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In the binomial expansion of a b 3 + b a 3 21 , the term containing same powers of a and b is

Options

  1. A11 t h
  2. B13 t h
  3. C12 t h
  4. D6 t h

Correct answer

B. 13 t h

Step-by-step solution

t r + 1 = C 21 r a b 21 - r 3 b r 3 a r 6 = C 21 r a 21 - r 3 - r 6 b r 3 - 21 - r 3 Since, power of a and b are the same ⇒ 21 - r 3 - r 6 = r 3 - 21 - r 3 ⇒ 2 21 - r 3 = r 3 + r 6 = r 2 84 - 4 r = 3 r ⇒ 7 r = 84 ⇒ r = 12 Hence, the 13 t h term contains the same powers of a and b .

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