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Osmotic Pressure

How n^C2 is e...

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How n^C2 is equal to n(n-1)/2?

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Q. If ^mC₁= ⁿC₂ , then
(a) 2 m = n
(b) 2 m = n (n + 1)
(c) 2 m = n (n − 1)
(d) 2 n = m (m − 1)

If $^{m} C_{1} =^{n} C_{2},$ then

Q. The value of

1^{2} .^{n} C_{1} + 2^{2} .^{n} C_{2} + 3^{2} .^{n} C_{3} + . . . + n^{2} .^{n} C_{n}

n \geq 2

is a positive integer, then the sum of the series

^{n + 1} C_{2} + 2 (^{2} C_{2} +^{3} C_{2} +^{4} C_{2} + \dots +^{n} C_{2})

1 \cdot^{n} C_{1} +

2 \cdot^{n} C_{2} +

3 \cdot^{n} C_{3} + . . . +

^{n} C_{n}

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