Expand using binomial theorem, 2 x - x 2 5

Using binomial theorem, we have, 2 x - x 2 5 = 5 0 2 x 5 - 5 1 2 x 4 x 2 1 + 5 2 2 x 3 x 2 2 - 5 3 2 x 2 x 2 3 + 5 4 2 x 1 x 2 4 - 5 5 x 2 5 = 2 x 5 - 5 2 x 4 x 2 1 + 10 2 x 3 x 2 2 - 10 2 x 2 x 2 3 + 5 2 x 1 x 2 4 - x 2 5 = 32 x 5 - 5 2 x 3 + 10 2 x - 10 x 2 + 5 x 2 3 - x 2 5 = 32 x 5 - 40 x 3 + 20 x - 5 x + 5 8 x 3 - 1 32

Simplify: ( x + x 2 - 1 ) 6 + ( x - x 2 - 1 ) 6

Let x 2 - 1 = y Then, ( x + x 2 - 1 ) 6 + ( x - x 2 - 1 ) 6 = ( x + y ) 6 + ( x - y ) 6 Using the result ( a + b ) n + ( a - b ) n = 2 n 0 a n + n 2 a n - 2 b 2 + n 4 a n - 4 b 4 + ⋯ we have, ( x + y ) 6 + ( x - y ) 6 = 2 6 0 x 6 + 6 2 x 4 y 2 + 6 4 x 2 y 4 + 6 6 y 6 = 2 x 6 + 15 x 4 y 2 + 15 x 2 y 4 + y 6 = 2 x 6 + 15 x 4 ( x 2 - 1 ) 2 + 15 x 2 ( x 2 - 1 ) 4 + ( x 2 - 1 ) 6 = 2 x 6 + 15 x 4 x 2 - 1 + 15 x 2 x 2 - 1 2 + x 2 - 1 3 = 2 x 6 + 15 x 6 - x 4 + 15 x 2 x 4 - 2 x 2 + 1 + x 6 - 3 x 4 + 3 x 2 - 1 = 2 x 6 + 15 x 6 - 15 x 4 + 15 x 6 - 30 x 4 + 15 x 2 + x 6 - 3 x 4 + 3 x 2 - 1 = 2 32 x 6 - 48 x 4 + 18 x 2 - 1 = 64 x 6 - 96 x 4 + 36 x 2 - 2

E M B I B E

Golden MATHEMATICS CLASS 11>Chapter 8 - Binomial Theorem>SELF EVALUATION TEST

A P Prabhakaran Solutions for Chapter: Binomial Theorem, Exercise 1: SELF EVALUATION TEST

Author:A P Prabhakaran

A P Prabhakaran Mathematics Solutions for Exercise - A P Prabhakaran Solutions for Chapter: Binomial Theorem, Exercise 1: SELF EVALUATION TEST

Attempt the free practice questions on Chapter 8: Binomial Theorem, Exercise 1: SELF EVALUATION TEST with hints and solutions to strengthen your understanding. Golden MATHEMATICS CLASS 11 solutions are prepared by Experienced Embibe Experts.

Questions from A P Prabhakaran Solutions for Chapter: Binomial Theorem, Exercise 1: SELF EVALUATION TEST with Hints & Solutions

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 8 - Binomial Theorem>SELF EVALUATION TEST>Q 1

Using binomial theorem, expand $(101)^{4}$

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 8 - Binomial Theorem>SELF EVALUATION TEST>Q 2

Expand using binomial theorem, ${(\frac{2}{x} - \frac{x}{2})}^{5}$

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 8 - Binomial Theorem>SELF EVALUATION TEST>Q 3

Simplify: $(x + \sqrt{x^{2} - 1})^{6} + (x - \sqrt{x^{2} - 1})^{6}$

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 8 - Binomial Theorem>SELF EVALUATION TEST>Q 4

Using binomial theorem, prove that $6^{n} - 5 n - 1$ is always divisible by $25,$ where $n$ is a natural number.

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 8 - Binomial Theorem>SELF EVALUATION TEST>Q 5

Find $k$ , if the fourth term from the end is $\frac{k}{x^{3}}$ in the expansion of ${(\frac{4 x}{5} - \frac{5}{2 x})}^{9}$

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 8 - Binomial Theorem>SELF EVALUATION TEST>Q 6

Find the middle term in the expansion of ${(\frac{2 x^{2}}{3} + \frac{3}{2 x^{2}})}^{10}$

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 8 - Binomial Theorem>SELF EVALUATION TEST>Q 7

Prove that the coefficient of the middle term in the expansion of $(1 + x)^{2 n}$ equal to the sum of the coefficients of the two middle terms in the expansion of $(1 + x)^{2 n - 1}$ .