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NDA2021MathematicsBinomial TheoremActual

Consider the expansion of (1+x)^n . Let p, q, r and s be the coefficients of first, second, n^ th and (n+1)^ th terms respectively. What is ( p s+q r ) equal to?

Options

  1. A1+2 n
  2. B1+2 n^2
  3. C1+n^2
  4. D1+4 n

Correct answer

C. 1+n^2

Step-by-step solution

According to question aligned & p= ^n C₀=1, q= ^n C₁=n & r= ^n C_ n-1 = ^n C₁=n and S= ^n C_n=1 & p s+q r=1 1+n n=1+n^2 aligned

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