# CBSE Class 11 Mathematics Study Material All Chapters

Download CBSE Class 11 Mathematics Study Material All Chapters in PDF format. All Revision notes for Class 11 Mathematics have been designed as per the latest syllabus and updated chapters given in your textbook for Mathematics in Class 11. Our teachers have designed these concept notes for the benefit of Class 11 students. You should use these chapter wise notes for revision on daily basis. These study notes can also be used for learning each chapter and its important and difficult topics or revision just before your exams to help you get better scores in upcoming examinations, You can also use Printable notes for Class 11 Mathematics for faster revision of difficult topics and get higher rank. After reading these notes also refer to MCQ questions for Class 11 Mathematics given on studiestoday

## Revision Notes for Class 11 Mathematics All topics

Class 11 Mathematics students should refer to the following concepts and notes for All topics in Class 11. These exam notes for Class 11 Mathematics will be very useful for upcoming class tests and examinations and help you to score good marks

### All topics Notes Class 11 Mathematics

CHAPTER-7

(PERMUTATION & COMBINATION)

Points to be remembered

1. Fundamental principle of counting:-

If one operation can be performed in 'm' different ways and if corresponding to each way of performing this operation,there are 'n' different ways of performing second operation ,the two operations together can be performed in (mXn) ways.

2. Factorial:-

The continued product of first 'n' natural numbers is called factorial 'n' or 'n' factorial and is denoted as 'n!'.

3. 0! has no meaning. Conventionally, we define 0! =1.

4. The number of permutation (arrangements of 'n' different things taken 'r' at a time given by nPr (0<=r<=n)
nPr = n!/(n-r)!

5. The number of ways in which 'r' vacant places can be filled up with 'n' different things is given by nr.

6. The number of permutations of 'n' things taken altogether,when 'p' of the things are alike of one kind, 'q' of them alike of another kind, 'r' of them alike of a third kind and the remaining all different is given by:- n!/(p!q!r!).

7. The number of ways of arranging 'n' distinct objects along a round table=(n-1)!

8. The number of ways of arranging 'n' persons along a round table so that no person has the same two neighbours=(n-1)!/2

9. In forming a necklace, there is no distinction between a clockwise and anticlock wise direction. Hence, the no. of necklace formed with 'n' beads of different colours =(n-1)!/2

10. The number of combination of 'n' different things taken 'r' at a time is given by nCr, (0<=r<=n)

nCr= n!/r!(n-r)!

11. nCr + nC(r-1) =(n+1)Cr where 1<=r<=n, and n,r belongs to N.

12. nCr/nC(r-1) = (n-r+1)/r where n,r belongs to N, 1<=r<=n.

13. The number of ways in which (m+n) things can be divided into two groups containing 'm' and 'n' things respectively is given by= (m+n)!/m! n!

1. Find HCF & LCM of 4!,5!,6!?

2. If 1/8! + 3/7! = x/9!, find x?

3. Find 'n' if 5 P(4,n)=6 P(5,n-1)?

4. In how many ways can the letters of the word "EQUATION" be arranged?

5. Ten students are participating in a race. In how many ways can the first three prizes be won?

6. In how many ways can 4 books on mathematics and 3 books on English be placed on a shelf so that books on the same subject always remain.

7. How many words can be formed out of letters of the word "TRIANGLE". How many of those will begin with 'T' and end with 'E'?

8. In how many ways can 3 prizes be given to 10 students when a student can receive any number of prizes?

9. How many different arrangements can be made from the letters of the word "ENGINEERING"?

10. In how many ways can 6 beads of different colours form a necklace?

11. Evaluate 10C7 + 10C6 ?

12. If C(2n,3):C(n,3):: 11:1 ,find 'n'?

13. Find the no. of straight lines and no. of triangles that can be formed from 15 non collinear points?

14. Find the no. of all 4-digit nos. with no digit being repeated?

15. Find the no. of all 3-digit even natural nos?

1. How many nos. greater than 56000 can be formed by using the digits 4,5,6,7,8 if no digit is repeated in any no.?

2. Find the no. of ways in which the letters of "ARRANGEMENT" can be arranged so that the 2 R's and 2 A's don't occur together?

3. A committee of 6 is to be formed from 6 boys and 4 girls. In how many ways can this be done if the committee contains :
(a) 2 girls?
(b) atleast 2 girls?

4. A man has 7 relatives , 4 of them are ladies and 3 gentlemen, his wife also has 7 relatives , 3 of them are ladies and 4 gentlement. In how many ways can they invite a dinner party of 3 ladies and 3 gentleman so that there are 3 of man's relatives and 3 of wife's relatives?

5. Find the no. of all possible arrangement of the letters of the word "MATHEMATICS" taken 4 at a time?

6. 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?

7. Find the no. of ways in which 5 boys and 5 girls can be seated in 10 seats in a row if the boys and girls are to be seated alternately?

8. In how many ways can the letters of the word "ASSASSINATION" be arranged so that all the S's are together?

9. In an experiment, a question paper consists of 12 questions divided into 2 parts i.e part1 & part2 containing 5 & 7 questions. A student is required to attempt 8 questions in all, selecting atleast 3 from each part. In how many ways can a student select the questions?

10. How many 6-digit nos. can be formed from the digits 0,1,3,5,7,9 which are divisible by 10 and no digit is repeated?

11. Prove that 2nCn= (1.3.5.7.....(2n-1)X2n)/n!

12. How many even nos. are there with 3-digits such that if 5 is one of the digits, then '7' is the next digit?

13.A teacher wants to arrange 5 students on the plat form such that the buy YUSUF occupies the first position and the girls GEETA & SEETA are always together. How many such arrangements are possible?

14. How many different nos. with distinct digits can be formed from the digits 2,3,5,7,9. How many of them are odd?

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### CBSE Class 11 Mathematics All topics Notes

We hope you liked the above notes for topic All topics which has been designed as per the latest syllabus for Class 11 Mathematics released by CBSE. Students of Class 11 should download and practice the above notes for Class 11 Mathematics regularly. All revision notes have been designed for Mathematics by referring to the most important topics which the students should learn to get better marks in examinations. Studiestoday is the best website for Class 11 students to download all latest study material.

### Notes for Mathematics CBSE Class 11 All topics

Our team of expert teachers have referred to the NCERT book for Class 11 Mathematics to design the Mathematics Class 11 notes. If you read the concepts and revision notes for one chapter daily, students will get higher marks in Class 11 exams this year. Daily revision of Mathematics course notes and related study material will help you to have a better understanding of all concepts and also clear all your doubts. You can download all Revision notes for Class 11 Mathematics also from www.studiestoday.com absolutely free of cost in Pdf format. After reading the notes which have been developed as per the latest books also refer to the NCERT solutions for Class 11 Mathematics provided by our teachers

#### All topics Notes for Mathematics CBSE Class 11

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#### All topics CBSE Class 11 Mathematics Notes

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#### Notes for CBSE Mathematics Class 11 All topics

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