Basic Mathematics Exam 2020 PDF

MAKNE PHYSICS CLASSES Class : Rept-NEET/AIIMS-2020 ( 6 to 8 am) Max. Marks : 180 Date : 07/07/2019 Time : 45 min. Basic Mathematics 01. Wha...

MAKNE PHYSICS CLASSES Class : Rept-NEET/AIIMS-2020 ( 6 to 8 am) Max. Marks : 180 Date : 07/07/2019 Time : 45 min. Basic Mathematics 01. What is the value of cos( 60 o ) d 3 07. ( x ) ...... 1 1 dx a)  b) 2 2 a) 2x 2 b) 3x 2 1 3 c) 2x 3 d) 4x 3 c) d) 2 2 d 08. ( x ) ...... 02. What is the value of tan 210 o dx 1 1 1 a) 3 b) a) b)  3 2 x 2 x 1 1 x c)  d) 1 c)  d) 3 x 2 03. What is the value of sin 300 o d 09. ( ax 2  bx  c) ...... 2 2 dx a) b)  3 3 a) ax  b b) 2ax  b c) ax 2  b d) 2ax  b 3 3 c) d)  2 2 d 10. (2 x3  e x ) ...... 04. What is the value of cos 120 o dx 1 1 a) e x b) 6 x3  e x a) b) 2 2 c) 6 x 2  e x d) 4 x 2  e x 3 1 d c) d) 11. (sin x  cos x) ....... 2 2 dx 05. What is the value of (v) sin(1485 o ) a) sin x  cos x b)  sin x  cos x 1 1 c) cos x  sin x d) sec x  sin x a) b)  2 2 d 12. (sin x  ex ) ....... dx 3 1 c) b) a) sin x  x b) cos x  x 2 2 06. If A  60 o then value of sin 2 A will be c)  cos x  e x d) cos x  e x 3 1 d (a) (b) 13. (sin t 2 ) ....... 2 2 dt 1 1 a) cos t 2 b) 2 cos t 2 (c) (d) 3 2 c) 2t cos t 2 d) 2t sin t 2 Page - 1  d sint d) 5 x 4  3 x 2  2 x 1/ 2  7 14. ( e ) ....... dt 23. f(x) = cos x + sin x, Find f (/2) a) 1 b) 2 a) esin t.cos t b) ecos t.cos t c) 3 d) 4 c) ecost d) esin t Q. 24 to 27 Find the derivative of given function w.r.t. d corresponding independent variable. 15. dt sin(t  ) ....... 24. y  x 2  x  8 a) cos ( t   ) b)  cos ( t   ) a) 2 x  1 b) 2 x  1 c) x  1 d) x  1 c)  sin ( t   ) d)  cos ( t   ) 25. s  5t 3  3t 5 3 a) 15 t 2  15 t 4 b) 15 t  15 t 4 16. If sin  = then cos  =.... 5 c) 15 t 2  15 t 4 d) 15 t 2  15 t a) 2/3 b) 5/3 c) 4/5 d) 3/2 26. y  5 sin x 3 a) 5cos x b) 4cos x 17. If sin  = then cot  =.... c) 2cos x d) cos x 5 a) 4/3 b) 3/4 27. y  x 2  sin x c) 2/3 d) 3/2 a) 2 x  cos x b) x  cos x 3 c) x  cos x d) 2 x  cos x 18. If sin  = then sec  =.... 5 Q. 28 to 32 Find the first derivative & second derivative a) 4/5 b) 5/4 of given functions w.r.t. corresponding independent c) 2/3 d) 3/5 variable. dy 19. Find , when y = x5 + x4 + 7 28. y  6x 2  10x  5x 2 dx a) 12 x  10  10 x 3 , 12  30x4 a) 4 x 4  3 x 3  7 b) 5 x 4  4 x3  7 b) 12 x  10  10 x3 , 12  30x4 4 3 4 3 c) 5 x  4 x d) 5 x  4 x  7 c) x  10  10 x 3 , 12  x 4 dy d) x  10  10 x3 , 12  x 4 20. Find , when y = x2 + 4x–1/2 – 3x–2 dx 12 4 1 a) 2 x 2  2 x 3/ 2  6 x 2 b) 2 x  2 x 3/ 2  6 x 29. r    3  4   c) 2 x  2 x 3/2  6 x 3 d) 2 x  2 x1/ 2  6 x 3 a) 12  2  12 4  4 5 , 24 3  48 5  20 6 dy b) 12 2  12 4  4 5 , 24 3  48 5  20 6 21. Find , when y = x7/2 dx c) 12 1  12 4  4 5 , 24  2  48 5  20 6 7 5/ 2 5 9/ 2 a) 2 x b) 2 x d) 12 1  12 4  4 2 , 24 2  48 2  20 4 30.   3 z 7  7 z 3  21z 2 7 9/ 2 5 3/ 2 c) 2 x d) x a) 21 z 6  21 z 2  42 z , 126 z 5  42 z  42 2 b) 21 z 6  21 z 2  42 z ,126 z 5  42 z  42 dy 22. Find , when y = x5 + x3 + 4x1/2 + 7 dx c) 21 z 2  21 z 2  42 z ,126 z 4  42 z  42 a) 5 x 4  3 x  2 x1/2 d) 21 z 2  21 z 2  22 z ,126 z 4  52 z  32 b) 5 x 4  3 x 2  2 x 1/ 2 c) 5 x 4  3 x 2  2 x 1/ 2  7 Page - 2 31. y  sin x  cos x 40. Suppose that the radius r and surface area S = 4 π r2 a) cos x  sin x,  sin x  cos x of a sphere are differentiable functions of t. Write an b) cos x  sin x,  sin x  cos x ds dr equation that relates to. dt dt c)  cos x  sin , sin x  cos x ds dr ds dr d)  cos x  sin ,  sin x  cos x a)  6 r b)  8r dt dt dt dt 32. y  nx  e x ds dr ds dr c)  6 d)  8 1 x 1x 1 x 1 x dt dt dt dt a) x  e ,  x 2  e b) x  e ,  x 2  e 41. Particle’s position as a function of time is given by 1 x 1 x 1 x 1 x x  t 2  4t  4 find the maximum value of position c) x 2  e ,   e d) x 2  e ,  e x x coordinate of particle. Q. 33 to 35 Find derivative of given functions w.r.t. the a) 4 b) 8 independent variable x. c) 12 d) 6 42. Find the maximum and minimum values of function 33. x sin x 2x 3  15 x 2  36 x  11 a) sin x  x cos x b) sin x  x cos x a) ymax = 39, ymin = 38 c) sin  x cos x d) sin  cos x b) ymax = 38, ymin = 39 34. y  e x  nx c) ymax = 18, ymin = 29 d) ymax = 29, ymin = 18 ex e a) e x nx  b) e x nx  dy x x 43. y  2u 3 & u  8 x  1, find dx ex e c) e x nx  d) e nx  dy  48 (8 x  1)2 dy  48(8 x  1) 2 x x a) b) dx dx 35. y  sin x cos x dy dy 2 a) cos2 x  sin2 x b) cos 2 x  sin 2 x c) dx  48(8 x  1) d) dx  38 (8 x  1) c) cos x  sin 2 x d) cos x  sin x dy dy 44. y  sin u & u  3x  1, find dx Q. 36 to 38 Find dx as a function of x a) 3cos(3x  1) b) cos(3x  1) 36. y  (4  3x )9 a) 27(4  3x)8 b) 27(4  3x )8 c) cos(3x  1) d) 3 cos(3 x  1) c) 27(4  3x )8 d) 27(4  3x )6 x dy 45. y  cos u & u   , find 3 dx 37. y  sin 5 x a) 5 cos 5 x b) 4cos 5x 1 x 1 x a) sin b)  sin 3 3 3 3 c) 4cos 4x d) 2cos 4x 2 x 2 x 38. y  2 sin(x  ) where w and f constants c) sin d) sin 3 3 3 2 a) 2 cos( x   ) b)  cos( x   ) c) 2 cos( x  ) d) cos( x   ) 39. Suppose that the radius r and area A = π r2 of a circle ------------------------------------------------------------------- are differentiable functions of t. Write an equation that relates dA / dt to dr / dt. dA dr dA dr a)  2 r b)  r dt dt dt dt dA dr dA dr c)  d)  dt dt dt dt Page - 3  MAKNE PHYSICS PHYSICSCLASSES CLASSES Basic Mathematics Rept-Physics Date : 07-07-19 Q.No. 1 2 3 4 5 6 7 8 Ans C B D A B A B A Q.No. 9 10 11 12 13 14 15 16 Ans B C C D C A B C Q.No. 17 18 19 20 21 22 23 24 Ans A B C C A B A B Q.No. 25 26 27 28 29 30 31 32 Ans C A D A A A A A Q.No. 33 34 35 36 37 38 39 40 Ans B C B B A C A B Q.No. 41 42 43 44 45 Ans B A A D B Page - 4