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Class 11
Maths :-NCERT Solutions - Permutations And Combinations.

Page No 138:
Question 1:
How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that
(i) repetition of the digits is allowed?
(ii) repetition of the digits is not allowed?


Page No 138:
Question 2:
How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?


Page No 138:
Question 3:
How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?


Page No 138:
Question 4:
How many 5–digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once


Page No 138:
Question 5:
A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?


Page No 138:
Question 6:
Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other


Page No 140:
Question 1:
Evaluate
(i) 8! (ii) 4! – 3!


Page No 141:
Question 2:
Is 3! + 4! = 7!?


Page No 141:
Question 3:
Compute 


Page No 141:
Question 5:
Evaluate, when
(i) n = 6, r = 2 (ii) n = 9, r = 5


Page No 148:
Question 1:
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?

Page No 148: Question 2: How many 4-digit numbers are there with no digit repeated?

Page No 148:
Question 3:
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?



Page No 148:
Question 4:
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?


Page No 148:
Question 5:
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?


Page No 148:
Question 6:
Find n if


Page No 148:
Question 8:
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?


Page No 148:
Question 9:
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time, (ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?


Page No 148:
Question 10:
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?


Page No 148:
Question 11:
In how many ways can the letters of the word PERMUTATIONS be arranged if the
(i) words start with P and end with S, (ii) vowels are all together,
(ii) there are always 4 letters between P and S?


Page No 153:
Question 2:
Determine n if
(i)  (ii) 
ANSWER:


Page No 153:
Question 3:
How many chords can be drawn through 21 points on a circle?


Page No 153:
Question 4:
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?



Page No 153:
Question 7:
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers


Page No 156:
Question 1:
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?


Page No 156:
Question 2:
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?


Page No 156:
Question 3:
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:
(i) exactly 3 girls? (ii) atleast 3 girls? (iii) atmost 3 girls?



Page No 156:
Question 4:
If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?


Page No 157:
Question 5:
How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?


Page No 157:
Question 6:
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?


Page No 157:
Question 7:
In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?


Page No 157:
Question 9:
It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?


Page No 157:
Question 10:
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?


Page No 157:
Question 11:
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?


Page No 166:
Question 1:
Expand the expression (1– 2x)5


Page No 166:

Question 2:

Expand the expression


NCERT Maths Class 11

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