• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer
  • RBSE Model Papers
    • RBSE Class 12th Board Model Papers 2020
    • RBSE Class 10th Board Model Papers 2020
    • RBSE Class 8th Board Model Papers 2020
    • RBSE Class 5th Board Model Papers 2020
  • RBSE Books
  • RBSE Solutions for Class 10
    • RBSE Solutions for Class 10 Maths
    • RBSE Solutions for Class 10 Science
    • RBSE Solutions for Class 10 Social Science
    • RBSE Solutions for Class 10 English
    • RBSE Solutions for Class 10 Hindi
    • RBSE Solutions for Class 10 Sanskrit
    • RBSE Solutions for Class 10 Rajasthan Adhyayan
    • RBSE Solutions for Class 10 Physical Education
  • RBSE Solutions for Class 9
    • RBSE Solutions for Class 9 Maths
    • RBSE Solutions for Class 9 Science
    • RBSE Solutions for Class 9 Social Science
    • RBSE Solutions for Class 9 English
    • RBSE Solutions for Class 9 Hindi
    • RBSE Solutions for Class 9 Sanskrit
    • RBSE Solutions for Class 9 Rajasthan Adhyayan
    • RBSE Solutions for Class 9 Physical Education
    • RBSE Solutions for Class 9 Information Technology
  • RBSE Solutions for Class 8
    • RBSE Solutions for Class 8 Maths
    • RBSE Solutions for Class 8 Science
    • RBSE Solutions for Class 8 Social Science
    • RBSE Solutions for Class 8 English
    • RBSE Solutions for Class 8 Hindi
    • RBSE Solutions for Class 8 Sanskrit
    • RBSE Solutions

RBSE Solutions

Rajasthan Board Textbook Solutions for Class 5, 6, 7, 8, 9, 10, 11 and 12

  • RBSE Solutions for Class 7
    • RBSE Solutions for Class 7 Maths
    • RBSE Solutions for Class 7 Science
    • RBSE Solutions for Class 7 Social Science
    • RBSE Solutions for Class 7 English
    • RBSE Solutions for Class 7 Hindi
    • RBSE Solutions for Class 7 Sanskrit
  • RBSE Solutions for Class 6
    • RBSE Solutions for Class 6 Maths
    • RBSE Solutions for Class 6 Science
    • RBSE Solutions for Class 6 Social Science
    • RBSE Solutions for Class 6 English
    • RBSE Solutions for Class 6 Hindi
    • RBSE Solutions for Class 6 Sanskrit
  • RBSE Solutions for Class 5
    • RBSE Solutions for Class 5 Maths
    • RBSE Solutions for Class 5 Environmental Studies
    • RBSE Solutions for Class 5 English
    • RBSE Solutions for Class 5 Hindi
  • RBSE Solutions Class 12
    • RBSE Solutions for Class 12 Maths
    • RBSE Solutions for Class 12 Physics
    • RBSE Solutions for Class 12 Chemistry
    • RBSE Solutions for Class 12 Biology
    • RBSE Solutions for Class 12 English
    • RBSE Solutions for Class 12 Hindi
    • RBSE Solutions for Class 12 Sanskrit
  • RBSE Class 11

RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise

May 29, 2019 by Prasanna Leave a Comment

Rajasthan Board RBSE Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise

Question 1.
If nPn-2 = 60, then n will be:
(A) 2
(B) 4
(C) 5
(D) 3
Solution:
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 1

Question 2.
nPr ÷ nCr is equal to:
(A) n!
(B) (n – r)!
(C) \frac { 1 }{ r! }
(D) r!
Solution:
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 2
Hence, the option (D) is correct.

Question 3.
How many ways 5 persons can sit around the round table:
(A) 120
(B) 24
(C) 60
(D) 12
Solution:
Total number of ways to sitting 5 persons around the round table
= (5 – 1)! = 4!
= 4 × 3 × 2 × 1 = 24.
Hence, option (B) is correct.

Question 4.
How many words can be formed using letters BHILWARA:
(A) \frac { 8! }{ 2! }
(B) 8!
(C) 7!
(D) \frac { 6! }{ 2! }
Solution:
There are 8 letters in the given word in which 2 A’s and other letters are different.
Then numbers of words formed by letters of BHILWARA = \frac { 8! }{ 2! }
Hence option (A) is correct.

Question 5.
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 3
Solution:
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 4
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 5

Question 6.
Find the value of 61C57 – 60C56:
(A) 61C58
(B) 60C57
(C) 60C58
(D) 60C56
Solution:
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 6

Question 7.
If 15C3r = 15Cr+3, then r is equal to:
(A) 5
(B) 4
(C) 3
(D) 2
Solution
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 7

Question 8.
There are 6 points on the circumference of a circle, the number of straight lines joining their points will be:
(A) 30
(B) 15
(C) 12
(D) 20
Solution:
Number of lines passing through n points = nC2
Number of lines passing through 6 points
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 8
Hence, option (B) is correct.

Question 9.
How many words can be formed using letters of BHOPAL?
(A) 124
(B) 240
(C) 360
(D) 720
Solution:
Here, the number of letters are 6 and every time we take 6 letters.
Hence, required number of = ⌊6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
Hence, option (D) is correct.

Question 10.
There are 4 points on the circumference of a circle by joining them how many triangles can be formed?
(A) 4
(B) 6
(C) 8
(D) 12
Solution:
There are three vertices in a triangle.
Given: There are 4 points on the circumference of a circle.
Then, the number of required triangles
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 9
Hence, option (A) is correct.

Question 11.
If nC2 = nC7, then find nC16
Solution:
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 10

Question 12.
Find the value of n:
(i) nC2 : nC2 = 12 : 1
(ii) 2nC3 : nC3 = 11 : 1
Solution:
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 11
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 12
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 13

Question 13.
Find the number of chords passing through 11 points on the circumference of a circle.
Solution:
Number of the point on the circumference of circle = 11
We know that a chord is formed by joining two points.
Hence taking 2 points out of 11 points number of chords = 11C2
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 14
Hence, the number of chords = 55.

Question 14.
Determine the number of combinations out of deck of 52 cards of each selection of 5 cards has exactly one ace.
Solution:
Number of cards in a deck = 52
Total number of aces = 4
Hence Number of remaining cards = 52 – 4 = 48
We have to make a collection of 5 cards, in which there is 1 ace and 4 other cards.
Hence, number of ways choosing 1 out of 4 ace.
Now,Number of ways choosing 4 cards out of 48 cards
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 15
Total number of collection having 5 cards
= 4C1 × 48C4 = 4 × 194580 = 778320
Hence, number of combinations formed by 5 cards = 778320.

Question 15.
There are n points in a plane in which m points are collinear. How many triangles will be formed by joining three points?
Solution:
For making a triangle we need three points thus if 3 points out of n points are not in a line, then nC3 triangle can be formed by n points but m point is in a line, thus mC3 triangle forms less.
Hence, required number of triangles = nC3 – mC3.

Question 16.
Find the number of diagonals of a decagon.
Solution:
There are 10 vertices in a decagon. Now by joining two vertices, we get a side of decagon or a diagonal.
Hence, the number of the line segment by joining of vertices of decagon = number of ways taking 2 points out of 10 points
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 16
Hence, the number of diagonals is 35.

Question 17.
There are 5 empty seats in a train, then in how many ways three travellers can sit on these seats?
Solution:
A number of ways of seating of 3 travellers out of 5 seats.
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 17
Hence, 3 travellers can be seated in 60 ways.

Question 18.
A group of 7 has to be formed from 6 boys and 4 girls. In how many ways a group can be formed if boys are in the majority in this group?
Solution:
Number of boys = 6
Number of girls = 4
Number of members in the group = 7
One putting boys in the majority in the group
We have to choose in the following ways :
4 boys + 3 girls
5 boys + 2 girls
6 boys + 1 girls
Number of ways choosing 4 boys and 3 girls = 6C4 × 4C3
Number of ways choosing 5 boys and 2 girls = 6C5 × 4C2
Number of ways choosing 6 boys and 1 girl = 6C6 × 4C1
Required number of ways forming the group
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 18
Hence, the group can be formed in 100 ways.

Question 19.
In the conference of 8 persons, every person handshake with each other only once, then find the total number of hand shook.
Solution:
When two persons shake hand with each other, then this is taken as one handshake.
Hence, the number of handshakes is equal to choosing 2 persons out of 8 persons.
Number of handshake
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 19
Hence, the required number of hand shaken is 28.

Question 20.
In how many ways 6 men and 6 women can sit around the round table whereas any two women never sit together?
Solution:
First, we sit the men in an order that there is a place vacant between two men.
Then, number of ways sitting 6 men = (6 – 1)! = 5!
Now a number of ways sitting 6 women in the vacant places = 6!
Number of permutations = (6 – 1)! = 5!
Now, the number of ways sitting 6 women in the vacant place = 6!
Number of permutaions = 5! × 6!
= (5 × 4 × 3 × 2 × 1) × (6 × 5 × 4 × 3 × 2 × 1)
= 86400.

Question 21.
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S are together?
Solution:
Number of letters in word ASSASSINATION = 13
In this word A comes 3 times, S comes 4 times, I comes 2 times, N comes 2 times and other letters are different.
Now, taking 4’s together, then consider it as one letter, now adding other 9 letters and thus the permutation formed by 10 letters
= \frac { 10! }{ 2!2!3! }
[Because I comes 2 times, N comes 2 times and A comes 3 times]
RBSE Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Miscellaneous Exercise 20
Hence, the total number of ways is 151200.

RBSE Solutions for Class 11 Maths

Share this:

  • Click to share on WhatsApp (Opens in new window)
  • Click to share on Twitter (Opens in new window)
  • Click to share on Facebook (Opens in new window)
  • Click to share on Google+ (Opens in new window)

Related

Filed Under: Class 11

Reader Interactions

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Primary Sidebar

Recent Posts

  • RBSE Solutions for Class 11 Maths Chapter 2 Relations and Functions Ex 2.4
  • Rajasthan Board Class 12 Books | RBSE 12th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 11 Books | RBSE 11th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 10 Books | RBSE 10th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 9 Books | RBSE 9th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 8 Books | RBSE 8th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 7 Books | RBSE 7th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 6 Books | RBSE 6th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 5 Books | RBSE 5th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 4 Books | RBSE 4th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 3 Books | RBSE 3rd Class Books PDF Download in English Hindi Medium

Footer

RBSE Solutions for Class 12
RBSE Solutions for Class 11
RBSE Solutions for Class 10
RBSE Solutions for Class 9
RBSE Solutions for Class 8
RBSE Solutions for Class 7
RBSE Solutions for Class 6
RBSE Solutions for Class 5
RBSE Solutions for Class 12 Maths
RBSE Solutions for Class 11 Maths
RBSE Solutions for Class 10 Maths
RBSE Solutions for Class 9 Maths
RBSE Solutions for Class 8 Maths
RBSE Solutions for Class 7 Maths
RBSE Solutions for Class 6 Maths
RBSE Solutions for Class 5 Maths
Target Batch
RBSE Class 11 Political Science Notes

Copyright © 2021 · Magazine Pro on Genesis Framework · WordPress · Log in