M Cr - m Cr-1- n C1 - m Cr-2- n C2 - - - n Cr-

The correct option is C #10; ^m+n C_r #10;Given equation is ^mC_r+ ^mC_r 1 ^nC_1... ^mC_1 ^nC_r 1+ ^nC_r .Vandermonde's identity states that. ...

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nCr Definitions and Properties

m Cr + m Cr-1...

Question

$^{m} C_{r} +^{m} C_{r - 1} \cdot^{n} C_{1} +^{m} C_{r - 2} \cdot^{n} C_{2} + . . . . . . . . +^{n} C_{r} =$

m +^{m} C_{r}

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^{m + n} C_{m + r}

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^{m + n} C_{r}

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^{m + n} C_{r} =^{m} C_{r} +^{m} C_{r - 1} \cdot n^{n} C_{1} +^{m} C_{r - 2} \cdot^{n} C_{2} + . . . . . +^{n} C_{r}

n < r < m

m, n, r

+ v e

m \sum i = 0 (\begin{matrix} 10 i \end{matrix}) (\begin{matrix} 20 m - i \end{matrix})

m = 15

^{m} C_{r}

r = \frac{m}{2} .

∣ ∣ ∣ ∣ \begin{matrix} ^{x} C_{r} & ^{x} C_{r + 1} & ^{x} C_{r + 2}^{y} C_{r} & ^{y} C_{r + 1} & ^{y} C_{r + 2}^{z} C_{r} & ^{z} C_{r + 1} & ^{z} C_{r + 2} \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^{x} C_{r} & ^{x + k} C_{r + k} & ^{x + m} C_{r + m}^{y} C_{r} & ^{y + p} C_{r + p} & ^{y + s} C_{r + s}^{z} C_{r} & ^{z + l} C_{r + l} & ^{z + t} C_{r + t} \end{matrix} ∣ ∣ ∣ ∣ ∣

k + m + p + s + l + t

0.125 M C r^{3 +}

M n O_{4}^{-}

C r_{2} O_{7}^{2 -}

M n^{2 +}

Assuming TFC is Rs 24. Complete the table:

$\begin{matrix} Output (units) & 1 & 2 & 3 ATC (Rs) & 50 & 40 & 45 AVC (Rs) MC (Rs) \end{matrix}$

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