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Test:- Permutations And Combinations - 6 - Mathematics MCQ


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20 Questions MCQ Test Topic-wise Tests & Solved Examples for Mathematics - Test:- Permutations And Combinations - 6

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Test:- Permutations And Combinations - 6 - Question 1

A code word consisis of three letters of the English alphabet followed by two digits of the decimal system. If neither letter nor digit is repeated in any code word, the total number of code words is:

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 1

Test:- Permutations And Combinations - 6 - Question 2

There are n straight lines in a plane in which no two are parallel and no three pass through the same point. Their points of intersection are joined. Show that the number of fresh lines thus introduced is

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 2

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Test:- Permutations And Combinations - 6 - Question 3

The number of signals that, can be generated by using 6 differently colored flags, when any number of them may be hoisted at a time is:

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 3

Total number signals can be generated by 6 diff. Hags = 
6 + 30 + 120 + 360 + 720 + 720 
= 1956

Test:- Permutations And Combinations - 6 - Question 4

 If n is even and nC0 < nC1 < nC2 < .... nCr > nCr+1 > nCr-2 > .... nCn  Then r = ?

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

r = n /2 gives the maximum value

Test:- Permutations And Combinations - 6 - Question 5

The principal wants to arrange 5 students on the platform such that the boy SALIM occupies the second position and such that the girl SITA is always adjacent to the girl RITA. How many such arrangement are possible:?

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 5

3 & 4 or 4 or 5 number places should go to the two girls; ways = 2 x 2! x 2! = 8

Test:- Permutations And Combinations - 6 - Question 6

For a set of five true/false questions, no student has written all correct answers, and no students have given the same sequence of answer. What is the maximum number of students in the class, for this to be possible?

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

Maximum number of student is
= 2- 1 = 31

Test:- Permutations And Combinations - 6 - Question 7

In a certain test, αi, students gave wrong answers to at least i questions, where i = 1,2,3.4...k. No student gave more than k wrong answers the total number of wrong answers given is :

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 7

Test:- Permutations And Combinations - 6 - Question 8

In how many ways can 10 balls be divided between two boys. One receiving two and the other eight balls?

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

Test:- Permutations And Combinations - 6 - Question 9

Three men have 4 coats, 5 waist coat and 6 caps. In how many ways can they wear them?

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 9

 4 coats, 5 waists coats, 6 caps 

Test:- Permutations And Combinations - 6 - Question 10

How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digit occupy even positions?

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 10

 9 digit number should be

Test:- Permutations And Combinations - 6 - Question 11

How many numbers greater than 10 lacs be formed from 2,3,0,3,4,2,3.

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 11

Total number greater than 10 lacs fomed with

Test:- Permutations And Combinations - 6 - Question 12

Five digil number divisible by 9 are to be formed by using the digit 0,1,2,3,4,7,8 (without repetition). The total number of such numbers is equal to

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 12

 If the sum of digit is dvisible by 9 then number is divisible by 9.
So, (0,7), (2,5) or (3,4)
will not be taken in formation of number.
So no. of ways 5!+2 (4 (4 !))
= 120 + 2(96)= 312

Test:- Permutations And Combinations - 6 - Question 13

Even numbers are formed with three digits such that if 5 is one of the digit then 7 is the next digit. The number of such numbers is (repetition is allowed).

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 13

5 will be followed by 7, but 7 can come independently, (none is correct)

Test:- Permutations And Combinations - 6 - Question 14

The number of divisiors of 9600 including 1 and 9600 is

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 14

number of divisor of 9600

Test:- Permutations And Combinations - 6 - Question 15

Out of 5 computers scientist and 7 mathematician a committee consisting of 2 computer scientists and 3 mathematicians is to be formed. The number of ways in which this can be done if any computer scientists and any mathematician can be included is :

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 15

No. of ways =

Test:- Permutations And Combinations - 6 - Question 16

If (rn ≠ 0) is positive integer, then the number of positive integeral solution of x + y + z + t = m is

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 16

Test:- Permutations And Combinations - 6 - Question 17

Number of diagonals in a convex n sided polygon is :

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 17

nc2 - n

Test:- Permutations And Combinations - 6 - Question 18

In a certain town the streets are arranged like the lines of a chess board. There are 6 street running north and south ard 10 running east and west. These number of ways in which a man can go N.W. corner to the S.E. corner covering the shortest possible distance in each case is :

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 18

No. of ways  =

Test:- Permutations And Combinations - 6 - Question 19

We have 5 locks and 5 keys to them. How many trails must we make in the least favourable cases to establish the correspondence between the locks and the keys?

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 19

4 + 3 + 2 + 1 = 10

Test:- Permutations And Combinations - 6 - Question 20

25 points, no 3 co-linear are given in a plane. How many triangles do they determine?

Detailed Solution for Test:- Permutations And Combinations - 6 - Question 20

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