Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2014MathematicsBinomial Theorem

The term independent of x in the expansions of ( x - 2 x )¹⁸ is

Options

  1. A- ¹⁸ C₉ 2^9
  2. B¹⁸ C₉ 2¹²
  3. C¹⁸ C₆ 2^6
  4. D¹⁸ C₆ 2^8

Correct answer

A. - ¹⁸ C₉ 2^9

Step-by-step solution

General term in the expansion of ( x - 2 x )¹⁸ is aligned T_ r+1 & = ¹⁸ C_r( x )^ 18-r (- 2 x )^r & = ¹⁸ C_r(x)^ 18-r 2 (-2)^r(x)^ - r 2 & = ¹⁸ C_r(-2)^r x^ 9-r aligned For independent of x , array rlrl & put 9-r & =0 & & r & =9 & & T₁₀ & = ¹⁸ C₉(-2)^9 & =- ¹⁸ C₉ 2^9 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 AP EAMCET PYQs