Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2017MathematicsBinomial TheoremActual

The coefficient of x 5 in the expansion of 1 + x 21 + 1 + x 22 + … + 1 + x 30 is

Options

  1. AC 5 51
  2. BC 5 9
  3. CC 6 31 - C 6 21
  4. DC 5 30 + C 5 20

Correct answer

C. C 6 31 - C 6 21

Step-by-step solution

1 + x 21 + 1 + x 22 + … … + 1 + x 30 = 1 + x 21 1 + 1 + x 1 + … + 1 + x 9 = 1 + x 21 1 + x 10 - 1 1 + x - 1 = 1 x 1 + x 31 - 1 + x 21 ∴ Coefficient of x 5 in the given expression = Coefficient of x 5 in 1 x 1 + x 31 - 1 + x 21 = Coefficient of x 6 in 1 + x 31 - 1 + x 21 = C 6 31 - C 6 21

Practice Binomial Theorem on Quantrex Academy →

More from Binomial Theorem

The coefficient of x^2 term in the binomial expansion of ( 1 3 x^ 1 2 +x^ -1 4 )¹⁰ is 2024The coefficient of x^n in the expansion of e^ 7 x +e^x e^ 3 x is 2024The coefficient of the highest power of x in the expansion of (x+ x^2-1 )^8+ (x- x^2-1 )^8 2024If the 17^ th and the 18^ th terms in the expansion of (2+a)⁵⁰ are equal, then the coefficient of x³⁵ in the expansion of (a+x)⁻² is 2024If x¹⁸ occurs in the rth term in the expansion of (x^4+ 1 x^3 )¹⁵ , then what is the value of r ? 2023The middle term in the expansion of ( 10 x + x 10 )¹⁰ is 2023The number of terms in the expansion of (1+5 2 x)^9+(1-5 2 x)^9 , is 2022If the sum of the coefficients in the expansion of (x+y)^n is 1024 , then the value of the greatest coefficient in the expansion is 2022 Full Binomial Theorem list All BITSAT PYQs