NCERT Solutions Class 11 Mathematics Chapter 8 Binomial Theorem Download In Pdf

Chapter 8 Binomial Theorem Download in pdf

**Expand each of the expressions in Exercises 1 to 5.
Using binomial theorem, evaluate each of the following:**

**Question 6.** (96)3

**Question 7.** (102)5

**Question 8.** (101)4

**Question 9.** (99)5

**Question 10.** Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.

**Question 11.** Find (a + b)4 â€“ (a â€“ b)4. Hence, evaluate ( 3 + 2)4â€“ ( 3 â€“ 2)4 .

**Question 12.** Find (x + 1)6 + (x â€“ 1)6. Hence or otherwise evaluate ( 2 + 1)6 + ( 2 â€“ 1)6.

**Question 13.** Show that 9n+1 â€“ 8n â€“ 9 is divisible by 64, whenever n is a positive integer.

EXERCISE 8.2

**Find the coefficient of**

**Question 1.** x5 in (x + 3)8 2. a5b7 in (a â€“ 2b)1

**Question 2.** Write the general term in the expansion of

**Question 3.** (x2 â€“ y)6

**Question 4.** (x2 â€“ yx)12, x â‰ 0.

**Question 5.** Find the 4th term in the expansion of (x â€“ 2y)12.

**Question 6.** Find the 13th term in the expansion of
18 9 1
3
x
x
, x â‰ 0.
Find the middle terms in the expansions of

**Question 7.** 3 7
6
3
âˆ’ x

**Question 8.** 10
9
3
x + y

**Question 9.** In the expansion of (1 + a)m+n, prove that coefficients of am and an are equal.

**Question 10.** The coefficients of the (r â€“ 1)th, rth and (r + 1)th terms in the expansion of (x + 1)n
are in the ratio 1 : 3 : 5. Find n and r.

**Question 11.** Prove that the coefficient of xn in the expansion of (1 + x)2n is twice the coefficient
of xn in the expansion of (1 + x)2n â€“ 1.

**Question 12.** Find a positive value of m for which the coefficient of x2 in the expansion
(1 + x)m is 6.

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- Chapter 1 Sets
- chapter 2 Relations And Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutations And Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences And Series
- Chapter 10 Straight Lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction To Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability

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