Test:- Permutations And Combinations - 8

# Test:- Permutations And Combinations - 8

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## 20 Questions MCQ Test Topic-wise Tests & Solved Examples for IIT JAM Mathematics | Test:- Permutations And Combinations - 8

Test:- Permutations And Combinations - 8 for Mathematics 2022 is part of Topic-wise Tests & Solved Examples for IIT JAM Mathematics preparation. The Test:- Permutations And Combinations - 8 questions and answers have been prepared according to the Mathematics exam syllabus.The Test:- Permutations And Combinations - 8 MCQs are made for Mathematics 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test:- Permutations And Combinations - 8 below.
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Test:- Permutations And Combinations - 8 - Question 1

### Eight chairs numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number of possible arrangement

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 1

Eight chair 1 to 8
2 women choose the chair from 1 to 4 = 4P2
3 men choose the chair from remaining = 6P3
4P2 x 6P3

Test:- Permutations And Combinations - 8 - Question 2

### If the letter of the word FATHER are written in all possible orders and these words are written out as in a dictionary, then the rank of the word FATHER is:

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 2

Rank of father

Test:- Permutations And Combinations - 8 - Question 3

### A five digit number divisible by 3 is to be formed using the number 0,1,2,3,4,5 without repetition The total number of ways this can be done is :

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 3

If the sum of digits of the number is divisible by 3 then number is divisible by 3

Total = 216

Test:- Permutations And Combinations - 8 - Question 4

An office has 5 computers that are connected together in a linear network (i.e. they will be arranged in 5 position on one straight on one straight connecting cable, see figure below). Communication can go either way along the cable. In how many different ways they are arranged?

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 4

Test:- Permutations And Combinations - 8 - Question 5

Total number of ways in which Six ‘+’ and four '-' signs occur together is :

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 5

-+-+-+-+-+-+-

Test:- Permutations And Combinations - 8 - Question 6

A bin of personal computer disks contains a large supply of disks from 4 different manufactures. In how many ways someone choose 6 disks from the bin?

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 6

a + b + c + d = 6

Test:- Permutations And Combinations - 8 - Question 7

How many numbers greater than 1000, but not greater than 4000 can be formed with the digits 2,1,2,3,4 repetition of the digit being allowed?

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 7

Numbers greater than 1000 but less than 4000 formed with digit 0,1,2,3,4 will be
3.5.5.5+1-1 = 375-1+1
= 375

Test:- Permutations And Combinations - 8 - Question 8

20 persons were invited for a party. The number of ways in which they and the host can be seated at a circular table such that two particulars persons be seated on either side of the host is:

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 8

2(18!)

Test:- Permutations And Combinations - 8 - Question 9

The number of triangle whose vertices are at the vertices of an octagon but none of whose sides come from the sides of the octagon is:

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 9

Test:- Permutations And Combinations - 8 - Question 10

A man has 7 relatives, 4 of them are ladies and 3 gentlemen. His wife has 7 relatives, 3 of them are ladies and 4 gentleman. Then the number of ways the couple can invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of the man’s relative and 3 of the wife's relatives is equal to:

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 10

Test:- Permutations And Combinations - 8 - Question 11

A box contain two white balls, three black balls and 4 red balls. In how many ways can three balls be drawn from the box, if at least one black ball is to be included in the draw is:

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 11

2W, 3B, 4R
1st method
At least one black ball out of 3 ball

= 84 - 20 = 64
2nd method

Test:- Permutations And Combinations - 8 - Question 12

If in a party everybody shake hand with everybody else and there are 36 handshakes in all how many persons are there in the party?

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 12

Test:- Permutations And Combinations - 8 - Question 13

If 15C3r = 15C3r+3' then r =

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 13

Test:- Permutations And Combinations - 8 - Question 14

There are 3 copies each of 4 different books in how many way can they be arranged in a shelf?

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 14

Test:- Permutations And Combinations - 8 - Question 15

The sum of all the numbers that can be formed with the digits the 2,3,4,5 taken all at a time is :

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 15

Test:- Permutations And Combinations - 8 - Question 16

The number of ways in which one or more balls can be selected out of 10, 9 green and 7 blue balls is:

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 16

Total ways (10 + 1) (9 + 1) (7 + 1)-1
= 110 x 8 - 1
= 880- 1 = 879

Test:- Permutations And Combinations - 8 - Question 17

The number of ways in which a score of 11 can be obtained from a throw by three persons each throwing a single dice is :

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 17

It is equal to sum of three integral values being equal to 11 with each of them lying from 1 to 6 i.e. 3 + 4 + 5 + 6 + 5 + 4 = 27 ways

Test:- Permutations And Combinations - 8 - Question 18

At an election, three ward of a town are canvassed by 4,5 and 8 men respectively, if 20 men are voluntier, in how many ways can they be allotted to the different wards?

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 18

Test:- Permutations And Combinations - 8 - Question 19

How many different permutation can be formed from the letter of the word EXAMINATION taken four at a time?

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 19

Test:- Permutations And Combinations - 8 - Question 20

A tea party is arranged for 16 people along table with eight chair on each side, four men wish to sit on one particular side and two on the other side. In how many ways they can be seated?

Detailed Solution for Test:- Permutations And Combinations - 8 - Question 20

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