Test:- Permutations And Combinations - 1


20 Questions MCQ Test Topic-wise Tests & Solved Examples for IIT JAM Mathematics | Test:- Permutations And Combinations - 1


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Attempt Test:- Permutations And Combinations - 1 | 20 questions in 60 minutes | Mock test for Mathematics preparation | Free important questions MCQ to study Topic-wise Tests & Solved Examples for IIT JAM Mathematics for Mathematics Exam | Download free PDF with solutions
QUESTION: 1

There are 3 candidate for a Mathematics, 5 for chemistry and 4 for a Physics scholarship. In how many ways can the scholarship be awarded.

Solution:

There are 3 candidates of math.
There arc 5 candidates of chemistry.
There arc 4 candidates of physics,
so total way = 3 * 4 * 5 = 60

QUESTION: 2

How many three-digits number can be formed without using the digits 0,1,2,3,7,9,?

Solution:

remaining digits are 4,5,6,8
so method are 43 = 64

QUESTION: 3

How many numbers are there between 1000 and 2000 such that even' digit is either 0, or 1, or 2?

Solution:

No. between 1000 and 2000 [0, 1,2]
1 3C1, 3C2, 3C1' = 27- 1 -26

QUESTION: 4

How many numbers are there between 2000 and 20000 such that 2 is in the unit place.

Solution:

QUESTION: 5

How many number are there between 100 and 1000 such that at least one of their digit is 3?

Solution:


QUESTION: 6

From 7 English and 4 American a committee of 6 is to be formed which contains at least two American. The number of ways in which this committee can be formed is :

Solution:

QUESTION: 7

The number of ways in which an arrangement of 4 letters of the word ‘PROPORTION’ can be made is :

Solution:

QUESTION: 8

Total number of positive integral solution of x + y + z = 24 is :

Solution:

QUESTION: 9

Total number of non-negative integral solution of
x + y + z + I = 15

Solution:

QUESTION: 10

The number of ways in which 15 coins, not distinguishable from one another may be divided among 4 person, so that no one may have less than three coins is :

Solution:

QUESTION: 11

Total number of integral solution of the equation
x1 + x2 + x3 = 15, where x1 ≥1, x2 ≥ 3, x3 ≥ 0 is :

Solution:

QUESTION: 12

How many integral solution are there to the system of equation x1 + x2 + x3+ x4 + x5 = 20 and x1 + x2 + x3 = 5, where xk ≥ 0;

Solution:

QUESTION: 13

The number of non-negative integral solution of
x1 + x2 + x3 + 3x4 = 18 is

Solution:

QUESTION: 14

The number of ways in which thirty-five apples can be distributed among 3 boys, so that each car. have any number of apple is :

Solution:

QUESTION: 15

Number of ways in which Rs. 22 can be distributed among four persons such that a first-person get less than Rs. 3 and second person gets multiple of Rs. 4 is:

Solution:

Rs. 22 is distributed among 4 person

QUESTION: 16

The total number of four digit numbers formed from the digit 0,3,4,5,6,9 such that even digits are placed on even place is - (Any digit will not be repeated)

Solution:

 0,3,4,5,6,9 solution for 4 digit number where even plane have even digit
3 3 2 2 = 36 ways

QUESTION: 17

How many four digit numbers which are divisible by 4 can be formed from the digit 1,2,3,4 and 5? (Any digit may be repeated)

Solution:

If first place will be filled by 0,4,8 then before that we write even thing and if last place will be filled by 2,6 then odd number.
so, two cases are there

so total way = 50 + 75 = 125

QUESTION: 18

Six person entered the lift cabin on ground floor of an 7-floor house. Suppose each of them can leave the cabin independently at any floor beginning with the first. The total number of ways in which each of the six person can leave the cabin at any one of the 6-floors.

Solution:

The total number of ways will be 66

QUESTION: 19

. How many numbers are there between 1000 and 4000 which have exactly one of their digit as 3?

Solution:

When we fill first place with 3, then

so between 1000 and 4000 1215 number contain 3.

QUESTION: 20

How many numbers are there between 400 and 1000 such that atleast one of their digit 3?

Solution:

It will be such 3 digit numbers starting with 4 onwards

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