Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2023MathematicsBinomial TheoremActual

Consider the following statements for a fixed natural number n : 1. C (n, r) is greatest if n=2 r 2. C (n, r) is greatest if n=2 r-1 and n=2 r+1 Which of the statements given above is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

D. Neither 1 nor 2

Step-by-step solution

C(n, r) is greatest (i) when n is even then n=2 r-2 (ii) when n is odd, For maximum value, n=2 r-1 and 2 r-3 .

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