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Test:- Permutations And Combinations - 4 - Mathematics MCQ


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20 Questions MCQ Test Topic-wise Tests & Solved Examples for Mathematics - Test:- Permutations And Combinations - 4

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Test:- Permutations And Combinations - 4 - Question 1

Between two functional stations A and B, there are 12 intermediate station. The number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive is :

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 1


Test:- Permutations And Combinations - 4 - Question 2

The number of non-negative integral solution of x - y + z ≤ 10 is

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 2


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Test:- Permutations And Combinations - 4 - Question 3

The number of ways in which a score of a 11 can be made from a throw by three persons, each throwing a single die once is :

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 3

Each value of roll should lie between 1 and 6 and sum should be 11.
= 3 + 4 + 5 + 6 + 5 + 4 = 27 ways 

Test:- Permutations And Combinations - 4 - Question 4

Given that n is odd, the number of ways in which three numbers in A.P. can be selected from 1,2,3,...n is :

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

1,2,3,....,n

Test:- Permutations And Combinations - 4 - Question 5

The number of triangles whose vertices are at the Venices of an octagon but none of whose sides happen to come from the sides of the octagon is :

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 5

Test:- Permutations And Combinations - 4 - Question 6

The number of signals, that can be generated by using 6 differently coloured flags is :

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 6

Total number of signal can be generated from 6 different colour

Test:- Permutations And Combinations - 4 - Question 7

In a game, 10 participants are there the number of ways in which, the rank of first participant is always above 10th participant is :

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 7

Total participants are 10 ; the rank of 1st participant is always above 10th participant in half of the total possible cases.
Total cases

Test:- Permutations And Combinations - 4 - Question 8

The sum of all numbers greater than 10.000 formed by using the digits 0,2,4,6.8. Non digit being repated in any number.

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

Sum of all number greater than 10000
formed by using digit 0. 2, 4, 6, 8 

Test:- Permutations And Combinations - 4 - Question 9

A person writes letters to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are placed in wrong envelopes, is :

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 9

Total friends = 6
so, required value = 
In our case at least two means all cases except all correct
= 6! - 1 = 720 - 1 = 719.

Test:- Permutations And Combinations - 4 - Question 10

A person writes letters to six friends and addresses the corresponding envelopes.

In above question in how many ways can the letters be placed in the envelops so that all the letters are in the wrong envelopes is :

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 10

Test:- Permutations And Combinations - 4 - Question 11

In an election, there are 10 candidates out of which 4 have to be elected. A voter can forecast hi most 4 votes. Then the number of ways in which he can forecast his vote is :

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 11

Test:- Permutations And Combinations - 4 - Question 12

The total number of ways of selecting six coins out of 20 one rupee coins, 10 fifty paise coins and 7 twenty five paise coins is :

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 12

 Six coins selection from 20 one  rupees 10,50 p and 7,25 p coins
i.e. x + y + z = 6

= 28 ways 

Test:- Permutations And Combinations - 4 - Question 13

The number of ways in which 7 pictures can be hung from 5 picture nails on the wall is :

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 13

Total number of way to picture nails on the wall
= nf= 57

Test:- Permutations And Combinations - 4 - Question 14

The number of ways in which 5 letters can be posted in 4 letter boxes is:

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 14

Total number of ways 5 letters can be posted is 4 letter box
= 45

Test:- Permutations And Combinations - 4 - Question 15

The number of ways of selecting 10 balls from unlimited number of red, black, white, and green balls is

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 15

Selecting 10 balls from unlimitted red. black white and green

Test:- Permutations And Combinations - 4 - Question 16

How many even numbers are there with three digits such that if 5 in one of the digits then 7 the next digits is:

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 16

Total number of even number of 3 digit
= 5 + 360 = 365

Test:- Permutations And Combinations - 4 - Question 17

The number of all three elements subsets of the set {1,2,3,... 10} which contains 4 is :

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 17

All three element subset of the set {1, 2 ,3 ...... 10} containing 4

Test:- Permutations And Combinations - 4 - Question 18

The number of ways in which one or more book can be selected out of 5 similar mathematics, 10 similar physics and 7 similar chemistry books is :

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 18

(5 + 1)(10 + 1)(7 + 1)-1 ways 
= 528-1
= 527

Test:- Permutations And Combinations - 4 - Question 19

The number of positive integer satisfying n+1Cn-2 - n+1Cn-1 ≤ 1000 is:

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 19


Test:- Permutations And Combinations - 4 - Question 20

The number of ways in which we can select four numbers from 1 to 30 so as to exclude every selection of four consecutive numbers is :

Detailed Solution for Test:- Permutations And Combinations - 4 - Question 20

We select from 1 to 30 so as to exclude every selection of four consecutive number  in 30C4 - 27 ways

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