JEE MAIN - Mathematics Hindi (2022 - 29th July Morning Shift - No. 5)
यदि $$\lim\limits_{x \rightarrow 0} \frac{\alpha \mathrm{e}^{x}+\beta \mathrm{e}^{-x}+\gamma \sin x}{x \sin ^{2} x}=\frac{2}{3}$$ है, जहाँ $$\alpha, \beta, \gamma \in \mathrm{R}$$ हैं, तो निम्न में से कौन सा सही नहीं है ?
$$\alpha^{2}+\beta^{2}+\gamma^{2}=6$$
$$\alpha \beta+\beta \gamma+\gamma \alpha+1=0$$
$$\alpha \beta^{2}+\beta \gamma^{2}+\gamma \alpha^{2}+3=0$$
$$\alpha^{2}-\beta^{2}+\gamma^{2}=4$$
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