2 for Mathematics helps you for every Mathematics entrance exam.
This contains 20 Multiple Choice Questions for Mathematics Test:- Permutations And Combinations - 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

How many numbers divisible by 5 and lying between 3000 and 5000 can be formed from the digit 0,3,4,5, and 7?

Solution:

First place will be filled by 3 or 4 2nd by 5, 3rd & 4^{th} by 2 so total way.

= 2 x 5 x 5 x 2 = 100-1

= 99 ; (-1 is to exclude 3000)

QUESTION: 2

Total number of natural numbers less than 4000 formed with digits 0,1,2,3,4,5 and 8 is :

Solution:

The one digit number will be 6

The 2 digit number will be

6 x 7 = 42

The 3 digit number will be

6 x 7 x 7 = 294

The 4 digit unit number will be

3 x 7 x 7 x 7 = 1029

so total number from 0 to 4000 excluding 4000 will be

6 + 42 + 294+ 1029= 1371

QUESTION: 3

Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of person in the room is

Solution:

Total handshakes = ^{n}C_{2} = 66

⇒ n = 12 (only) as negative answer is not valid.

QUESTION: 4

The sum of the digits in the digits unit place of all the numbers formed with the help of 3,4,5,6 taken all at a time is :

Solution:

We can arrange this number in 4! way i.c. 24 way and each digit appear 3! times at each place, so each number come on unit place 6 time so sum = (3 + 4 + 5 +6) * 6

= 18 x 6 = 108

QUESTION: 5

If^{ n}C_{n-1} = 36; ^{n}C_{r} = 84 and ^{n}C_{r+1} = 126, then r is equal to:

Solution:

⇒ n - 9 and r = 3

QUESTION: 6

If ^{n}P_{r}=^{ n}P_{r+1} and ^{n}C_{r}= ^{n}C_{r-1} then (n,r) are

Solution:

QUESTION: 7

If ^{28}C_{r} : ^{24}C_{n+4} = 225 : 11, then

Solution:

so, r = 14

QUESTION: 8

If ^{n}C_{r} + ^{n}C_{r+1} = ^{n+3}C_{x}, then x =

Solution:

QUESTION: 9

The total number of arrangement that can be made out of the letter of the word RAMANEA is:

Solution:

QUESTION: 10

If ^{n-1}c_{3} / ^{n-1}c_{4} > ^{n}c_{3}, then the least value of n is:

Solution:

QUESTION: 11

If the letter of the word BROTHER are written in all possible order and these word are written out as in a dictionary, then the rank of the word BROTHER is:

Solution:

BROTHER B, E, T, H, O : 1, R : 2

Total = 249

QUESTION: 12

The rank of the word ‘RAMANEA’ in the dictionary made by the letters of this word is:

Solution:

QUESTION: 13

The sum of the numbers formed by the digit 1,3,5 and 7 taking all at a time is:

Solution:

The sum of all number formed by the digit 1,3,5,7 is

QUESTION: 14

Let A be a set containing 10 distinct elements, Then the total number of distinct function from A to A is. :

Solution:

The total number of distinct function is 10^{10}.

QUESTION: 15

There are 10 lamps in a hall. Each one of them can be switched on independently. The number of ways in which the hall can be illuminated is :

Solution:

The total number of way in which way we can do switches are

2^{10} -1 = 1024-1=1023

-1 so that at least one switch will be on for light in the hall.

QUESTION: 16

Out of 16 players of cricket team, 4 are bowlers and 2 are wicket keepers. A team of 11 players is to be chosen so as to contain at least 3 bowlers and at least one wicket keeper. The number of ways in which the team be selected is :

Solution:

QUESTION: 17

Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to :

Solution:

Selecting 2 vowels and 3 consonants from 4 vowels and 5 consonants will be in

and the number of way in which we can arrange the 5 letters is 5!

so, 60 x 5! = 60 x 120 = 7200

QUESTION: 18

The total number of 9 digits number which have all different digits is :

Solution:

We have number from 0 to 9 so on first place we will put any 9 letter and after that we put digits into remaining place in ^{9}P_{8} = 9! ways

so, total ways

= 9x 9!

QUESTION: 19

The number of different number of six digits each (without repetition of digit) can be formed from the digits 4,5,6.7,8,9 such that they are not divisible by 5 is :

Solution:

Last place we will be of 5 types because we exclude 5 there and a fter that simply use all freely.

QUESTION: 20

A polygon has 54 diagonals, then the number of its sides arc :

Solution:

We have a very good formula

where x in number of diagonal and n stand for number of sides so putting the value.

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