If (1/(¹⁵C₀)+1/(¹⁵C₁))(1/(¹⁵C₁)+1/(¹⁵C₂)) (1/(¹⁵C₁₂)+1/(¹⁵C₁₃))= α¹³ ¹⁴C₀ ¹⁴C₁ ¹⁴C₁₂, then 30α is equal to _ _ _.

Binomial Theorem and Its Simple Applications: JEE Main 2026 Mathematics question

JEE Main 2026 · 21 Jan, Evening shift · Q21

JEE Main 202621 Jan, Evening shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

\left(\frac{1}{^{15}C_0}+\frac{1}{^{15}C_1}\right)\left(\frac{1}{^{15}C_1}+\frac{1}{^{15}C_2}\right)\cdots\left(\frac{1}{^{15}C_{12}}+\frac{1}{^{15}C_{13}}\right)=\frac{\alpha^{13}}{^{14}C_0\,^{14}C_1\cdots{}^{14}C_{12}}

, then

30\alpha

is equal to ______.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2026 · 21 Jan, Evening shift · Q21

JEE Main 202621 Jan, Evening shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

\left(\frac{1}{^{15}C_0}+\frac{1}{^{15}C_1}\right)\left(\frac{1}{^{15}C_1}+\frac{1}{^{15}C_2}\right)\cdots\left(\frac{1}{^{15}C_{12}}+\frac{1}{^{15}C_{13}}\right)=\frac{\alpha^{13}}{^{14}C_0\,^{14}C_1\cdots{}^{14}C_{12}}

, then

30\alpha

is equal to ______.

Your answerType your answer. Integers and decimals are accepted.