Teachoo MCQ Test

10 Question MCQ (including Assertion)

Chapter 6 Class 11 Permutations and Combinations | 10 questions

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Question 1 of 10
Question 1 of 10
NCERT Exemplar
The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is
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Question 2 of 10
Assertion (A): A committee of 3 members is to be formed from 3 boys and 2 girls. The number of ways to form this committee such that it contains at least one girl is 9.

Reason (R): The number of combinations with "at least one" restriction can be calculated by subtracting the number of combinations with "none" from the "total" possible combinations without restriction.
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Question 3 of 10

A suitcase has a 4-wheel number lock using the digits 0 to 9. The correct code has no repeated digit. The first digit is known to be 7, as shown below. How many possible settings remain to be checked?

Four-wheel number lockThe first wheel is fixed at 7 and the other three wheels are unknown.7???

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Question 4 of 10

Assertion: A chairperson and a vice-chairperson can be chosen from 8 persons in \({}^{8}C_{2}=28\) ways.


Reason: Assigning A as chairperson and B as vice-chairperson is different from assigning B as chairperson and A as vice-chairperson.

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Question 5 of 10
Assertion (A): The number of ways to arrange the letters of the word "ROSE" such that the vowels (O, E) are always together is 12.

Reason (R): When specific objects must occur together, they are treated as a single object for the arrangement, and then arranged internally among themselves.
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Question 6 of 10

Assertion: Using the digits 1, 2, 3, 4, 5 and 6 without repetition, 60 different 3-digit even numbers can be formed.


Reason: Since the digits are not repeated and their order matters, the problem involves permutations.

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Question 7 of 10
NCERT Exemplar
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is
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Question 8 of 10

Assertion: When all distinct arrangements of the letters of AGAIN are written in dictionary order, the 50th word is NAAIG.


Reason: There are 24 words beginning with A, 24 beginning with G and 24 beginning with I; therefore, 72 words occur before the first word beginning with N.

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Question 9 of 10

Assertion: Five distinct girls and three distinct boys can be seated in a row in 14400 ways so that no two boys sit together.


Reason: After arranging the girls in \(5!\) ways, there are 6 available gaps, and the three distinct boys can be placed in these gaps in \({}^{6}P_{3}\) ways.

× G × G × G × G × G ×
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Question 10 of 10
In an examination there are three multiple choice questions and each question has 4 choices. Number of ways in which a student can fail to get all answer correct is
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