#### Chapters

Chapter 2: Algebra

Chapter 3: Analytical Geometry

Chapter 4: Trigonometry

Chapter 5: Differential Calculus

Chapter 6: Applications of Differentiation

Chapter 7: Financial Mathematics

Chapter 8: Descriptive Statistics and Probability

Chapter 9: Correlation and Regression Analysis

Chapter 10: Operations Research

## Chapter 2: Algebra

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

**Resolve into partial fraction for the following:**

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

**Resolve into partial fraction for the following:**

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

**Resolve into partial fraction for the following:**

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

**Resolve into partial fraction for the following:**

`1/(x^2 - 1)`

**Resolve into partial fraction for the following:**

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

**Resolve into partial fraction for the following:**

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

**Resolve into a partial fraction for the following:**

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

**Resolve into partial fraction for the following:**

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

**Resolve into a partial fraction for the following:**

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

**Resolve into a partial fraction for the following:**

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

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

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

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

If (n+2)! = 60[(n–1)!], find n

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?

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

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

If nP_{4} = 12(nP_{2}), find n.

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

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?

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

- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?

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

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

If ^{n}P_{r} = 1680 and ^{n}C_{r} = 70, find n and r.

Verify that ^{8}C_{4} + ^{8}C_{3} = ^{9}C_{4}.

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

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

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

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

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?

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

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

- There is no restriction on the selection.
- A particular player is always chosen.
- A particular player is never chosen.

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

- atleast two ladies are included.
- atmost two ladies are included.

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

**By the principle of mathematical induction, prove the following:**

1^{3} + 2^{3} + 3^{3} + ….. + n^{3} = `("n"^2("n + 1")^2)/4` for all x ∈ N.

**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.

**By the principle of mathematical induction, prove the following:**

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

**By the principle of mathematical induction, prove the following:**

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

**By the principle of mathematical induction, prove the following:**

3^{2n} – 1 is divisible by 8, for all n ∈ N.

**By the principle of mathematical induction, prove the following:**

a^{n} – b^{n} is divisible by a – b, for all n ∈ N.

**By the principle of mathematical induction, prove the following:**

5^{2n} – 1 is divisible by 24, for all n ∈ N.

**By the principle of mathematical induction, prove the following:**

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

**By the principle of mathematical induction, prove the following:**

2^{n} > n, for all n ∈ N.

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

**Expand the following by using binomial theorem.**

(2a – 3b)^{4}

**Expand the following by using binomial theorem.**

`(x + 1/y)^7`

**Expand the following by using binomial theorem.**

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

**Evaluate the following using binomial theorem:**

(101)^{4}

**Evaluate the following using binomial theorem:**

(999)^{5}

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

**Find the middle terms in the expansion of**

`(x + 1/x)^11`

**Find the middle terms in the expansion of**

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

**Find the middle terms in the expansion of**

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

**Find the term independent of x in the expansion of**

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

**Find the term independent of x in the expansion of**

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

**Find the term independent of x in the expansion of**

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

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

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

### 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

If nC_{3} = nC_{2} then the value of nC_{4} is:

2

3

4

5

The value of n, when np_{2} = 20 is:

3

6

5

4

The number of ways selecting 4 players out of 5 is

4!

20

25

5

If nP_{r} = 720(nC_{r}), then r is equal to:

4

5

6

7

The possible outcomes when a coin is tossed five times:

2

^{5}5

^{2}10

`5/2`

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

nC

_{2}nC

_{2}– 2nC

_{2}– nnC

_{2}– 1

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

2

6

20

24

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

For all n > 0, nC_{1} + nC_{2} + nC_{3} + …… + nC_{n} is equal to:

2n

2

^{n}– 1n

^{2}n

^{2}– 1

The term containing x^{3} in the expansion of (x – 2y)^{7} is:

3rd

4th

5th

6th

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

10C

_{4}`(1/x)`10C

_{5}10C

_{6}10C

_{7}x^{2}

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

156

165

162

160

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

81

16

8

2

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

9

11

5

7

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

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

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

The value of (5C_{0} + 5C_{1}) + (5C_{1} + 5C_{2}) + (5C_{2} + 5C_{3}) + (5C_{3} + 5C_{4}) + (5C_{4} + 5C_{5}) is:

2

^{6}– 22

^{5}– 12

^{8}2

^{7}

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

10!

9!

9 × 9!

10 × 10!

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

120

240

720

6

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

715

78

286

13

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!

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

8

7

6

9

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

r

^{n}n

^{r}`(n!)/((n - r)!)`

`(n!)/((n + r)!)`

Sum of the binomial coefficients is

2

^{n}n

^{2}2n

n + 17

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

**Resolve into Partial Fractions:**

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

**Resolve into Partial Fractions:**

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

**Decompose into Partial Fractions:**

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

**Decompose into Partial Fractions:**

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

**Evaluate the following.**

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

**Evaluate the following.**

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

**Evaluate the following.**

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

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

- cannot be repeated
- can be repeated
- cannot be repeated but must begin with E
- cannot be repeated but end with CAB.

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?

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?

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?

Find the Co-efficient of x^{11} in the expansion of `(x + 2/x^2)^17`

## Chapter 2: Algebra

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

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

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