Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2016MathematicsBinomial Theorem

The number of positive integers satisfying the inequality n+1 n-2 - n+1 n-1 50 is

Options

  1. A9
  2. B8
  3. C7
  4. D6

Correct answer

B. 8

Step-by-step solution

aligned & Given, n+1 n-2 - n+1 n-1 50 & (n-1)! 3!(n-2)! - (n+1)! 2!(n-2)! 50 aligned (n+1)! 3! [ 1 (n-2)! - 3 (n-1)! ] 50 array lr & (n+1)! ( n-1-3 (n-1)! ) 300 & (n+1) n(n-4) 300 array For n=8 , it satisfy to the above inequality. But n=1 it does not satisfy the above inequality.

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