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 864
Question 1 of 10
Advertisement
Question 1 of 10

If \(\dfrac{1}{6!}+\dfrac{1}{7!}=\dfrac{x}{8!}\), then the value of \(x\) is

Select one option. Answers are shown after the test.
Question 2 of 10

Assertion: A 3-member committee can be selected from 8 persons in \({}^{8}C_{3}=56\) ways.


Reason: In a committee, selecting A, B and C gives the same committee regardless of the order in which they are selected.

Select one option. Answers are shown after the test.
Question 3 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
Select one option. Answers are shown after the test.
Question 4 of 10
NCERT Exemplar
The number of possible outcomes when a coin is tossed 6 times is
Select one option. Answers are shown after the test.
Question 5 of 10

Assertion: If \({}^{n}C_{8}={}^{n}C_{2}\), then \(n=10\) and \({}^{n}C_{2}=45\).


Reason: If \({}^{n}C_{r}={}^{n}C_{s}\) and \(r\neq s\), then \(r+s=n\).

Select one option. Answers are shown after the test.
Question 6 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.
Select one option. Answers are shown after the test.
Question 7 of 10
NCERT Exemplar
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
Select one option. Answers are shown after the test.
Question 8 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???

Select one option. Answers are shown after the test.
Question 9 of 10
Assertion (A): If \({}^nC_x = {}^nC_y\) and \(x \neq y\), then \(n = x - y\).

Reason (R): The formula for complementary combinations states that \({}^nC_r = {}^nC_{n-r}\).
Select one option. Answers are shown after the test.
Question 10 of 10
NCERT Exemplar
The total number of 9 digit numbers which have all different digits is
Select one option. Answers are shown after the test.