Teachoo MCQ Test

10 Question MCQ (including Assertion)

Preparing for CBSE

Chapter 6 Class 11 Permutations and Combinations | 10 questions

Timed test. Answer every question before time runs out. Correct answers and solutions appear after submission.
Time remaining 912
Question 1 of 10
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Question 1 of 10
Assertion (A): The number of ways to select a team of 3 players from a group of 5 players is 60.

Reason (R): In a combination, the order of selection is not important.
Select one option. Answers are shown after the test.
Question 2 of 10

Assertion: If 12 persons each shake hands once with every other person, the total number of handshakes is 66.


Reason: Each person shakes hands with 11 others, so there are \(12\times 11=132\) different handshakes.

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Question 3 of 10
Assertion (A): The number of ways to arrange 3 boys and 2 girls in a row is 120.

Reason (R): The number of permutations of \(n\) different objects taken all at a time is \(n!\).
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Question 4 of 10
Assertion (A): The value of \({}^{15}C_{10}\) is exactly equal to the value of \({}^{15}C_{5}\).

Reason (R): Selecting \(r\) objects out of \(n\) is the same as rejecting \((n-r)\) objects, hence \({}^nC_r = {}^nC_{n-r}\).
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Question 5 of 10
Assertion (A): If \({}^nP_3 = 60\), then the value of \(n\) is 5.

Reason (R): The number of permutations is given by \({}^nP_r = \frac{n!}{(n-r)!}\).
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Question 6 of 10

Assertion: The letters of DAUGHTER can be arranged in 4320 ways if all three vowels are together.


Reason: Since all eight letters of DAUGHTER are distinct, their total number of unrestricted arrangements is \(8!\).

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Question 7 of 10

Evaluate \(\dfrac{8!}{6!}\).

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Question 8 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 9 of 10
NCERT Exemplar
Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is
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Question 10 of 10
NCERT Exemplar
The number of possible outcomes when a coin is tossed 6 times is
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