Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

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

## Chapter 2: Algebra

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4Exercise 2.5Exercise 2.6Exercise 2.7Exercise 2.7Miscellaneous Problems
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]

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

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

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