Find the 4 th term from the end in the expansion of 4 x 5 - 5 2 x 9 .

The r t h term from end in expansion of x + a n ⇒ n + 2 - r t h term from beginning ∴ 4 th term from end in expansion of 4 x 5 - 5 2 x 9 ⇒ 9 + 2 - 4 th term from beginning ⇒ 7 th term from beginning T 7 = T 6 + 1 = C 6 9 4 x 5 9 - 6 . - 5 2 x 6 = C 6 9 4 5 3 5 2 6 1 x 3 = 10500 x 3

Find the coefficient of x 10 in the expansion of 2 x 2 - 1 x 20 .

Let r + 1 t h term contains x 10 in the binomial expansion of 2 x 2 - 1 x 20 ∴ T r + 1 = C r 20 2 x 2 20 - r . - 1 x r = - 1 r . C r 20 2 20 - r . x 40 - 3 r ...(i) T r + 1 contains x 10 ∴ 40 - 3 r = 10 ⇒ r = 10 So 10 + 1 = 11 th term contains x 10 Put r = 10 in (i), we get T 11 = - 1 10 . C 10 20 2 20 - 10 x 10 ∴ The coefficient of term contains x 10 is C 10 20 2 10 .

Find the coefficient of x 7 in the expansion of x - 1 x 2 40 .

Let r + 1 t h term contains x 7 in expansion of x - 1 x 2 40 ∴ T r + 1 = C r 40 x 40 - r - 1 x 2 r = - 1 r C r 40 x 40 - 3 r ...(i) T r + 1 contains x 7 ∴ 40 - 3 r = 7 ⇒ r = 11 ⇒ r + 1 t h = 11 + 1 t h = 12 t h term contain x 7 Put r = 11 in (i), we get T 11 = - 1 11 . C 11 40 x 7 ∴ Coefficient of x 7 = - C 11 40

Find the coefficient of x - 15 in the expansion of 3 x 2 - a 3 x 3 10 .

Let r + 1 t h term contains x - 15 in expansion of 3 x 2 - a 3 x 2 10 ∴ T r + 1 = C r 10 3 x 2 10 - r . - a 3 x 3 r = 10 C r 3 10 - 2 r - a r . x 20 - 5 r ...(i) T r + 1 contains x - 15 ∴ 20 - 5 r = - 15 ⇒ r = 7 Put r = 7 in (i), we get T 7 + 1 = C 7 10 3 - 4 - a 7 x - 15 ∴ Coefficient of x - 15 = C 7 - 10 × 3 - 4 a 7 = - 40 27 a 7 .

Find the coefficient of x m in the expansion of x + 1 x n .

Let r + 1 t h term contains x m in expansion of x + 1 x n ∴ T r + 1 = C r n x n - r . 1 x r = C r n x n - 2 r ...(i) r + 1 t h term contains x m ∴ n -2 r = m ⇒ r = n - m 2 Put r = n - m 2 in (i), we get T n - m 2 + 1 = n C n - m 2 x m ∴ Coefficient of x m = C n - m 2 n = n ! n - m 2 ! × n + m 2 !

E M B I B E

MATHEMATICS for CLASS XI>Chapter 18 - Binomial Theorem>EXERCISE 18.2

R D Sharma Solutions for Chapter: Binomial Theorem, Exercise 2: EXERCISE 18.2

Author:R D Sharma

R D Sharma Mathematics Solutions for Exercise - R D Sharma Solutions for Chapter: Binomial Theorem, Exercise 2: EXERCISE 18.2

Attempt the free practice questions on Chapter 18: Binomial Theorem, Exercise 2: EXERCISE 18.2 with hints and solutions to strengthen your understanding. MATHEMATICS for CLASS XI solutions are prepared by Experienced Embibe Experts.

Questions from R D Sharma Solutions for Chapter: Binomial Theorem, Exercise 2: EXERCISE 18.2 with Hints & Solutions

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 18 - Binomial Theorem>EXERCISE 18.2>Q 7

Find the $4^{th}$ term from the end in the expansion of $= \frac{10500}{x^{3}}$ .

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 18 - Binomial Theorem>EXERCISE 18.2>Q 9

Find the coefficient of $x^{10}$ in the expansion of ${(2 x^{2} - \frac{1}{x})}^{20}$ .

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 18 - Binomial Theorem>EXERCISE 18.2>Q 9

Find the coefficient of $x^{7}$ in the expansion of ${(x - \frac{1}{x^{2}})}^{40}$ .

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 18 - Binomial Theorem>EXERCISE 18.2>Q 9

Find the coefficient of $x^{- 15}$ in the expansion of ${(3 x^{2} - \frac{a}{3 x^{3}})}^{10}$ .

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 18 - Binomial Theorem>EXERCISE 18.2>Q 9

Find the coefficient of $x^{m}$ in the expansion of ${(x + \frac{1}{x})}^{n}$ .

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 18 - Binomial Theorem>EXERCISE 18.2>Q 16

If the term independent of $x$ in the expansion of ${(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{9}$ is $p$ , then find the value of $18 p .$

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 18 - Binomial Theorem>EXERCISE 18.2>Q 38

Find $n$ in the binomial ${(\sqrt[3]{2} + \frac{1}{\sqrt[3]{3}})}^{n}$ , if the ratio of $7^{t h}$ term from the beginning to the $7^{t h}$ term from the end is $\frac{1}{6}$ .