#### Chapters

Chapter 2: Basic Algebra

Chapter 3: Trigonometry

Chapter 4: Combinatorics and Mathematical Induction

Chapter 5: Binomial Theorem, Sequences and Series

Chapter 6: Two Dimensional Analytical Geometry

Chapter 7: Matrices and Determinants

Chapter 8: Vector Algebra

Chapter 9: Differential Calculus - Limits and Continuity

Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation

Chapter 11: Integral Calculus

Chapter 12: Introduction to probability theory

## 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 Exercise 5.1 [Page 210]

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

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

Compute 102^{4}

Compute 99^{4}

Compute 9^{7}

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

Find the coefficient of x^{15} in `(x^2 + 1/x^3)^10`

Find the coefficient of x^{2} and the coefficient of x^{6} in `(x^2 -1/x^3)^6`

Find the coefficient of x^{4} in the expansion `(1 + x^3)^50 (x^2 + 1/x)^5`

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

Find the last two digits of the number 3^{600}

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

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

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

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

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

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

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

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

### 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]

Write the first 6 terms of the sequences whose n^{th} 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))`

Write the first 6 terms of the sequences whose n^{th} 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))`

Write the first 6 terms of the sequences whose n^{th} 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"`

^{th} terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them

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

^{th} 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)`

^{th} terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them

2018

^{th} 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))`

Write the first 6 terms of the sequences whose n^{th} term a_{n} is given below

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

Write the first 6 terms of the sequences whose n^{th} term a_{n} is given below

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

Write the first 6 terms of the sequences whose n^{th} term a_{n} is given below

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

Write the n^{th} term of the following sequences.

2, 2, 4, 4, 6, 6, . . .

Write the n^{th} term of the following sequences.

`1/2, 2/3, 3/4, 4/5, 5/6, ...`

Write the n^{th} term of the following sequences.

`1/2, 3/4, 5/6, 7/8, 9/10, ...`

Write the n^{th} term of the following sequences.

6, 10, 4, 12, 2, 14, 0, 16, −2, . . .

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

Write the n^{th} 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

If t_{k} is the k^{th} term of a G.P., then show that t_{n – k}, t_{n}, t_{n + k} also form a GP for any positive integer k

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

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

If the roots of the equation (q – r)x^{2} + (r – p)x + p – q = 0 are equal, then show that p, q and r are in AP

If a , b , c are respectively the p^{th}, q^{th} and r^{th} terms of a G . P show that (q – r) log a + (r – p) log b + (p – q) log c = 0

### 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]

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

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

Compute the sum of first n terms of the following series:

8 + 88 + 888 + 8888 + ...

Compute the sum of first n terms of the following series:

6 + 66 + 666 + 6666 + ...

Compute the sum of first n terms of 1 + (1 + 4) + (1 + 4 + 4^{2}) + (1 + 4 + 4^{2} + 4^{3}) + ...

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

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

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

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?

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?

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 2^{nd} hour, 4^{th} hour and n^{th} hour?

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

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?

### 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]

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

`1/(5 + x)`

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`

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)`

`(x + 2) - 2/3`

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

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

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

Write the first 6 terms of the exponential series

e^{5x}

Write the first 6 terms of the exponential series

`"e"^(-2x)`

Write the first 6 terms of the exponential series

`"e"^(1/2x)`

Write the first 4 terms of the logarithmic series

log(1 + 4x) Find the intervals on which the expansions are valid.

Write the first 4 terms of the logarithmic series

log(1 – 2x) Find the intervals on which the expansions are valid.

Write the first 4 terms of the logarithmic series

`log((1 + 3x)/(1 -3x))` Find the intervals on which the expansions are valid.

Write the first 4 terms of the logarithmic series

`log((1 - 2x)/(1 + 2x))` Find the intervals on which the expansions are valid.

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) + ...`

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)`

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

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

### 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

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)

Choose the correct alternative:

The coefficient of x^{6} in (2 + 2x)^{10} is

^{10}C_{6}2

^{6}^{10}C_{6}2^{6}^{10}C_{6}2^{10}

Choose the correct alternative:

The coefficient of x^{8}y^{12} in the expansion of (2x + 3y)^{20} is

0

2

^{8}3^{12}2

^{8}3^{12}+ 2^{12}3^{8}^{20}C_{8}2^{8}3^{12}

Choose the correct alternative:

If ^{n}C_{10} > ^{n}C_{r} for all possible r, then a value of n is

10

21

19

20

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

Choose the correct alternative:

If (1 + x^{2})^{2} (1 + x)^{n} = a_{0} + a_{1}x + a_{2}x^{2} + …. + x^{n + 4} and if a_{0}, a_{1}, a_{2} are in AP, then n is

1

2

3

4

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

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

Choose the correct alternative:

The HM of two positive numbers whose AM and GM are 16, 8 respectively is

10

6

5

4

Choose the correct alternative:

If S_{n} denotes the sum of n terms of an AP whose common difference is d, the value of S_{n} − 2S_{n−1} + S_{n−2} is

d

2d

4d

d

^{2}

Choose the correct alternative:

The remainder when 38^{15} is divided by 13 is

12

1

11

5

Choose the correct alternative:

The n^{th} term of the sequence 1, 2, 4, 7, 11, …… is

n

^{2}+ 3n^{2}+ 2nn

^{3}– 3n^{2}+ 3n`("n"("n" + 1)("n" + 2))/3`

`("n"^2 - "n" + 2)/2`

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`

Choose the correct alternative:

The n^{th} term of the sequence `1/2, 3/4, 7/8, 15/16, ...` is

2

^{n}– n – 11 – 2

^{-n}2

^{-n}+ n – 12

^{n-1}

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

Choose the correct alternative:

The value of the series `1/2 + 7/4 + 13/8 + 19/16 + ...` is

14

7

4

6

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`

Choose the correct alternative:

The coefficient of x^{5} in the series e^{-2x} is

`2/3`

`3/2`

`- 4/15`

`4/15`

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")`

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

## 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