Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201921 Apr 2019Evening ShiftMathematicsBinomial TheoremActual

The first negative coefficient in the terms occurring in the expansion of ( 1 + x ) 21 5 is

Options

  1. A- 6160 15625
  2. B- 416 3125
  3. C- 616 5 7
  4. D- 616 5 6

Correct answer

C. - 616 5 7

Step-by-step solution

The expansion of 1 + x 21 5 = 1 + 21 5 x + 21 5 21 5 - 1 2 ! x 2 + 21 5 21 5 - 1 21 5 - 2 3 ! x 3 + … Simplify the above expansion. 1 + x 21 5 = 1 + 21 5 x + 21 × 16 5 2 × 2 ! x 2 + 21 × 16 × 11 5 3 × 3 ! x 3 + 21 × 16 × 11 × 6 5 4 × 4 ! + . . The first negative coefficient in the terms occurring in the expansion of ( 1 + x ) 21 5 is = - 21 × 16 × 11 × 6 × 1 × 4 5 6 × 6 ! = - 88704 5 7 × 144 = - 616 5 7

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