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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 :

Solution:

QUESTION: 2

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

Solution:

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 :

Solution:

Each value of roll should lie between 1 and 6 and sum should be 11.

= 3 + 4 + 5 + 6 + 5 + 4 = 27 ways

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 :

Solution:

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

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 :

Solution:

QUESTION: 6

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

Solution:

Total number of signal can be generated from 6 different colour

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 :

Solution:

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

Total cases

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.

Solution:

Sum of all number greater than 10000

formed by using digit 0. 2, 4, 6, 8

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 :

Solution:

Total friends = 6

so, required value =

In our case at least two means all cases except all correct

= 6! - 1 = 720 - 1 = 719.

QUESTION: 10

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 :

Solution:

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 :

Solution:

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 :

Solution:

Six coins selection from 20 one rupees 10,50 p and 7,25 p coins

i.e. x + y + z = 6

= 28 ways

QUESTION: 13

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

Solution:

Total number of way to picture nails on the wall

= n^{f}= 5^{7}

QUESTION: 14

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

Solution:

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

= 4^{5}

QUESTION: 15

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

Solution:

Selecting 10 balls from unlimitted red. black white and green

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:

Solution:

Total number of even number of 3 digit

= 5 + 360 = 365

QUESTION: 17

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

Solution:

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

Solution:

(5 + 1)(10 + 1)(7 + 1)-1 ways

= 528-1

= 527

QUESTION: 19

The number of positive integer satisfying ^{n+1}C_{n-2} - ^{n+1}C_{n-1} ≤ 1000 is:

Solution:

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 :

Solution:

We select from 1 to 30 so as to exclude every selection of four consecutive number in ^{30}C_{4} - 27 ways

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