Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Highly selective Backlog Qs for JEE MainMathematicsBinomial Theorem

The coefficient of x²⁰ in the expansion of (1+3 x+3 x^2+x^3 )²⁰ is

Options

  1. A60 40
  2. B30 20
  3. C¹⁵ C ₂
  4. DNone of these

Correct answer

A. 60 40

Step-by-step solution

Given expansion is (1+3 x+3 x^2+x^3 )²⁰ aligned & = ((1+x)^3 )²⁰ & =(1+x)⁶⁰ aligned In the expansion of (a+b)^n,(r+1) th term is given by t_ r+1 = ^n C_r a^r b^ n-r or t_ r+1 = ^n C_r a^ n-r b^r 21 st term in Eq. (i) will contain the coefficient of x²⁰ and it is given by t₂₁= 60 20 x²⁰, 1⁴⁰= 60 20 x²⁰ Coefficient of x²⁰ in (1+x)⁶⁰ is 60 20 or 60 40 .

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 Highly selective Backlog Qs for JEE Main PYQs