Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

In the expansion of x 4 5 + x - 1 5 n , the coeficient of the 8 t h and 19 t h terms are equal. The term independent of x is given by

Options

  1. AC 21 27
  2. BC 20 25
  3. CC 21 25
  4. DC 22 27

Correct answer

B. C 20 25

Step-by-step solution

Since there is no constant term the coefficient of 8 th and 19 th term are same as the binomial coefficients of 8 th and 19 th term. C 7 n = n C 18 ⇒ n = 7 + 18 = 25 T n + 1 = 25 C r x 4 5 25 - r r - 1 5 r C r 25 x 4 5 ( 25 - r ) - r 5 To be independent of x , 100 - 5 r 5 = 0 ⇒ r = 20 Hence, the required term is C 20 25

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 NTA Abhyas JEE Main PYQs