JEE Advanced 2014 Paper 1 Mathematics Q17

Mathematics

Problem

The largest value of the nonnegative integer aa for which lim⁡x→1{−ax+sin⁡(x−1)+ax+sin⁡(x−1)−1}1−x1−x=14\displaystyle\lim_{x\to1}\left\{\frac{-ax+\sin(x-1)+a}{x+\sin(x-1)-1}\right\}^{\frac{1-x}{1-\sqrt{x}}}=\frac14 is

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