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Origin of Earth

How much time...

Question

How much time did the Earth take to cool down and the water bodies to be formed?

125 cr years

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100 cr years

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80 cr years

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75 cr years

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Solution

The correct option is C 80 cr years
It took around 80 crore years for the Earth to cool down and the water bodies to be formed.

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∣ ∣ ∣ ∣ \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 + 1} C_{r + 1} & ^{x + 2} C_{r + 2}^{y} C_{r} & ^{y + 1} C_{r + 1} & ^{y + 2} C_{r + 2}^{z} C_{r} & ^{z + 1} C_{r + 1} & ^{z + 2} C_{r + 2} \end{matrix} ∣ ∣ ∣ ∣ ∣

\frac{{^{n} C}_{r} + 4 {^{n} C}_{r + 1} + 6 {^{n} C}_{r + 2} + 4 {^{n} C}_{r + 3} + {^{n} C}_{r + 4}}{{^{n} C}_{r} + 3 {^{n} C}_{r + 1} + 3 {^{n} C}_{r + 2} + {^{n} C}_{r + 3}} = \frac{n + k}{r + k}

\sum_{r = 0}^{n - 1} \frac{{^{n} C}_{r}}{{^{n} C}_{r} + {^{n} C}_{r + 1}}

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