Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202318 May 2023Evening ShiftMathematicsBinomial TheoremActual

Let x be a real number and -2 < x < 2 . When x 1 (x+3)(x-2) is expanded in powers of x , then the coefficient of x^3 is

Options

  1. A- 55 1296
  2. B- 97 216
  3. C- 13 216
  4. D- 119 1800

Correct answer

A. - 55 1296

Step-by-step solution

aligned & x+1 (x+3)(x-2) = 3 5 1 (x-2) + 2 5 1 (x+3) & =- 3 5 2 (1- x 2 )⁻¹+ 2 5 3 (1+ x 3 )⁻¹ & x+1 (x+3)(x-2) =- 3 10 (1+ ( x 2 )+ ( x 2 )^2+ ( x 2 )^3+ ) & + 2 5 (1- ( x 3 )+ ( x 3 )^2- ( x 3 )^3+ ) & The coefficient of x^3=- 3 10 ( 1 2 )^3- 2 15 1 27 & =- 55 1296 aligned

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