JEE MAIN - Mathematics Bengali (2022 - 24th June Morning Shift - No. 20)
ধর $$\mathop {Max}\limits_{0\, \le x\, \le \,2} \,\left\{ {{{9 - {x^2}} \over {5 - x}}} \right\} = \alpha $$
এবং $$\mathop {Min}\limits_{0\, \le x\, \le \,2} \,\left\{ {{{9 - {x^2}} \over {5 - x}}} \right\} = \beta $$
যদি $$\int\limits_{\beta - {8 \over 3}}^{2\alpha - 1} {} Max\,\left\{ {{{9 - {x^2}} \over {5 - x}},x} \right\}dx = {\alpha _1} + {\alpha _2}{\log _e}\left( {{8 \over {15}}} \right)$$ হয়, তাহলে $${\alpha _1} + {\alpha _2}$$ = ______
এবং $$\mathop {Min}\limits_{0\, \le x\, \le \,2} \,\left\{ {{{9 - {x^2}} \over {5 - x}}} \right\} = \beta $$
যদি $$\int\limits_{\beta - {8 \over 3}}^{2\alpha - 1} {} Max\,\left\{ {{{9 - {x^2}} \over {5 - x}},x} \right\}dx = {\alpha _1} + {\alpha _2}{\log _e}\left( {{8 \over {15}}} \right)$$ হয়, তাহলে $${\alpha _1} + {\alpha _2}$$ = ______
Answer
34
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