If ( 1/¹⁵C₀ + 1/¹⁵C₁) ( 1/¹⁵C₁ + 1/¹⁵C₂) … ( 1/¹⁵C₁₂ + 1/¹⁵C₁₃) =… | JEE Main 2026 Mathematics PYQ

NVAMediumJEE Main 2026 · 21 January, Shift 2Applications of P&C

If $\left( \frac{1}{{}^{15}C_0} + \frac{1}{{}^{15}C_1} \right) \left( \frac{1}{{}^{15}C_1} + \frac{1}{{}^{15}C_2} \right) \dots \left( \frac{1}{{}^{15}C_{12}} + \frac{1}{{}^{15}C_{13}} \right) = \frac{\alpha^{13}}{{}^{14}C_0 {}^{14}C_1 \dots {}^{14}C_{12}}$ , then $30\alpha$ is equal to _____.

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