Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2014MathematicsBinomial Theorem

The term independent of x in [ ( x 3 ) + ( 3 2 x² ) ]¹⁰ is

Options

  1. A5 4
  2. B7 4
  3. C9 4
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

Given, expansion is [ ( x 3 ) + ( 3 2 x² ) ]¹⁰ Let t_ r+1 be general term, then aligned t_ r+1 &= 10 r ( x 3 )^ 10-r ( 3 2 x² )^ r &= 10 r x 10-r 2 10-r 2 3^ i / 2 2^ r / 2 x^ r = 10 r x- r 2 -r 3^ r-5 2^ r / 2 aligned For the term independent of x . Puts 5- r 2 -r=0 5- 3 2 r=0 3 2 r=5 r= 10 3 Fractional value of r is not possible. So, no term is independent of x .

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