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💡 Solution & Explanation
For More Material Join: @JEEAdvanced_2025 AITS-FT-I (Paper-2)-PCM(Sol.)-JEE(Advanced)/2025 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 13 Sol. (Q.48 – 49) We have, 3 f x x a b …….(i) Since, Rolle’s theorem is applicable to g x at x 2, So g a g b and g' 2 0 2 0 f b f a a b f ' b 3 b a and a 2 f " 2 6 2 a 0 f b f a f ' b 3 b a b a ……(ii) and f " 2 6 …….(iii) (As a 2 , think) (i) As, f " 2 6 [using (iii) in (i)] 6 2 a 6 a 1 . (ii) Using (i) in (ii), we get 3 5 b a b 2 2 . 5 2 3 1 5 321 x 1 dx 2 64