Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202017 Sep 2020Evening ShiftMathematicsBinomial TheoremActual

The coefficient of (x⁵⁰ ) in the expansion of (( l +x)¹⁰⁰⁰+x( l +x)⁹⁹⁹ ) (+x^2(1+x)⁹⁹⁸+ +x¹⁰⁰⁰ ) is

Options

  1. A( 1000 50 )
  2. B( ⁹⁹⁹ C ₅₀ )
  3. C( 1000 51 )
  4. D( 1001 50 )

Correct answer

D. ( 1001 50 )

Step-by-step solution

Expression given is, ( aligned & f(x)=(l+x)¹⁰⁰⁰+x(l+x)⁹⁹⁹+x^2(l+x)⁹⁹⁸ + .+x¹⁰⁰⁰, aligned ) This is a Geometric progression, common ratio (= x 1+x ) and number of terms 1001 . So, ( aligned f(x) & = (1+x)¹⁰⁰⁰ (1- ( x 1+x )¹⁰⁰¹ ) (1- x 1+x ) & =(1+x)¹⁰⁰¹-x¹⁰⁰¹ aligned ) So, coefficient of (x⁵⁰ ) ( aligned & = coefficient of x⁵⁰ in (1+x)¹⁰⁰¹ & = ^n C₅₀= 1001 50 aligned )

Practice Binomial Theorem on Quantrex Academy →

More from Binomial Theorem

If n 13 , n 14 and n 15 are in arithmetic progression, then the positive integer value of ' n ' can be 2026If the coefficients of x^2 and x^3 in the expansion of (3 + kx)^9 are equal, then the value of ' k ' is 2026The remainder when 7¹⁰³ is divided by 25 is 2026_ r=1 ¹⁵ r^2 ( ¹⁵ C_r 15 r-1 )= 20251 81^ n - ^ 2 n C ₁ 10 81^ n + ^ 2 n C ₂ 10^2 81^ n - + 10^ 2 n 81^ n = 2025If x is positive real number and the first negative term in the expansion of (1+ x )^ 27 / 5 is t _ k then k = 2025In the binomial expansion of (p-q)¹⁴ , if the sum of 7^ th term and 8^ th term is zero, then p+q p-q = 2025The numerically greatest term in the expansion of (x+3 y)¹³ , when x= 1 2 and y= 1 3 is 2025 Full Binomial Theorem list All AP EAMCET PYQs