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MCQ (MTH108) ( Units -1,II, III)

1.The general solution of the differential equation [pic] is

a) [pic]

b) [pic]

c) [pic]

d) [pic]

2. What is the wronskian of [pic]

[pic] [pic]

(b) [pic]

(c) [pic]

(d) [pic]

3. If differential equation [pic] is normal over the interval I then I is

(a) [pic]

(b) [pic]

(c) [pic]

(d) [pic]

4. If [pic] then by the method of undetermined coefficient the assumed particular integral

(a) [pic]

(b) [pic]

(c) [pic]

(d) [pic]

5. Particular integral for the differential equation [pic] is

(a) [pic]

(b)[pic]

(c) [pic]

(d) [pic]

6. The particular integral of the differential equation [pic] if [pic] is

(a) [pic]

(b) [pic]

(c) [pic]

(d) [pic]

7. The general solution of the differential equation [pic] is

(a) [pic]

(b) [pic]

(c) [pic]

(d) [pic]

8. If [pic] where [pic] then the characteristic equation of A is

(a) [pic]

(b) [pic]

(c) [pic]

(d) [pic]

9. For the system of the differential equations

[pic] , the value of [pic] is given by

a) [pic]

b) [pic]

c) [pic]

d) [pic]

10. If [pic] is solution of [pic] then [pic] is

a) 1 b) 2 c) [pic] d) [pic]

11. what is lowest order of differential equation whose particular integral is [pic]

a) 2 b) 3 c) 4 d) 6

12. If system of equations [pic] be solved by matrix method then its eigen values are

a) -2, -2 b) -5, 1 c) -1, -3 d) -6, 2

13. If system of equations [pic] , has eigen values 1 and [pic] then which of following is not Eigen vectors corresponding to value 1

a) [pic] b) [pic] c) [pic] d)[pic]

14. If [pic] be second order differential equation where a , b , c are functions of x and [pic] on any interval then wronskian according to Abel’s formula is

a) [pic] b) [pic] c) [pic] d) None.

15. If [pic] be second order differential equation then its roots are real and distinct if

a) [pic] b) [pic] c) [pic] d) both a and b

16. [pic] be solution of

a) [pic] b) [pic] c) [pic] d) [pic]

17. If [pic] then [pic]

a) [pic] b)[pic] c)[pic] d)[pic]

18. Which of the following is true?

a) [pic] b) [pic]

c) [pic] d) [pic]

19. If the system of non-homogeneous simultaneous equations are given by [pic] where [pic] and A= [pic] and [pic] then the trial solution for the particular integral of above system is given by (Where[pic])

a)[pic] b)[pic] c)[pic]d) None of

above

20. If [pic] satisfy the equations [pic]=0, [pic]=0 and [pic] is the second order differential equation satisfied by [pic] then what is the value of b

a) 5 b) [pic] c) 3 d)[pic]

21. When the given system of linear differential equation[pic]are expressed into a matrix form [pic] where [pic] then what is the value of A

a)[pic] (b)[pic] (c)[pic] (d)[pic]

22. For a given system of linear differential equation[pic], the second order linear differential satisfied by the [pic] is

a)[pic] b)[pic] c)[pic] (d)none

23. The general solution of system of simultaneous equations given by [pic] , where [pic] and A= [pic] is

a ) [pic] , where [pic]are corresponding vectors of eigen values.

b) [pic] , where [pic]are corresponding vectors of eigen values

c) [pic] , where [pic]are corresponding vectors of eigen values

d) [pic] , where [pic]are corresponding vectors of eigen values

24. What are the characteristic roots of a homogeneous LDE having 4 + x e2x as its particular solution?

a) 0, 2 b) 4, 2 c) 4, 2 ,2 d) 0, 2, 2

25. The general solution of y(4) - 2y’’’ = 0 is given by

a) A + B e2x b) A + B + Ce2x c) A + Bx + Cx2 + De2x d) A + Bx + Cx2 + Dxe2x

where A, B, C and D are arbitrary constants.

26. The DE x2y’’ – 4xy’ +6y = 0 on (0, ∞) has ___ linearly independent solutions.

a) 2 b) 3 c) infinite d) Can’t say

27. The general solution of the equation 4y’’ - 4y’ + y = 8ex/2 is given by

a) Aex/2 + Bex/2 + x2ex/2

b) Aex/2 + Bxex/2 + x2ex/2

c) Aex/2 + Bex/2 + ex/2

d) Aex/2 + Bxex/2 + xex/2

28. If [pic], then what will be the Complementary Factor?

a) [pic] b) [pic] c)[pic] d) [pic]

29. If [pic], then Particular Integral will be written as

a) [pic][pic] b) [pic] c)[pic]d) [pic]

30. The auxiliary equation of [pic]

a) [pic]

b) [pic]

c) [pic]

d) [pic]

31. The auxiliary equation of the second order Euler Cauchy differential equation

[pic] has roots

a) -3, 2

b) 3, 2

c) -3 ± 2i

d) 3 ± 2i

32. The characteristic equation of [pic] has double root ½, what is its general solution?

a) (A + B lnx) x1/2

b) (A + Bx) ex/2

c) Ax1/2

d) Aex/2

33.If m-1 and m+2 are factors of auxiliary equation of [pic] then general solution is

(a) [pic] (b) [pic] (c) [pic] (d) [pic]

34. The Wronskian of the functions f(x)=secx and g(x)=tanx is

(a) 1 (b) -1 (c) secx (d) tanx

35. If [pic] and [pic] are solutions of [pic] then roots of auxiliary equation are

a) 1 and -2 (b) -1 and 2 (c) 1 and 2 (d) -1 and -2

36. The general solution of [pic] is

(a) [pic] (b) [pic] (c) [pic] (d) [pic]

37. The general solution of [pic] is

(a) [pic] (b) [pic]

(c) [pic] (d) [pic]

38. The general solution of [pic] is

(a)[pic] (b) [pic]

(c) [pic] (d) [pic]

39. If D is a differential operator then value of [pic]

(a) [pic] (b) [pic] [pic](c)[pic] [pic](d) [pic]

40. Particular Integral of [pic] is

(a) [pic] (b) [pic] (c) [pic] (d) [pic][pic]

41. Particular Integral of [pic]is

(a) [pic] (b) [pic] (c) [pic] (d) [pic][pic]

42. If D is a linear differential operator then [pic]

(a) [pic] , [pic] (b) [pic]

(c) [pic] , [pic] (d) [pic] , [pic]

43. In method of undetermined coefficients if complimentary function [pic] of equation [pic] then choice of particular integral will be

(a) [pic] (b)[pic] (c)[pic] (d)[pic]

44. In method of undetermined coefficients. If complementary function [pic] of equation[pic] then choice of particular integral

(a) c1 xCos2x+ c2Sin2x (b) c1Cos2x+ c2xSin2x

(c) x[c1Cos2x+ c2Sin2x] (d) c1Cos2x+ c2Sin2x

45. General solution of [pic]

(a) [pic] (b) [pic] (c) [pic] (d) [pic]

46. General solution of [pic]

(a) [pic] (b) [pic] (c) [pic] (d) [pic]

47. General solution of system of simultaneous equations [pic] [pic]

(a) [pic] (b) [pic]

(c) [pic] (d) [pic]

48. General solution of system of simultaneous equations [pic]

[pic]

(a) [pic]

(b) [pic]

(c) [pic]

(d) [pic]

49.The equation [pic] is normal in any of the subintervals of

a) [pic] b) [pic] c) [pic] d) [pic]

50. A2x+B(6x+3)+C(3x+2)=0 will be linearly independent when

a) A=B=C b) A=B=C=0 c) Wronskian(A,B,C)=0 d) A=B=C=1

51. General solution of [pic] is

a)[pic] b)[pic] c) [pic] d)[pic]

52. General solution of [pic] is given by

a)[pic] b)[pic] c)[pic] d)[pic]

53. Particular integral for [pic] is

a) [pic] b) [pic] c) [pic] d) None of these

54. The diff. equation of [pic] has P.I.

a) [pic] b) [pic] c) [pic] d) None of these

55.By method of undetermined coefficient , the choice of particular integral for [pic] is

a) [pic] b) [pic] c) [pic] d) [pic]

56. By variation of parameters [pic] ,the value of wronskian is

a)1 b) 2 c) 4 d) none of these

57. General solution of [pic] is

a) [pic] b) [pic] c) [pic] d) none of these

58. The solution of diff. equation [pic] is

a) [pic] b) [pic] c) [pic] d) None of these

59.By elimination, solution of [pic] in the simultaneous system [pic]

[pic] will be

a)[pic] b) [pic] c) 0 d) Does not exist

60.[pic] has auxiliary equation

a) m2+2m-4=0 b) m2-4=0 c) m2-2m-4=0 d) m2+4=0

61. The roots of auxiliary equation of [pic] are

a)3,3 b) [pic] c) [pic] d)

62. By matrix method , Eigen values for [pic] will be

a) 6,1 b) -6,-1 c) 2,3 d) -3, -2

NOTE- Take more MCQ questions from reference book B.S.Grewal 43rd edition page no. 500-501

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