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NDA2022MathematicsBinomial TheoremActual

What is _ r=0 ^n 2^r C(n, r) equal to?

Options

  1. A2^n
  2. B3^ n
  3. C2^ 2 n
  4. D3^ 2 n

Correct answer

B. 3^ n

Step-by-step solution

aligned & _ r=0 ^n 2^r ^ n C r= ^ n C₀ 2^0+ ^ n C₁ 2^1+ ^ n C₂ 2^2+ + ^ n C₂ 2^ n & =(1+2)^ n =3^ n aligned

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