If an alkane has number of carbon atoms equal to n, then the number of moles of oxygen required for its complete combustion is?

\frac{3 n + 1}{2}

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2 n

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\frac{n}{2}

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(2 n + 1)

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Solution

The correct option is A $\frac{3 n + 1}{2}$
CH $_{4}$ +2O $_{2}$ $\to$ CO $_{2}$ +2H $_{2}$ O
C $_{2} H_{6}$ + $\frac{7}{2} O_{2}$ $\to$ 2CO $_{2}$ +3H $_{2}$ O
On observing these two reactions we can make general formula for requirement of oxygen molecules.
In general for an alkalane having 'n' number of carbon atoms
no. of moles of oxygen required will be= $\frac{3 n + 1}{2}$

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(1 + x)^{n} = n \sum r = 0^{n} C_{r} x^{n},

\frac{C_{0}}{1 \cdot 2} 2^{2} + \frac{C_{1}}{2 \cdot 3} 2^{3} + \frac{C_{2}}{3 \cdot 4} 2^{4} + \dots + \frac{C_{n}}{(n + 1) (n + 2)} 2^{n + 2}

If f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + x^{n} & (1 - x)^{n} & 2 + x^{n} (2 + x)^{n} & (2 + x)^{n} & 1 (3 - x)^{n} & 1 & 3 + x \end{matrix} ∣ ∣ ∣ ∣ ∣

then the constant term in the expansion is

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