SAGAR PUBLIC SCHOOL - CBSEGuess
Sample Paper 2011
Class- XII
Subject - Mathematics
1MARK
1. [pic] 2. [pic] 3. [pic]4. [pic]5.[pic]
.
6. [pic]7. [pic]8. [pic]9. [pic]10. [pic]
11.[pic] 12. [pic]13. [pic]14. [pic]
15. [pic]16.[pic] 17.[pic] 18. [pic]
19. [pic]20. .∫{f’’(ax+b)/f(ax+b)} dx 21. [pic]22. [pic]
23. [pic] 24. Prove that [pic]
4MARKS
1. Evaluate : [pic] dx 2.[pic] dx 3. [pic]
4. [pic] 5.[pic]dx . 6.[pic]. 7. [pic]
8. [pic]9. [pic]10. [pic]11. [pic]
12. [pic] 13.[pic]14. [pic]15. [pic]16. [pic]
17. [pic]18. [pic] 19.[pic]20.[pic]
21. [pic]22. [pic] 23.[pic] 24.[pic] 25. [pic]26. 26. [pic]27. [pic]28. [pic]29. [pic]30. [pic]
31. [pic]32. [pic]33. [pic]34. [pic] 35. [pic]
36. [pic]37. [pic] 38. [pic] 39.[pic]
40. [pic]41. [pic]42. [pic]43. [pic]
44. [pic]45. [pic]46.[pic] 47.[pic]48. [pic]
49. ( cot3 dx 50. ( [pic] 51 [pic] 52 .[pic] 53.[pic] 54.[pic]55. [pic]56. [pic]57.[pic]
58.[pic]59. [pic] 60. [pic] 61.[pic]62. [pic]
63. [pic]64. [pic]65.[pic]66.[pic] 67.[pic]68.[pic]69.[pic]
6MARKS
1. [pic] 2.[pic]3.[pic]4.[pic]
5.[pic] 6.[pic] 7. [pic]
8.[pic]9.[pic]10.[pic]11.[pic]
12.[pic] 13[pic]
DEFINITE INTEGRALS
4/6MARKS
1.[pic]2.[pic]3.[pic]4.[pic] . 5.[pic] 6.[pic]7. [pic]8. [pic]
9. [pic]10. Evaluate [pic] as a limit of a sum11.[pic] 28. 12.[pic] 13. [pic] 14.[pic] 15. [pic] 16.[pic] 17.[pic] 18. [pic]
19.Evaluate [pic] 20.[pic].21.[pic]
22.Evaluate as limit sum [pic]dx 23.Evaluate: [pic]24.[pic]
25. Evaluate [pic] 26. Evaluate [pic] as limit of a sum.
27.Evaluate :- [pic] as a limit of a sum.
APPLICATIONS OF DEFINITE INTEGRALS
1. Using integration find the area of the region bounded by the triangle whose vertices are (-1,1), (0,5)
and (3,2).
2. Find the area of smaller region bounded by the ellipse [pic] and the straight line [pic]
3. Sketch the region enclosed between circles x2 + y2 = 1 and x2 + (y – 1)2 = 1.
Also find the area of region using integration
4. Find the area of the region enclosed between the two curves [pic]
5. Find the area of the region [pic]
6. Sketch the region common to the circle [pic] and the parabola [pic] Also, find the area of the region, using integration.
7. Make the rough sketch and find the area of the region (using integration) enclosed by the curves y2=4ax and x2=4ay.
8. Make the rough Sketch and find the area of the region
[pic]
9. Draw a rough Sketch of the region [pic]
DIFFERENTIAL EQUATIONS
4/6 MARKS
1) Solve the differential equation [pic]
2) Solve the differential eqn, given that y=1 when x=2: [pic]
3) Find the differential equation of the family of the curve given by [pic]
4) Solve tany dx + sec2y tanx dy =0.
5) Solve: (x2-y2) dx + 2xy dy = 0.
6) Solve : x dy/dx + y = y2 log x
7) Show that y=cos (cosx) is a solution of the differential equation:-
[pic]
8) Solve the differential equation[pic]
9) Solve the differential equations x [pic]+ y = x cos x + sin x given that y(2) = 1
10) Solve the differential equation [pic]
11) Solve the differential [pic]
12)Solve that differential equation [pic]
13)Solve the differential equation: [pic]
14)Solve differential equation y dx – x dx = xy dx
15)find the solution of [pic]+ [pic]which satisfies y(2) = 2;
16)Solve differential equation Sec2y . (1+x2) dy + 2x tan y dx = 0given that [pic] when x = 1
17)If y= (sin-1x)2, Prove that [pic]
18.)Solve the differential equation [pic]
19) Solve dy/dx = xy + y + x + 1.
20) dy/dx = y + xex
21)Solve [pic]
22)Find the differential equation of the system of parabola’s having latus-rectum 7 and axis parallel to x-axis.
23)Solve the differential equation [pic] given that y[pic]=1.
24. Solve (x2 +xy ) dy = (x2+y2).
25. cos x(1 + cos y)dx – sin y(1 + sin x)dy = 0
26. y - x dy/dx = a(y2 + dy/dx)
27. dy/dx = y cot2x , given y((/4) = 2
28. (3xy + y2 )dx + (x2 + xy)dy = 0
29. (x3 + y3 )dy = x2 y dx
30.{xcos(y/x)}(ydx + xdy) = {ysin(y/x)}(xdy – ydx)
31. dy/dx – 2y = cos3x
32. (1 + y2 )dx = (tan-1 y – x)dy
33.dy/dx + ycotx = 2x + x2 cotx , guven that y(0) = 0
34. (1 + x²)dy/dx + 2xy = 4x² given y(0) = 0
35.(1 + x²)dy/dx + 2xy = (x² + 4)1/2
36.secx dy/dx = y + sinx
37.(x(x² + y²)1/2 - y² )dx + xy dy = 0
38.Find the equation of the curve whose differential equation is (1 + y²)dx – xy dy = 0 and passes through the point (1,0).
39.tan y dy/dx = sin(x + y) + sin(x – y)
40. Solve e2x – 3y dy + e2y – 3x dx = 0
.
Prepared by:
Name epraveen
Email estherpraveen@
Phone No. 043340191
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INDEFINITE INTEGRAL
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