# CBSE Solutions for Class 11 Maths

#### Select CBSE Solutions for class 10 Subject & Chapters Wise :

Evaluate each of the following : 3P3

3P3 = 3! / (3−3)!   = 3! /0! = 3!  (Since, 0! = 1)            = 6

Evaluate each of the following : 9P1

9P1 =9! / (9−1)!   = 9! /8!   =9

Evaluate each of the following : P (10, 2)

P (10, 2)
it can also be written as 10P2.
10P2 = 10! /8!         = 10(9)      = 90

Evaluate each of the following : 5P5

5P5 = 5! / (5−5)!  = 5! /0!  = 5!

(Since, 0! = 1)  = 120

Evaluate each of the following : 10P1

10P1 =10! / (10−1)!    = 10! /9!  =10

Evaluate each of the following : 10P2

10P2 =10! / (10−2)! = 10! /8! = 9x10 = 90

Evaluate each of the following : P (6, 2)

P (6, 2)
it can also be written as 6P2.
6P2 = 6! /4!         = 6(5)      = 30

Evaluate each of the following : 6P5

6P5 = 6! / (6−5)!= 6! /1! = 6!(Since , 0! = 1)  = 720

Evaluate each of the following : 10P3

10P3 =10! / (10−3)!= 10! /7!=10(9) (8) (7!)/7! =10×9×8  = 720

Evaluate each of the following : 8P2

8P2 =8! / (8−2)! = 8! /6! =8(7) (6!)/ 6! =8×7 = 56

If 10C0 = 10Cr, find r

10

If 40C20 = 20Cr, find r

20

If 10C4 = 20Cr, find r

6

If nC4 = nC6, find n

10

If nC4 = nC3, find n

7

If nC1 = nC6, find n

7

If 20C4 = 20Cr, find r

16

If nC4 = nC46, find n

50

If nC4 = nC60, find n

64

20C3 = 20Cr, find r

17

If 45C5 = 45Cr, find r

40

If 27C7 = 27Cr, find r

20

If 24C4 = 24Cr, find r

20

If 18C4 = 18Cr, find r

14

There are 5 books on Mathematics and 6 books on Chemistry  in a book shop. In how many ways can a students buy a Mathematics book and a Chemistry

Number of  books on mathematics = 5
Number of books on Chemistry  = 6
Number of ways of buying a mathematics book = 5
Similarly, number of ways of buying a Chemistry book = 6

By using fundamental principle of multiplication:
Number of ways of buying a mathematics and a Chemistry book = 6×5 = 30

There are 5 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next two have 2 each?

Number of ways of answering the first three questions = 4 each
Number of ways of answering the remaining three questions = 2 each
∴ Total number of ways of answering all the questions = 4×4×4×2×2 = 256

In how many ways can an examinee answer a set of 9 true/false type questions?

Number of ways of answering the first question = 2 (either true or false)
Similarly, each question can be answered in 2 ways.
∴ Total number of ways of answering all the 9 questions = 2×2×2×2×2×2×2×2×2= 29 = 512

A coin is tossed 4 times and outcomes are recorded. How many possible outcomes are there?

Number of outcomes when the coin is tossed for the first time = 2
Number of outcomes when the coin is tossed for the second time = 2
Thus, there would be 2 outcomes, each time the coin is tossed.
Total number of possible outcomes on tossing the coin five times = 2×2×2×2 = 16

There are three parcels and five post-offices. In how many different ways can the parcels be sent by registered post?

Number of ways of sending 1 parcel via registered post = 5
Number of ways of sending 3 parcels via registered post through 5 post offices = 5×5×5 = 125

A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?

The first day of the year can be any one of the days of the week, i.e the first day can be selected in 7 ways.
But, the year could also be a leap year.
So, the mint should prepare 7 calendars for the non-leap year and 7 calendars for the leap year.
So, total number of calendars that should be made = 7 + 7 = 14

From Chennai to Bombay there are two roots; air, and sea. From Bombay to Delhi there are three routes; air, rail and road. From Chennai to Delhi via Bombay, how many kinds of routes are there?

Number of routes from Chennai to Bombay = 2
Number of routes from Bombay to Delhi = 3
Using fundamental principle of multiplication:
Number of routes from Chennai to Delhi via Bombay = 2 × 3 = 6

A person wants to buy one Blue pen, one Black pen and one pencil from a stationery shop. If there are 10 Blue pen varieties, 12 Black pen varieties and 5 pencil varieties, in how many ways can he select these articles?

Number of blue  pen varieties = 10
Number of  black pen varieties = 12
Number of pencil varieties = 5
Ways to select a blue pen = 10
Ways to select a black pen = 12
Ways to select a pencil = 5

Ways to select a blue pen, a black pen and a pencil = 10 × 12 × 5 = 600

In a class there are 14 boys and 27 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?

No. of boys in the class = 14
No. of girls in the class = 27
Ways to select a boy = 14
Similarly, ways to select a girl = 27
Number of ways to select 1 boy and 1 girl = 14 × 27 = 378

 1 8P2 A 30 2 10P3 B 6 3 6P1 C 720 4 P(6,2) D 56

1-D, 2-C, 3-B, 4-A

 1 10P2 A 120 2 10P1 B 9 3 5P5 C 90 4 P(9,1) D 10

1-C, 2-D, 3-A, 4-B

 1 9P1 A 7 2 3P1 B 9 3 6P1 C 3 4 7P1 D 6

1-B, 2-C, 3-D, 4-A

Find r

 1 10C0 = 10Cr A 14 2 18C4 = 18Cr B 20 3 24C4 = 24Cr C 10

1-C, 2-A, 3-B

Find n

 1 nC4 = nC6 A 50 2 nC4 = nC3 B 64 3 nC4 = nC60 C 10 4 nC4 = nC46 D 7