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If frac 1 15 C 0 frac 1 15 C 1 frac 1 15 C 1 frac 1 15 C 2 f: null (Mathematics) | DivineJEE

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Mathematics

JEE Mains 2026 21st January Shift 2

Mathematics

If\\

\left(\frac{1}{{ }^{15} \mathrm{C}_{0}}+\frac{1}{{ }^{15} \mathrm{C}_{1}}\right)\left(\frac{1}{{ }^{15} \mathrm{C}_{1}}+\frac{1}{{ }^{15} \mathrm{C}_{2}}\right) \ldots\left(\frac{1}{{ }^{15} \mathrm{C}_{12}}+\frac{1}{{ }^{15} \mathrm{C}_{13}}\right) =\frac{\alpha^{13}}{{ }^{14} \mathrm{C}_{0}{ }^{14} \mathrm{C}_{1} \ldots{ }^{14} \mathrm{C}_{12}}

, then

30 \alpha

is equal to

\_\_\_\_

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