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Most Important Selected Qs for JEE AdvancedMathematicsBinomial Theorem

The value of _ n _ r=1 ^n ( _ t=0 ^ r-1 1 5^n ^n C_r ^r C_t 3^t ) is equal to

Options

  1. A4
  2. B3
  3. C1
  4. Dnone of these

Correct answer

C. 1

Step-by-step solution

_ n _ r=1 ^n 1 5^n ^n C_r ( _ t=0 ^ r-1 ^r C_t 3^t )= _ n _ r=1 ^n 1 5^n ^n C_r (4^r-3^r )= _ n 1 5^n ( _ r=1 ^n ^n C_r 4^r- _ r=1 ^n ^n C_r 3^r )= _ n 1 5^n (5^n-4^n )=1

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