Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th
Advertisement Remove all ads

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide chapter 2 - Algebra [Latest edition]

Chapters

Class 11th Business Mathematics and Statistics Answers Guide - Shaalaa.com
Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

Chapter 2: Algebra

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4Exercise 2.5Exercise 2.6Exercise 2.7Exercise 2.7`Miscellaneous Problems
Advertisement Remove all ads
Exercise 2.1 [Page 29]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 2 AlgebraExercise 2.1 [Page 29]

Exercise 2.1 | Q 1 | Page 29

Resolve into partial fraction for the following:

`(3x + 7)/(x^2 - 3x + 2)`

Exercise 2.1 | Q 2 | Page 29

Resolve into partial fraction for the following:

`(4x + 1)/((x - 2)(x + 1))`

Exercise 2.1 | Q 3 | Page 29

Resolve into partial fraction for the following:

`1/((x - 1)(x + 2)^2)`

Exercise 2.1 | Q 4 | Page 29

Resolve into partial fraction for the following:

`1/(x^2 - 1)`

Exercise 2.1 | Q 5 | Page 29

Resolve into partial fraction for the following:

`(x - 2)/((x + 2)(x - 1)^2)`

Exercise 2.1 | Q 6 | Page 29

Resolve into partial fraction for the following:

`(2x^2 - 5x - 7)/(x - 2)^3`

Exercise 2.1 | Q 7 | Page 29

Resolve into a partial fraction for the following:

`(x^2 - 6x + 2)/(x^2 (x + 2))`

Exercise 2.1 | Q 8 | Page 29

Resolve into partial fraction for the following:

`(x^2 - 3)/((x + 2)(x^2 + 1))`

Exercise 2.1 | Q 9 | Page 29

Resolve into a partial fraction for the following:

`(x + 2)/((x - 1)(x + 3)^2)`

Exercise 2.1 | Q 10 | Page 29

Resolve into a partial fraction for the following:

`1/((x^2 + 4)(x + 1))`

Exercise 2.2 [Page 32]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 2 AlgebraExercise 2.2 [Page 32]

Exercise 2.2 | Q 1 | Page 32

Find x if `1/(6!) + 1/(7!) = x/(8!)`

Exercise 2.2 | Q 2 | Page 32

Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.

Exercise 2.2 | Q 3 | Page 32

If (n+2)! = 60[(n–1)!], find n

Exercise 2.2 | Q 4 | Page 32

How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?

Exercise 2.2 | Q 5 | Page 32

How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?

Exercise 2.3 [Pages 35 - 36]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 2 AlgebraExercise 2.3 [Pages 35 - 36]

Exercise 2.3 | Q 1 | Page 35

If nP4 = 12(nP2), find n.

Exercise 2.3 | Q 2 | Page 35

In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?

Exercise 2.3 | Q 3 | Page 35

How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?

Exercise 2.3 | Q 4 | Page 36

Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.

Exercise 2.3 | Q 5 | Page 36
  1. In how many ways can 8 identical beads be strung on a necklace?
  2. In how many ways can 8 boys form a ring?
Exercise 2.3 | Q 6 | Page 36

Find the rank of the word ‘CHAT’ in the dictionary.

Exercise 2.4 [Page 38]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 2 AlgebraExercise 2.4 [Page 38]

Exercise 2.4 | Q 1 | Page 38

If nPr = 1680 and nCr = 70, find n and r.

Exercise 2.4 | Q 2 | Page 38

Verify that 8C4 + 8C3 = 9C4.

Exercise 2.4 | Q 3 | Page 38

How many chords can be drawn through 21 points on a circle?

Exercise 2.4 | Q 4 | Page 38

How many triangles can be formed by joining the vertices of a hexagon?

Exercise 2.4 | Q 5 | Page 38

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

Exercise 2.4 | Q 6 | Page 38

If four dice are rolled, find the number of possible outcomes in which atleast one die shows 2.

Exercise 2.4 | Q 7 | Page 38

There are 18 guests at a dinner party. They have to sit 9 guests on either side of a long table, three particular persons decide to sit on one side and two others on the other side. In how many ways can the guests to be seated?

Exercise 2.4 | Q 8 | Page 38

If a polygon has 44 diagonals, find the number of its sides.

Exercise 2.4 | Q 9 | Page 38

In how many ways can a cricket team of 11 players be chosen out of a batch of 15 players?

  1. There is no restriction on the selection.
  2. A particular player is always chosen.
  3. A particular player is never chosen.
Exercise 2.4 | Q 10 | Page 38

A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways this can be done when

  1. atleast two ladies are included.
  2. atmost two ladies are included.
Exercise 2.5 [Page 41]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 2 AlgebraExercise 2.5 [Page 41]

Exercise 2.5 | Q 1 | Page 41

By the principle of mathematical induction, prove the following:

13 + 23 + 33 + ….. + n3 = `("n"^2("n + 1")^2)/4` for all x ∈ N.

Exercise 2.5 | Q 2 | Page 41

By the principle of mathematical induction, prove the following:

1.2 + 2.3 + 3.4 + … + n(n + 1) = `(n(n + 1)(n + 2))/3` for all n ∈ N.

Exercise 2.5 | Q 3 | Page 41

By the principle of mathematical induction, prove the following:

4 + 8 + 12 + ……. + 4n = 2n(n + 1), for all n ∈ N.

Exercise 2.5 | Q 4 | Page 41

By the principle of mathematical induction, prove the following:

1 + 4 + 7 + ……. + (3n – 2) = `("n"(3"n" - 1))/2`  for all n ∈ N.

Exercise 2.5 | Q 5 | Page 41

By the principle of mathematical induction, prove the following:

32n – 1 is divisible by 8, for all n ∈ N.

Exercise 2.5 | Q 6 | Page 41

By the principle of mathematical induction, prove the following:

an – bn is divisible by a – b, for all n ∈ N.

Exercise 2.5 | Q 7 | Page 41

By the principle of mathematical induction, prove the following:

52n – 1 is divisible by 24, for all n ∈ N.

Exercise 2.5 | Q 8 | Page 41

By the principle of mathematical induction, prove the following:

n(n + 1) (n + 2) is divisible by 6, for all n ∈ N.

Exercise 2.5 | Q 9 | Page 41

By the principle of mathematical induction, prove the following:

2n > n, for all n ∈ N.

Exercise 2.6 [Page 45]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 2 AlgebraExercise 2.6 [Page 45]

Exercise 2.6 | Q 1. (i) | Page 45

Expand the following by using binomial theorem.

(2a – 3b)4

Exercise 2.6 | Q 1. (ii) | Page 45

Expand the following by using binomial theorem.

`(x + 1/y)^7`

Exercise 2.6 | Q 1. (iii) | Page 45

Expand the following by using binomial theorem.

`(x + 1/x^2)^6`

Exercise 2.6 | Q 2. (i) | Page 45

Evaluate the following using binomial theorem:

(101)4

Exercise 2.6 | Q 2. (ii) | Page 45

Evaluate the following using binomial theorem:

(999)5

Exercise 2.6 | Q 3 | Page 45

Find the 5th term in the expansion of (x – 2y)13.

Exercise 2.6 | Q 4. (i) | Page 45

Find the middle terms in the expansion of

`(x + 1/x)^11`

Exercise 2.6 | Q 4. (ii) | Page 45

Find the middle terms in the expansion of

`(3x + x^2/2)^8`

Exercise 2.6 | Q 4. (iii) | Page 45

Find the middle terms in the expansion of

`(2x^2 - 3/x^3)^10`

Exercise 2.6 | Q 5. (i) | Page 45

Find the term independent of x in the expansion of

`(x^2 - 2/(3x))^9`

Exercise 2.6 | Q 5. (ii) | Page 45

Find the term independent of x in the expansion of

`(x - 2/x^2)^15`

Exercise 2.6 | Q 5. (iii) | Page 45

Find the term independent of x in the expansion of

`(2x^2 + 1/x)^12`

Exercise 2.6 | Q 6 | Page 45

Prove that the term independent of x in the expansion of `(x + 1/x)^(2n)` is `(1*3*5...(2n - 1)2^n)/(n!)`.

Exercise 2.6 | Q 7 | Page 45

Show that the middle term in the expansion of is (1 + x)2n is `(1*3*5...(2n - 1)2^nx^n)/(n!)`

Exercise 2.7, Exercise 2.7` [Pages 45 - 47]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 2 AlgebraExercise 2.7, Exercise 2.7` [Pages 45 - 47]

Choose the correct answer

Exercise 2.7 | Q 1 | Page 45

If nC3 = nC2 then the value of nC4 is:

  • 2

  • 3

  • 4

  • 5

Exercise 2.7 | Q 2 | Page 45

The value of n, when np2 = 20 is:

  • 3

  • 6

  • 5

  • 4

Exercise 2.7 | Q 3 | Page 46

The number of ways selecting 4 players out of 5 is

  • 4!

  • 20

  • 25

  • 5

Exercise 2.7 | Q 4 | Page 46

If nPr = 720(nCr), then r is equal to:

  • 4

  • 5

  • 6

  • 7

Exercise 2.7 | Q 5 | Page 46

The possible outcomes when a coin is tossed five times:

  • 25

  • 52

  • 10

  • `5/2`

Exercise 2.7 | Q 6 | Page 46

The number of diagonals in a polygon of n sides is equal to

  • nC2

  • nC2 – 2

  • nC2 – n

  • nC2 – 1

Exercise 2.7 | Q 7 | Page 46

The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:

  • 2

  • 6

  • 20

  • 24

Exercise 2.7 | Q 8 | Page 46

If n is a positive integer, then the number of terms in the expansion of (x + a)n is:

  • n

  • n + 1

  • n - 1

  • 2n

Exercise 2.7 | Q 9 | Page 46

For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:

  • 2n

  • 2n – 1

  • n2

  • n2 – 1

Exercise 2.7 | Q 10 | Page 46

The term containing x3 in the expansion of (x – 2y)7 is:

  • 3rd

  • 4th

  • 5th

  • 6th

Exercise 2.7 | Q 11 | Page 46

The middle term in the expansion of `(x + 1/x)^10` is

  • 10C4 `(1/x)`

  • 10C5

  • 10C6

  • 10C7 x2

Exercise 2.7 | Q 12 | Page 46

The constant term in the expansion of `(x + 2/x)^6` is

  • 156

  • 165

  • 162

  • 160

Exercise 2.7 | Q 13 | Page 46

The last term in the expansion of (3 + √2 )8 is:

  • 81

  • 16

  • 8

  • 2

Exercise 2.7 | Q 14 | Page 46

If `(kx)/((x + 4)(2x - 1)) = 4/(x + 4) + 1/(2x - 1)` then k is equal to:

  • 9

  • 11

  • 5

  • 7

Exercise 2.7 | Q 15 | Page 46

The number of 3 letter words that can be formed from the letters of the word ‘NUMBER’ when the repetition is allowed are:

  • 206

  • 133

  • 216

  • 300

Exercise 2.7 | Q 16 | Page 46

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is:

  • 18

  • 12

  • 9

  • 6

Exercise 2.7 | Q 17 | Page 46

There are 10 true or false questions in an examination. Then these questions can be answered in

  • 240 ways

  • 120 ways

  • 1024 ways

  • 100 ways

Exercise 2.7 | Q 18 | Page 46

The value of (5C0 + 5C1) + (5C1 + 5C2) + (5C2 + 5C3) + (5C3 + 5C4) + (5C4 + 5C5) is:

  • 26 – 2

  • 25 – 1

  • 28

  • 27

Exercise 2.7 | Q 19 | Page 46

The total number of 9 digit number which has all different digit is:

  • 10!

  • 9!

  • 9 × 9!

  • 10 × 10!

Exercise 2.7 | Q 20 | Page 47

The number of ways to arrange the letters of the word “CHEESE”:

  • 120

  • 240

  • 720

  • 6

Exercise 2.7 | Q 21 | Page 47

Thirteen guests have participated in a dinner. The number of handshakes that happened in the dinner is:

  • 715

  • 78

  • 286

  • 13

Exercise 2.7 | Q 22 | Page 47

The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:

  • 7!

  • 3!

  • 8!

  • 5!

Exercise 2.7` | Q 23 | Page 47

Sum of binomial coefficient in a particular expansion is 256, then number of terms in the expansion is:

  • 8

  • 7

  • 6

  • 9

Exercise 2.7 | Q 24 | Page 47

The number of permutation of n different things taken r at a time, when the repetition is allowed is:

  • rn

  • nr

  • `(n!)/((n - r)!)`

  • `(n!)/((n + r)!)`

Exercise 2.7 | Q 25 | Page 47

Sum of the binomial coefficients is

  • 2n

  • n2

  • 2n

  • n + 17

Miscellaneous Problems [Page 47]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 2 AlgebraMiscellaneous Problems [Page 47]

Miscellaneous Problems | Q 1 | Page 47

Resolve into Partial Fractions:

`(5x + 7)/((x-1)(x+3))`

Miscellaneous Problems | Q 2 | Page 47

Resolve into Partial Fractions:

`(x - 4)/(x^2 - 3x + 2)`

Miscellaneous Problems | Q 3 | Page 47

Decompose into Partial Fractions:

`(6x^2 - 14x - 27)/((x + 2)(x - 3)^2)`

Miscellaneous Problems | Q 4 | Page 47

Decompose into Partial Fractions:

`(5x^2 - 8x + 5)/((x - 2)(x^2 - x + 1))`

Miscellaneous Problems | Q 5. (i) | Page 47

Evaluate the following.

`(3! xx 0! + 0!)/(2!)`

Miscellaneous Problems | Q 5. (ii) | Page 47

Evaluate the following.

`(3! + 1!)/(2^2!)`

Miscellaneous Problems | Q 5. (iii) | Page 47

Evaluate the following.

`((3!)! xx 2!)/(5!)`

Miscellaneous Problems | Q 6 | Page 47

How many code symbols can be formed using 5 out of 6 letters A, B, C, D, E, F so that the letters

  1. cannot be repeated
  2. can be repeated
  3. cannot be repeated but must begin with E
  4. cannot be repeated but end with CAB.
Miscellaneous Problems | Q 7 | Page 47

From 20 raffle tickets in a hat, four tickets are to be selected in order. The holder of the first ticket wins a car, the second a motor cycle, the third a bicycle and the fourth a skateboard. In how many different ways can these prizes be awarded?

Miscellaneous Problems | Q 8 | Page 47

In how many different ways, 2 Mathematics, 2 Economics and 2 History books can be selected from 9 Mathematics, 8 Economics and 7 History books?

Miscellaneous Problems | Q 9 | Page 47

Let there be 3 red, 2 yellow and 2 green signal flags. How many different signals are possible if we wish to make signals by arranging all of them vertically on a staff?

Miscellaneous Problems | Q 10 | Page 47

Find the Co-efficient of x11 in the expansion of `(x + 2/x^2)^17`

Chapter 2: Algebra

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4Exercise 2.5Exercise 2.6Exercise 2.7Exercise 2.7`Miscellaneous Problems
Class 11th Business Mathematics and Statistics Answers Guide - Shaalaa.com

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide chapter 2 - Algebra

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide chapter 2 (Algebra) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Tamil Nadu Board of Secondary Education Class 11th Business Mathematics and Statistics Answers Guide solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Tamil Nadu Board Samacheer Kalvi textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11th Business Mathematics and Statistics Answers Guide chapter 2 Algebra are Partial Fractions, Permutations, Combinations, Mathematical Induction, Binomial Theorem.

Using Tamil Nadu Board Samacheer Kalvi Class 11th solutions Algebra exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Tamil Nadu Board Samacheer Kalvi Solutions are important questions that can be asked in the final exam. Maximum students of Tamil Nadu Board of Secondary Education Class 11th prefer Tamil Nadu Board Samacheer Kalvi Textbook Solutions to score more in exam.

Get the free view of chapter 2 Algebra Class 11th extra questions for Class 11th Business Mathematics and Statistics Answers Guide and can use Shaalaa.com to keep it handy for your exam preparation

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×