Permutations And Combinations CBSE Questions & Answers

Permutations And Combinations

This is Mathematics Class 11 Permutations and Combinations CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
In a multiple choice question, there are 4 alternatives, of which one or more are correct. The number of ways in which a candidate can attempt this question is
  • A
    \({2^5}\)
  • B
    4
  • C
    none of these
    Correct
  • D
    16
2
In how many ways can the letters of the word ‘MATHEMATICS ‘be permuted so that consonants always occur together?
  • A
    \({{7!5!} \over {2!2!2!}}\)
    Correct
  • B
    \({{7!4!} \over {2!2!2!}}\)
  • C
    none of these
  • D
    \({{8!5!} \over {2!2!2!}}\)
3
The number of triangles that can be formed with 6 points on a circle is
  • A
    6
  • B
    20
    Correct
  • C
    15
  • D
    12
4
Number of ways in which 10 different things can be divided into two groups containing 6 and 4 things respectively is
  • A
    C(10 , 4)
    Correct
  • B
    P(10,6)
  • C
    P(10,4)
  • D
    P(10,2)
5
The number of selections of n different things taken r at a time which exclude a particular thing is
  • A
    r C(n-1,r)
  • B
    C(n-1,r)
    Correct
  • C
    nC(n-1,r-1)
  • D
    none of these
6
The number of arrangements of n different things taken r at a time which include a particular thing is
  • A
    n P(n-1,r)
  • B
    r P (n-1,r-1)
    Correct
  • C
    P(n-1, r-1 )
  • D
    none of these
7
The number of arrangements of n different things taken r at a time which exclude a particular thing is
  • A
    P(n.r)
  • B
    nP(n-1,r-1)
  • C
    none of these
  • D
    P(n-1,r)
    Correct
8
5 persons board a lift on the ground floor of an 8 storey building. In how many ways can they leave the lift?
  • A
    \({7^5}\)
    Correct
  • B
    \({}^7{P_5}\)
  • C
    none of these
  • D
    \({5^7}\)
9
If C(12,4) + C(12,5) = C(n,5) ,then n is equal to
  • A
    none of these
  • B
    13
    Correct
  • C
    12
  • D
    11
10
The number of ways in which a necklace can be formed by using 5 identical red beads and 6 identical white beads is:
  • A
    \({{10!} \over {2(6!5!)}}\)
    Correct
  • B
    \({{11!} \over {2(6!5!)}}\)
  • C
    \({{10!} \over {(6!5!)}}\)
  • D
    none of these.
11
A fair dice is rolled n times. The number of all the possible outcomes is
  • A
    \({6^n}\)
    Correct
  • B
    none of these
  • C
    6n
  • D
    \({n^6}\)
12
The sum of all the numbers which can be formed by using the digits 1 , 3 , 5 , 7 ,9 all at a time and which have no digit repeated is
  • A
    \({\text{25 }} \times {\text{ 11111 }} \times 5!\)
  • B
    \({\text{11111}} \times {\text{ }}4!\)
  • C
    \({\text{25 }} \times {\text{ 11111 }} \times 4!\)
    Correct
  • D
    \({\text{25 }} \times 4!\)
13
4 boys and 4 girls are to be seated in a row. The number of ways in which this can be done, if the boys and girls sit alternately, is
  • A
    \({\text{2 }} \times 4!{\text{ }} \times {\text{ }}4!\)
    Correct
  • B
    none of these
  • C
    P(8,8)
  • D
    \(4!{\text{ }} \times {\text{ }}4!\)
14
The letters of the word ‘SOCIETY’ are arranged in such a manner that the vowels and consonants occur alternately, the number of different words so obtained is
  • A
    none of these
  • B
    \(2{\text{ }} \times {\text{ }}4!{\text{ }} \times {\text{ }}3!\)
  • C
    \({\text{7}}!\)
  • D
    \({\text{4}}!{\text{ }} \times {\text{ }}3!\)
    Correct
15
There are 10 true-false questions. The number of ways in which they can be answered is
  • A
    10
  • B
    \({2^{10}}\)
    Correct
  • C
    \({\text{1}}0!\)
  • D
    none of these