Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2011MathematicsBinomial TheoremActual

What is the ratio of coefficient of x¹⁵ to the term independent of x in (x^2+ 2 x )¹⁵ ?

Options

  1. A1 / 64
  2. B1 / 32
  3. C1 / 16
  4. D1 / 4

Correct answer

B. 1 / 32

Step-by-step solution

aligned n c₅ (2^5 ) n c₁₀(2)¹⁰ & = 15! 5!10! (2^5 ) 15! (2¹⁰ ) & = 32 32 32 = 1 32 aligned

Practice Binomial Theorem on Quantrex Academy →

More from Binomial Theorem

A set S contains (2n+1) elements. If the number of subsets of S which contain at most n elements is 1024 , then what is the value of n ? 2026Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: Consider the following statements : I. (u+v 2026Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: What is the value of u ? 2026What is the greatest value of r satisfying the inequality 15 r+1 >2 ¹⁵C_r ? 2026Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: What is the value of uv ? 2026Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: What is the value of (v+f) ? 2026Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: What is the multiplicative inverse of ( 2 + 2026If the sum of binomial coefficients in the expansion of (x + y)^n is 256, then the greatest binomial coefficient occurs in which one of the following terms? 2025 Full Binomial Theorem list All NDA PYQs