Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2006MathematicsBinomial TheoremActual

If the expansion in powers of x of the function 1 (1-a x)(1-b x) is a₀+a₁ x+a₂ x^2+a₃ x^3+ , then a_n is

Options

  1. Ab^n-a^n b-a
  2. Ba^n-b^n b-a
  3. Ca^ n+1 -b^ n+1 b-a
  4. Db^ n+1 -a^ n+1 b-a

Correct answer

D. b^ n+1 -a^ n+1 b-a

Step-by-step solution

(1-a x)⁻¹(1-b x)⁻¹= (1+a x+a^2 x^2+ ) (1+b x+b^2 x^2+ . ) coefficient of x^n=b^n+a b^ n-1 +a^2 b^ n-2 + .+a^ n-1 b+a^n= b^ n+1 -a^ n+1 b-a a_n= b^ n+1 -a^ n+1 b-a

Practice Binomial Theorem on Quantrex Academy →

More from Binomial Theorem

If 26 ( 2^3 3 12 2 + 2^5 5 12 4 + 2^7 7 12 6 + + 2¹³ 13 12 12 ) = 3¹³ - , then is equal to: 2026If (1 - x^3)¹⁰ = _ r=0 ¹⁰ a_r x^r (1-x)^ 30-2r , then 9a₉ a₁₀ is equal to __________. 2026If the coefficients of the middle terms in the binomial expansions of (1 + x)²⁶ and (1 - x)²⁸ , 0 , are equal, then the value of is: 2026The coefficient of x^2 in the expansion of (2x^2 + 1 x )¹⁰ , x 0 , is : 2026If the sum of the coefficients of x^7 and x¹⁴ in the expansion of ( 1 x^3 - x^4 )^n , x 0 , is zero, then the value of n is __________. 2026In the expansion of (9x- 1 3 x )¹⁸ , x>0 , if the term independent of x is (221)k , then k is equal to: 2026Let the smallest value of k N , for which the coefficient of x^3 in (1+x)^3 + (1+x)^4 + (1+x)^5 + + (1+x)⁹⁹ + (1+kx)¹⁰⁰ , x 0 , is (43n + 101 4 ) (¹⁰⁰C₃ ) for some n N , be p . The 2026If for 3 r 30 , 30 30-r + 3 30 31-r + 3 30 32-r + 30 33-r = m r , then m equals: 2026 Full Binomial Theorem list All JEE Main PYQs