Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202418 May 2024Morning ShiftMathematicsBinomial TheoremActual

The coefficient of x^5 in (3+x+x^2 )^6 is

Options

  1. A18
  2. B540
  3. C1620
  4. D2178

Correct answer

D. 2178

Step-by-step solution

Since, the general term in the expansion (3+x+x^2 )^6= 6! p!q!r! 3^p x^q (x^2 )^r , where p+q+r=6= 6!.3^p x^ q+2 r p!q!r! , where, p+q+r=6 Since, q+2 r=5 q=5-2 r and, p+5-2 r+r=6 p=1+r If r=0 p=1, q=5 . If r=1 p=2, q=3 If r=2 p=3, q=1 . So, co-efficient of x^5= 6!3^1 1!.5! .0! + 6!3^2 2!.3! 1! + 6!.3^3 3! 1! 2! =18+540+1620=2178

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 AP EAMCET PYQs