NCERT solution Class 11 binomial theorem

NCERT Solutions

Class 11 Maths

Binomial Theorem

NCERT Questions

Ex.8.1 Q.1
Ex.8.1 Q.2
Ex.8.1 Q.3
Ex.8.1 Q.4
Ex.8.1 Q.5
Ex.8.1 Q.6
Ex.8.1 Q.7
Ex.8.1 Q.8
Ex.8.1 Q.9
Ex.8.1 Q.10
Ex.8.1 Q.11
Ex.8.1 Q.12
Ex.8.1 Q.13
Ex.8.1 Q.14
Ex.8.2 Q.1
Ex.8.2 Q.2
Ex.8.2 Q.3
Ex.8.2 Q.4
Ex.8.2 Q.5
Ex.8.2 Q.6
Ex.8.2 Q.7
Ex.8.2 Q.8
Ex.8.2 Q.9
Ex.8.2 Q.10
Ex.8.2 Q.11
Ex.8.2 Q.12
Ex.Misc Q.1
Ex.Misc.Q.2
Ex.Misc.Q.3
Ex.Misc.Q.4
Ex.Misc.Q.5
Ex.Misc.Q.6
Ex.Misc.Q.7
Ex.Misc.Q.8
Ex.Misc.Q.9
Ex.Misc.Q.10

Ex.Misc.Q.9

Expand using Binomial Theorem (1 + – )⁴, x ≠ 0.

Using Binomial Theorem, the given expression (1 + – )⁴ can be expanded as

(1 + – )⁴ = {(1 + ) – }⁴

= ⁴C₀ (1 + )⁴ - ⁴C₁ (1 + )³ ( ) + ⁴C₂ (1 + )² ( )² - ⁴C₃ (1 + )( )³ + ⁴C₄ ( )⁴

= (1 + )⁴ - 4(1 + )³ ( ) + 6(1 + )² (4 ÷ x²) - 4(1 + )(8 ÷ x³) + (16 ÷ x⁴)

= (1 + )⁴ - (1 + x2 )³ (8x ) + (1 + x + (x² ÷ 4)) (24 ÷ x²) - (1 + )(32 ÷ x³) + (16 ÷ x⁴)

= (1 + )⁴ - (1 + x2 )³ ( ) + (24 ÷ x²) + + 6 – (32 ÷ x³) – (16 ÷ x²) + (16 ÷ x⁴)

= (1 + )⁴ - (1 + )³ ( ) + (8 ÷ x²) + (24 ÷ x) + 6 – (32 ÷ x³) + (16 ÷ x⁴)

=> (1 + – )⁴ = (1 + )⁴ - (1 + )³ ( ) + (8 ÷ x²) + + 6 – (32 ÷ x³) + (16 ÷ x⁴) ………. (1)

Again, by using Binomial Theorem, we obtain

(1 + )⁴ = ⁴C₀ (1)⁴ + ⁴C₁ (1)³ ( ) + ⁴C₂ (1)² ( )² + ⁴C₃ (1) ( )³ + ⁴C₄ ( )⁴

= 1 + 4 × (x2 ) + 6 × (x² ÷ 4) + 4 × (x³ ÷ 8) + (x⁴ ÷ 16)

=> (1 + )⁴ = 1 + 2x + (3x² ÷ 2) + (x³ ÷ 2) + (x⁴ ÷ 16) …………... (2)

(1 + )³ = ³C₀ (1)³ + ³C₁ (1)² ( ) + ³C₂ (1) ( )² + ³C₃ ( )³

=> (1 + )³ = 1 + + 3(x² ÷ 4) + (x³ ÷ 8) …………... (3)

From equation (1), (2), and (3), we get

(1 + – )⁴ = 1 + 4 × ( ) + 6 × (x² ÷ 4) + 4 × (x³÷ 8) + (x⁴ ÷ 16) –

[1 + + (3x²÷ 4) + (x³ ÷ 8)] ( ) + (8 ÷ x²) + (24 ÷ x) + 6 – (32 ÷ x³) + (16 ÷ x⁴)

= 1 + 2x + x² + (x³ ÷ 2) + (x⁴ ÷ 16) – - 12 – 6x – x² + (8 ÷ x²) + (24 ÷ x) + 6 – (32 ÷ x³) + (16 ÷ x⁴)

= + (8 ÷ x²) – (32 ÷ x³) +(16 ÷ x⁴) + (x² ÷ 2) + (x³ ÷ 2) + (x⁴ ÷ 16) - 5

Video solution:

Binomial Theorem Class 11 Maths NCERT Chapter 7 NCERT Solutions

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NCERT solutions of Binomial Theorem Class 11 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 11 Maths Binomial Theorem NCERT solutions.