Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2022MathematicsBinomial Theorem

The coefficient of the middle term in the binomial expansion in powers of x of (1+ x)^4 and (1- x)^6 is the same, if is equal to

Options

  1. A- 5 3
  2. B10 3
  3. C- 3 10
  4. D3 5

Correct answer

C. - 3 10

Step-by-step solution

The coefficient of the middle term in power of x(1+ x)^4= ^4 C₂ ^2 The coefficient of the middle term in power of x(1- x)^6= ^6 C₃(- )^3 According to given condition, array rlrl & & ^4 C₂ ^2 & = ^6 C₃(- )^3 & 4! 2!2! ^2 & =- 6! 3!3! ^3 & 6 ^2 & =-20 ^3 & & =- 6 20 & & & =- 3 10 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 Manipal MET PYQs