If ${}^{22}{\mathrm{P}}_{r+1}{:}^{20}{\mathrm{P}}_{r+2}=11:52$, find $r$

Important Questions on Permutations and Combinations

MEDIUM

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 7 - Permutations and Combinations>OBJECTIVE TYPE QUESTIONS>Q 1

Everybody in a room shakes hands with everybody else. The total number of handshakes is $66$. The total number of persons in the room is 

MEDIUM

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 7 - Permutations and Combinations>OBJECTIVE TYPE QUESTIONS>Q 2

The number of words which can be formed using the letters of the word $ARTICLE$, so that vowels occupy even places? 

MEDIUM

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 7 - Permutations and Combinations>OBJECTIVE TYPE QUESTIONS>Q 3

The number of parallelograms that can be formed from a set of $4$ parallel lines intersected by another set of $3$ parallel lines is 

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 7 - Permutations and Combinations>OBJECTIVE TYPE QUESTIONS>Q 4

If ${}^n\mathrm{C}_{12}{=}^n{\mathrm{C}}_8$, then $n$ is 

HARD

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 7 - Permutations and Combinations>OBJECTIVE TYPE QUESTIONS>Q 5

A five digit number divisible by $3$ is to be formed using the digits $0, 1, 2, 3, 4,$ and $5$ without repetition. Total number of ways this can be done is

MEDIUM

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 7 - Permutations and Combinations>OBJECTIVE TYPE QUESTIONS>Q 6

The Number of ways in which a committee can be chosen from four men and six women so that the committee includes two men and exactly twice as many women as men is 

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 7 - Permutations and Combinations>OBJECTIVE TYPE QUESTIONS>Q 7

The number of ways in which a team of $11$players can be selected from $22$players always including$2$of them and excluding$4$ of them is 

Note: The question has some grammatical error in the book. I have made the change according to the requirement.

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 7 - Permutations and Combinations>OBJECTIVE TYPE QUESTIONS>Q 8

The number of possible outcomes when a coin is tossed $5$times is