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Most Important Selected Qs for JEE AdvancedMathematicsBinomial Theorem

Let (1+x^2 )^2(1+x)^n=A₀+A₁ x+A₂ x^2+ . If A₀, A₁, A₂ are in A.P. then the value of n is

Options

  1. A2
  2. B3
  3. C5
  4. D7

Correct answer

B. 3

Step-by-step solution

(1+x^2 )^2(1+x)^n= (1+2 x^2+x^4 ) ( ^n C₀+ ^n C₁ x+ ^n C₂ x^2+ )= ^n C ₀+ ^n C ₁ x + ( ^n C ₂+2 ^n C ₀ ) x ^2+ Hence, A₀=1 ; A₁= ^n C₁ ; A₂= ^n C₂+2 which are in A.P.

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