JEE Main 2022 (29 July Morning Shift)

Question

If $\lim_{x 	o 0} \dfrac{\alpha e^{x^2} + \beta e^{-x} + \gamma \sin x}{x \sin^2 x} = \dfrac{2}{3}$, where $\alpha, \beta, \gamma \in \mathbb{R}$, then which of the following is NOT correct?

Accepted Answer

$\ \alpha \beta^2 + \beta \gamma^2 + \gamma \alpha^2 + 3 = 0$

Answer

$\ \alpha^2 + \beta^2 + \gamma^2 = 6$

Answer

$\ \alpha \beta + \beta \gamma + \gamma \alpha + 1 = 0$

Answer

$\ \alpha^2 - \beta^2 + \gamma^2 = 4$

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