Coefficient of x48 in - r-0 50 50 C r - x-2 r - 3 50-r- is

The correct option is C ^ 50 C _ 2 Given :∑ _ r=0 ^ 50 ^ 50 C _ r (x 2) ^ r . 3 ^ 50 r To find : Coefficient of x^48 Sol. : ...

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Binomial Coefficients

Coefficient o...

Question

Coefficient of $x^{48}$ in $50 \sum r = 0^{50} C_{r} . {(x - 2)}^{r} . 3^{50 - r}$ , is

^{50} C_{2}

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^{48} C_{2}

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3^{48}

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none of these

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Solution

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(\frac{50}{0}) (\frac{50}{1}) + (\frac{50}{1}) (\frac{50}{2}) + . . . . + (\frac{50}{49}) (\frac{50}{50})

^{n} C_{r} = (\frac{n}{r})

50 \sum r = 0 (- 1)^{r} \frac{^{50} C_{r}}{r + 2}

x^{50}

(x +^{50} C_{0}) (x + {3.}^{50} C_{1}) (x + {5.}^{50} C_{2}) . . . . . [x + (101) .^{50} C_{50}]

If R denotes circum radius, then, in $△ A B C, \frac{b^{2} - c^{2}}{2 a R}$ is equal to

x^{33}

50 \sum r = 0^{50} C_{r} (x - 4)^{50 - r} 3^{r}

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