Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2023Morning ShiftMathematicsBinomial TheoremActual

The coefficient of x²⁹ in the expansion of (1-3 x+3 x^2-x^3 )¹⁵ is

Options

  1. A- 45 16
  2. B45 28
  3. C45 30
  4. D45 29

Correct answer

A. - 45 16

Step-by-step solution

The given expression is (1 - 3x + 3x^2 - x^3 )¹⁵ . Observe that 1 - 3x + 3x^2 - x^3 = (1 - x)^3 . Substituting this into the expression, we get ((1 - x)^3)¹⁵ = (1 - x)⁴⁵ . The general term in the binomial expansion of (1 - x)^ n is given by ^ n C_ r (1)^ n-r (-x)^ r = ^ n C_ r (-1)^ r x^ r . For the expansion of (1 - x)⁴⁵ , the term containing x²⁹ corresponds to r = 29 . The coefficient is ⁴⁵C₂₉ (-1)²⁹ = -⁴⁵C₂₉ . Since ⁴⁵C₂₉ = ⁴⁵C_ 45-29 = ⁴⁵C₁₆ , the coefficient is -⁴⁵C₁₆ . Answer: - 45 16

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 COMEDK PYQs