See image — AITS & Test Series Chemistry Question

💡 Solution & Explanation

  2 2 t x f x cost f t cos x cos x lim t x x       2 2 cos x f x sinx f x cosx x      2 2 dy cos x y sinx cosx dx x    2 dy cosx ytanx dx x   (which is a linear diff. equation) I.F. = tan x dx e sec x   2 1 y sec x dx x   1 y sec x c x   given  1 f   c = 0  cos x f x x          2 2 x sinx cosx sinx x cot x f x x x        O  /2 y= –x y= cotx  (A) sign scheme of f(x) /2   – +  ( /2, ) (B) Incorrect    2 sinx f x x cot x x    – ve x 0, 3         . TG ~ @bohring_bot TG ~ @bohring_bot | @HeyitsyashXD AITS-PT-I (Paper-1)-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 15 (C)     1 3 2 1/2 sinx x x cot x x          dx   1 1/2 xsinx x cot x dx 0     , True (D)  3 3 2 x cosx x f x x cosx x     2 2 6 2 2 x x x x cosx x 1 .... 2! 4! 6!            4 6 2 x x x ..... 2 24     4 2 2 2 x x x cosx x 2    1 1 1 4 2 2 2 0 0 0 x x dx x cosx dx x dx 2       1 2 0 7 1 x cosxdx 30 3    .