Let $\beta(m, n)=\int_0^1 x^{m-1}(1-x)^{n-1} d x, m, n0$. If $\int_0^1\left(1-x^{10}\right)^{20} d x=a \times \beta(b, c)$, then $100(a+b+c)$ equals [JEE Main 2024, 5 Apr (Shift 2)]

Question

Let $\beta(m, n)=\int_0^1 x^{m-1}(1-x)^{n-1} d x, m, n>0$. If $\int_0^1\left(1-x^{10}\right)^{20} d x=a \times \beta(b, c)$, then $100(a+b+c)$ equals [JEE Main 2024, 5 Apr (Shift 2)]

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Let \(\beta(m, n)=\int_0^1 x^{m-1}(1-x)^{n-1} d x, m, n>0\). If \(\int_0^1\left(1-x^{10}\right)^{20} d x=a \times \be…

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Let \(\beta(m, n)=\int_0^1 x^{m-1}(1-x)^{n-1} d x, m, n&gt;0\). If \(\int_0^1\left(1-x^{10}\right)^{20} d x=a \times \be…

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Let \(\beta(m, n)=\int_0^1 x^{m-1}(1-x)^{n-1} d x, m, n>0\). If \(\int_0^1\left(1-x^{10}\right)^{20} d x=a \times \be…