Tamil Nadu Board of Secondary EducationHSC Science Class 11th

# Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 5 - Binomial Theorem, Sequences and Series [Latest edition]

#### Chapters ## Chapter 5: Binomial Theorem, Sequences and Series

Exercise 5.1Exercise 5.2Exercise 5.3Exercise 5.4Exercise 5.5
Exercise 5.1 [Page 210]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 5 Binomial Theorem, Sequences and Series Exercise 5.1 [Page 210]

Exercise 5.1 | Q 1. (i) | Page 210

Expand (2x^2 - 3/x)^3

Exercise 5.1 | Q 1. (ii) | Page 210

Expand (2x^2 -3sqrt(1 - x^2))^4 + (2x^2 + 3sqrt(1 - x^2))^4

Exercise 5.1 | Q 2. (i) | Page 210

Compute 1024

Exercise 5.1 | Q 2. (ii) | Page 210

Compute 994

Exercise 5.1 | Q 2. (iii) | Page 210

Compute 97

Exercise 5.1 | Q 3 | Page 210

Using binomial theorem, indicate which of the following two number is larger: (1.01)^(1000000), 10

Exercise 5.1 | Q 4 | Page 210

Find the coefficient of x15 in (x^2 + 1/x^3)^10

Exercise 5.1 | Q 5 | Page 210

Find the coefficient of x2 and the coefficient of x6 in (x^2 -1/x^3)^6

Exercise 5.1 | Q 6 | Page 210

Find the coefficient of x4 in the expansion (1 + x^3)^50 (x^2 + 1/x)^5

Exercise 5.1 | Q 7 | Page 210

Find the constant term of (2x^3 - 1/(3x^2))^5

Exercise 5.1 | Q 8 | Page 210

Find the last two digits of the number 3600

Exercise 5.1 | Q 9 | Page 210

If n is a positive integer, using Binomial theorem, show that, 9n+1 − 8n − 9 is always divisible by 64

Exercise 5.1 | Q 10 | Page 210

If n is an odd positive integer, prove that the coefficients of the middle terms in the expansion of (x + y)n are equal

Exercise 5.1 | Q 11 | Page 210

If n is a positive integer and r is a non-negative integer, prove that the coefficients of xr and xn−r in the expansion of (1 + x)n are equal

Exercise 5.1 | Q 12 | Page 210

If a and b are distinct integers, prove that a − b is a factor of an − bn, whenever n is a positive integer. [Hint: write an = (a − b + b)n and expaand]

Exercise 5.1 | Q 13 | Page 210

In the binomial expansion of (a + b)n, if the coefficients of the 4th and 13th terms are equal then, find n

Exercise 5.1 | Q 14 | Page 210

If the binomial coefficients of three consecutive terms in the expansion of (a + x)n are in the ratio 1 : 7 : 42, then find n

Exercise 5.1 | Q 15 | Page 210

In the binomial expansion of (1 + x)n, the coefficients of the 5th, 6th and 7th terms are in AP. Find all values of n

Exercise 5.1 | Q 16 | Page 210

Prove that "C"_0^2 + "C"_1^2 + "C"_2^2 + ... + "C"_"n"^2 = (2"n"!)/("n"!)^2

Exercise 5.2 [Pages 217 - 218]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 5 Binomial Theorem, Sequences and Series Exercise 5.2 [Pages 217 - 218]

Exercise 5.2 | Q 1. (i) | Page 217

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them

1/(2^("n"+ 1))

Exercise 5.2 | Q 1. (ii) | Page 217

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them

(("n" + 1)("n" + 2))/(("n" + 3)("n" + 4))

Exercise 5.2 | Q 1. (iii) | Page 217

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them

4 (1/2)^"n"

Exercise 5.2 | Q 1. (iv) | Page 217

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them

(- 1)^"n"/"n"

Exercise 5.2 | Q 1. (v) | Page 217

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them

(2"n" + 3)/(3"n" + 4)

Exercise 5.2 | Q 1. (vi) | Page 217

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them

2018

Exercise 5.2 | Q 1. (vii) | Page 217

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them

(3"n" - 2)/(3^("n" - 1))

Exercise 5.2 | Q 2. (i) | Page 217

Write the first 6 terms of the sequences whose nth term an is given below

an = {{:("n" + 1,  "if"  "n is odd"),("n",  "if"  "n is even"):}

Exercise 5.2 | Q 2. (ii) | Page 217

Write the first 6 terms of the sequences whose nth term an is given below

an = {{:(1,  "if n" = 1),(2,  "if n" = 2),("a"_("n" - 1) + "a"_("n" - 2),  "if n" > 2):}}

Exercise 5.2 | Q 2. (iii) | Page 217

Write the first 6 terms of the sequences whose nth term an is given below

an = {{:("n",  "if n is"  1","  2  "or"  3),("a"^("n" - 1) + "a"_("n" - 2) + "a"_("n" - 3), "if n" > 3):}

Exercise 5.2 | Q 3. (i) | Page 218

Write the nth term of the following sequences.
2, 2, 4, 4, 6, 6, . . .

Exercise 5.2 | Q 3. (ii) | Page 218

Write the nth term of the following sequences.
1/2, 2/3, 3/4, 4/5, 5/6, ...

Exercise 5.2 | Q 3. (iii) | Page 218

Write the nth term of the following sequences.
1/2, 3/4, 5/6, 7/8, 9/10, ...

Exercise 5.2 | Q 3. (iv) | Page 218

Write the nth term of the following sequences.
6, 10, 4, 12, 2, 14, 0, 16, −2, . . .

Exercise 5.2 | Q 4 | Page 218

The product of three increasing numbers in GP is 5832. If we add 6 to the second number and 9 to the third number, then resulting numbers form an AP. Find the numbers in GP

Exercise 5.2 | Q 5 | Page 218

Write the nth term of the sequence 3/(1^2 2^2), 5/(2^2 3^2), 7/(3^2 4^2), ... as a difference of two terms

Exercise 5.2 | Q 6 | Page 218

If tk is the kth term of a G.P., then show that tn – k, tn, tn + k also form a GP for any positive integer k

Exercise 5.2 | Q 7 | Page 218

If a, b, c are in geometric progression, and if "a"^(1/x) = "b"^(1/y) = "C"^(1/z), then prove that x, y, z are in arithmetic progression

Exercise 5.2 | Q 8 | Page 218

The AM of two numbers exceeds their GM by 10 and HM by 16. Find the numbers

Exercise 5.2 | Q 9 | Page 218

If the roots of the equation (q – r)x2 + (r – p)x + p – q = 0 are equal, then show that p, q and r are in AP

Exercise 5.2 | Q 10 | Page 218

If a , b , c are respectively the pth, qth and rth terms of a G . P show that (q – r) log a + (r – p) log b + (p – q) log c = 0

Exercise 5.3 [Page 220]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 5 Binomial Theorem, Sequences and Series Exercise 5.3 [Page 220]

Exercise 5.3 | Q 1 | Page 220

Find the sum of the first 20-terms of the arithmetic progression having the sum of first 10 terms as 52 and the sum of the first 15 terms as 77

Exercise 5.3 | Q 2 | Page 220

Find the sum up to the 17th term of the series 1^3/1 + (1^3 + 2^3)/(1 + 3) + (1^3 + 2^3 + 3^3)/(1 + 3 + 5) + ...

Exercise 5.3 | Q 3. (i) | Page 220

Compute the sum of first n terms of the following series:
8 + 88 + 888 + 8888 + ...

Exercise 5.3 | Q 3. (ii) | Page 220

Compute the sum of first n terms of the following series:
6 + 66 + 666 + 6666 + ...

Exercise 5.3 | Q 4 | Page 220

Compute the sum of first n terms of 1 + (1 + 4) + (1 + 4 + 42) + (1 + 4 + 42 + 43) + ...

Exercise 5.3 | Q 5 | Page 220

Find the general term and sum to n terms of the sequence 1, 4/3, 7/9, 10/27, ......

Exercise 5.3 | Q 6 | Page 220

Find the value of n, if the sum to n terms of the series sqrt(3) + sqrt(75) + sqrt(243) + ...... is 435 sqrt(3)

Exercise 5.3 | Q 7 | Page 220

Show that the sum of (m + n)th and (m − n)th term of an AP. is equal to twice the mth term

Exercise 5.3 | Q 8 | Page 220

A man repays an amount of Rs.3250 by paying Rs.20 in the first month and then increases the payment by Rs.15 per month. How long will it take him to clear the amount?

Exercise 5.3 | Q 9 | Page 220

In a race, 20 balls are placed in a line at intervals of 4 meters, with the first ball 24 meters away from the starting point. A contestant is required to bring the balls back to the starting place one at a time. How far would the contestant run to bring back all balls?

Exercise 5.3 | Q 10 | Page 220

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour?

Exercise 5.3 | Q 11 | Page 220

What will Rs.500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?

Exercise 5.3 | Q 12 | Page 220

In a certain town, a viral disease caused severe health hazards upon its people disturbing their normal life. It was found that on each day, the virus which caused the disease spread in Geometric Progression. The amount of infectious virus particle gets doubled each day, being 5 particles on the first day. Find the day when the infectious virus particles just grow over 1,50,000 units?

Exercise 5.4 [Page 231]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 5 Binomial Theorem, Sequences and Series Exercise 5.4 [Page 231]

Exercise 5.4 | Q 1. (i) | Page 231

Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid

1/(5 + x)

Exercise 5.4 | Q 1. (ii) | Page 231

Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid

2/(3 + 4x)^2

Exercise 5.4 | Q 1. (iii) | Page 231

Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid

(5 + x^2)^(2/3)

Exercise 5.4 | Q 1. (iv) | Page 231

Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid

(x + 2) - 2/3

Exercise 5.4 | Q 2 | Page 231

Find root(3)(10001) approximately (two decimal places

Exercise 5.4 | Q 3 | Page 231

Prove that root(3)(x^3 + 6) - root(3)(x^3 + 3) is approximately equal to 1/x^2 when x is sufficiently large

Exercise 5.4 | Q 4 | Page 231

Prove that sqrt((1 - x)/(1 + x)) is approximately euqal to 1 - x + x^2/2 when x is very small

Exercise 5.4 | Q 5. (i) | Page 231

Write the first 6 terms of the exponential series
e5x

Exercise 5.4 | Q 5. (ii) | Page 231

Write the first 6 terms of the exponential series
"e"^(-2x)

Exercise 5.4 | Q 5. (iii) | Page 231

Write the first 6 terms of the exponential series
"e"^(1/2x)

Exercise 5.4 | Q 6. (i) | Page 231

Write the first 4 terms of the logarithmic series
log(1 + 4x) Find the intervals on which the expansions are valid.

Exercise 5.4 | Q 6. (ii) | Page 231

Write the first 4 terms of the logarithmic series
log(1 – 2x) Find the intervals on which the expansions are valid.

Exercise 5.4 | Q 6. (iii) | Page 231

Write the first 4 terms of the logarithmic series
log((1 + 3x)/(1 -3x)) Find the intervals on which the expansions are valid.

Exercise 5.4 | Q 6. (iv) | Page 231

Write the first 4 terms of the logarithmic series
log((1 - 2x)/(1 + 2x)) Find the intervals on which the expansions are valid.

Exercise 5.4 | Q 7 | Page 231

If y = x + x^2/2 + x^3/3 + x^4/4  ..., then show that x = y - y^2/(2!) + y^3/(3!) - y^4/(4) + ...

Exercise 5.4 | Q 8 | Page 231

If p − q is small compared to either p or q, then show root("n")("p"/"q") (("n" + 1)"p" + ("n" - 1)"q")/(("n"- 1)"p" +("n" + 1)"q"). Hence find root(8)(15/16)

Exercise 5.4 | Q 9 | Page 231

Find the coefficient of x4 in the expansion (3 - 4x + x^2)/"e"^(2x)

Exercise 5.4 | Q 10 | Page 231

Find the value of sum_("n" = 1)^oo 1/(2"n" - 1) (1/(9^("n" - 1)) + 1/(9^(2"n"- 1)))

Exercise 5.5 [Pages 232 - 233]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 5 Binomial Theorem, Sequences and Series Exercise 5.5 [Pages 232 - 233]

#### MCQ

Exercise 5.5 | Q 1 | Page 232

Choose the correct alternative:
The value of 2 + 4 + 6 + … + 2n is

• ("n"("n" - 1))/2

• ("n"("n" + 1))/2

• (2"n"(2"n" + 1))/2

• n(n + 1)

Exercise 5.5 | Q 2 | Page 232

Choose the correct alternative:
The coefficient of x6 in (2 + 2x)10 is

• 10C6

• 26

• 10C626

• 10C6210

Exercise 5.5 | Q 3 | Page 232

Choose the correct alternative:
The coefficient of x8y12 in the expansion of (2x + 3y)20 is

• 0

• 28312

• 28312 + 21238

• 20C828312

Exercise 5.5 | Q 4 | Page 232

Choose the correct alternative:
If nC10 > nCr for all possible r, then a value of n is

• 10

• 21

• 19

• 20

Exercise 5.5 | Q 5 | Page 232

Choose the correct alternative:
If a is the arithmetic mean and g is the geometric mean of two numbers, then

• a ≤ g

• a ≥ g

• a = g

• a > g

Exercise 5.5 | Q 6 | Page 232

Choose the correct alternative:
If (1 + x2)2 (1 + x)n = a0 + a1x + a2x2 + …. + xn + 4 and if a0, a1, a2 are in AP, then n is

• 1

• 2

• 3

• 4

Exercise 5.5 | Q 7 | Page 232

Choose the correct alternative:
If a, 8, b are in A.P, a, 4, b are in G.P, if a, x, b are in HP then x is

• 2

• 1

• 4

• 16

Exercise 5.5 | Q 8 | Page 232

Choose the correct alternative:
The sequence = 1/sqrt(3), 1/(sqrt(3) + sqrt(2)), 1/(sqrt(3) + 2sqrt(2)) ... form an

• AP

• GP

• HP

• AGP

Exercise 5.5 | Q 9 | Page 232

Choose the correct alternative:
The HM of two positive numbers whose AM and GM are 16, 8 respectively is

• 10

• 6

• 5

• 4

Exercise 5.5 | Q 10 | Page 232

Choose the correct alternative:
If Sn denotes the sum of n terms of an AP whose common difference is d, the value of Sn − 2Sn−1 + Sn−2 is

• d

• 2d

• 4d

• d2

Exercise 5.5 | Q 11 | Page 232

Choose the correct alternative:
The remainder when 3815 is divided by 13 is

• 12

• 1

• 11

• 5

Exercise 5.5 | Q 12 | Page 232

Choose the correct alternative:
The nth term of the sequence 1, 2, 4, 7, 11, …… is

• n2 + 3n2 + 2n

• n3 – 3n2 + 3n

• ("n"("n" + 1)("n" + 2))/3

• ("n"^2 - "n" + 2)/2

Exercise 5.5 | Q 13 | Page 232

Choose the correct alternative:
The sum up to n terms of the series 1/(sqrt(1)  +sqrt(3)) + 1/(sqrt(3) + sqrt(5)) + 1/(sqrt(5) + sqrt(7)) + ... is

• sqrt(2"n" + 1)

• sqrt(2"n" + 1)/2

• sqrt(2"n" + 1) - 1

• (sqrt(2"n" + 1) - 1)/2

Exercise 5.5 | Q 14 | Page 232

Choose the correct alternative:
The nth term of the sequence 1/2, 3/4, 7/8, 15/16, ... is

• 2n – n – 1

• 1 – 2-n

• 2-n + n – 1

• 2n-1

Exercise 5.5 | Q 15 | Page 232

Choose the correct alternative:
The sum up to n terms of the series sqrt(2) + sqrt(8) + sqrt(18) + sqrt(32) + ... is

• ("n"("n" + 1))/2

• 2n(n +  1)

• ("n"("n" + 1))/sqrt(2)

• 1

Exercise 5.5 | Q 16 | Page 233

Choose the correct alternative:
The value of the series 1/2 + 7/4 + 13/8 + 19/16 + ... is

• 14

• 7

• 4

• 6

Exercise 5.5 | Q 17 | Page 233

Choose the correct alternative:
The sum of an infinite GP is 18. If the first term is 6, the common ratio is

• 1/3

• 2/3

• 1/6

• 3/4

Exercise 5.5 | Q 18 | Page 233

Choose the correct alternative:
The coefficient of x5 in the series e-2x is

• 2/3

• 3/2

• - 4/15

• 4/15

Exercise 5.5 | Q 19 | Page 233

Choose the correct alternative:
The value of 1/(2!) + 1/(4!) + 1/(6!) + ... is

• ("e"^2 + 1)/(2"e")

• ("e" + 1)^2/(2"e")

• ("e" - 1)^2/(2"e")

• ("e"^2 - 1)/(2"e")

Exercise 5.5 | Q 20 | Page 233

Choose the correct alternative:
The value of 1 - 1/2(2/3) + 1/3(2/3)^2  1/4(2/3)^3 + ... is

• log (5/3)

• 3/2 log (5/3)

• 5/3 log (5/3)

• 2/3 log (2/3)

## Chapter 5: Binomial Theorem, Sequences and Series

Exercise 5.1Exercise 5.2Exercise 5.3Exercise 5.4Exercise 5.5 ## Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 5 - Binomial Theorem, Sequences and Series

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 5 (Binomial Theorem, Sequences and Series) 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 Mathematics Volume 1 and 2 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 Mathematics Volume 1 and 2 Answers Guide chapter 5 Binomial Theorem, Sequences and Series are Introduction to Binomial Theorem, Sequences and Series, Binomial Theorem, Particular Cases of Binomial Theorem, Finite Sequences, Finite Series, Infinite Sequences and Series.

Using Tamil Nadu Board Samacheer Kalvi Class 11th solutions Binomial Theorem, Sequences and Series 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 5 Binomial Theorem, Sequences and Series Class 11th extra questions for Class 11th Mathematics Volume 1 and 2 Answers Guide and can use Shaalaa.com to keep it handy for your exam preparation