CUET Mathematics

ANSWERS 157 F [  F [ F Z  F Z Z 40. (b) F Z  FZ FZ = FZ f (x) = E UKP Z  F EQU Z C EQU Z D UKP Z 16. (b) = Z . C UKP Z  D EQU Z E EQU Z F UKP Z E UKP Z  F EQU Z = CF DE . E UKP Z  F EQU Z hl 41. (c) We have f (x) 0, g(x) 0, x  (1, 10).  h(x) = (gof)(x) = (g(f(x))) r = g(f(x)) f (x)  0  h(x) is a decreasing function on (1, 10). 17. (b) Let S be the area of curved surface.  h(x)  h(1) for x (1, 10)  S = rl = r T  J  h(x)  1for x (1, 10). Also, h(x) = f(g(x)) [1, 10]  x  [1, 10]  h(x) = 1 for x (1, 10).  h(2) = 1.  F5 = r.  (r2 + h2)– 1/2 (0 + 2h).  NQI G  Z  NQI   Z FJ  42. (b) f (x) =   Z G Z 18. (a) Let A and B be the positions of men A and B NQI G  Z after time t. B = G  Z NQI G  Z   Z NQI   Z   Z G  Z NQI G  Z Now, e <   e + x <  + x Vt s  (e + x) log (e + x) – ( + x) log ( + x) < 0  f (x) < 0 (Q Denom. > 0)  f (x) is decreasing on (0, ). 45° 43. (c) Let h(x) = f (x) – g(x). O Vt A  h(x0) = f (x0) – g(x0) = 0 and h(x) = f (x) – g(x) > 0  OA = OB = Vt Let AB = s  h(x) > h(x0) for x > x0  h(x) > 0 for x > x0  cos 45° = 1#  1$ #$  f(x) > g(x) for all x > x0.  1# 1$ 44. (a) h(x) = f (x) – 2f (x)f (x) + 3(f (x))2 f (x)  8V  8V U = f (x)[1 – 2f ((x)) + 3(f (x))2]  8V  = = 3f (x)  H Z      H Z   s =   Vt.  f (x) – 1 2  2 = 3f (x) 3   25. (a) Let x1, x2  R and x1 < x2. 9   f(x1)  f (x2)  g(f (x1))  g(f (x2))  h(x) and f (x) behave alike.  (gof)(x1)  (gof)(x2). 45. (a) Let f (x) = 3 sin x – 4 sin3 x 27. (a) (/2, 3/2) and cosec is not defined.  f (x) = sin 3x and f (x) = 3 cos 3x 0 if 3x [– /2, /2] 35. (c) f (x) =  GZ Z  Z  FZ   f(x) is increasing if x  [– /6, /6]. f (x) = ex(x – 1)(x – 2).