Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2012MathematicsBinomial Theorem

Given positive integers r 1, n 2 and the coefficient of (3r) th and (r+2) th terms in the binomial expansion of (1+x)^ 2 n are equal, then

Options

  1. An=2 r
  2. Bn=2 r+1
  3. Cn=3 r
  4. DNone of these

Correct answer

A. n=2 r

Step-by-step solution

3 r th term in the expansion of (1+x)^ 2 n = 2 3 r-1 x^ 3 r-1 and (r+2) th term in the expansion of (1+x)^ 2 n = 2 n r+1 x^ r+1 Given that the binomial coefficients of (3r)th and (r+2) th terms are equal. array ll & 2 n 3 r-1 = 2 n r+1 & 3 r-1=r+1 or & 2 n=(3 r-1)+(r+1) & 2 r=2 or 2 n=4 r & r=1 or n=2 r But & r 1 & n=2 r array

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 Manipal MET PYQs