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Class XI Maths Binomial Theorem 2

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Question 1

Assuming x to be so small that x³ and higher powers of x can be neglected, then value of

Question 2

The coefficient of x⁷ in the expansion of (1 - x - x² + x³)⁶ is

Question 3

If the expansion in powers of x of the function (1 / ((1-ax)(1-bx))) is a₀ + a₁x + a₂x² + a₃x³ +… then a_n is

Question 4

For natural numbers m, n if (1 – y)^m(1 + y)ⁿ = 1 + a₁y + a₂y² + … , and a₁ = a₂ = 10, then (m, n) is

Question 5

The coefficient of xⁿ in the expansion of (1+x)(1-x)ⁿ is

Question 6

and

, then

is equal to

Question 7

The sum of the series ²⁰C₀ – ²⁰C₁ + ²⁰C₂ – ²⁰C₃ + ....... - ²⁰C₉ is

Question 8

If C₀, C₁, C₂, ............ C_n are the Binomial coefficients in the expansion of (1 + x)ⁿ, n being even, then C₀ + (C₀ + C₁) + (C₀ + C₁ + C₂) + ..... + (C₀ + C₁ + C₂ + ........+ C_n–1) is equal to

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