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For JEE aspirants, a popular question …

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<font face ="Times New Roman">For JEE aspirants, a popular question of quest:
Find the greatest non-negative value of 'a' for which ,
$$\displaystyle \lim_{x \to 1}\left[\dfrac{a + sin(x-1) - ax}{x + sin(x-1) - 1}\right]^{\dfrac{1-x}{1-\sqrt{x}}} = \dfrac{1}{4}$$
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