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

1.The general solution of the differential equation is

(a)

(b)

(c)

(d)2. What is the wronskian of

(b)

(c)

(d)

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

(a)

(b)

(c)

(d)

4. If then by the method of undetermined coefficient the assumed particular integral (a)

(b)

(c)

(d)

5. Particular integral for the differential equation is

(a)

(b)

(c)

(d)

6. The particular integral of the differential equation if is

(a)

(b)

(c)

(d)

7. The general solution of the differential equation is

(a)

(b)

(c)

(d)

8. If where then the characteristic equation of A

is (a)

(b)

(c)

(d)

9. For the system of the differential equations , the value of is given by

(a)

(b)

(c)

(d)

10. If is solution of then is

a) 1 b) 2 c) d)

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

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

12. If system of equations 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 , has eigen values 1 and then

which of following is not Eigen vectors corresponding to value 1

a) b) c) d)

14. If be second order differential equation where a , b , c are

functions of x and on any interval then wronskian according to Abel’s formula is

a) b) c) d) None.

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

a) b) c) d) both a and b

16. be solution of

a) b) c) d)

17. If then

a) b) c) d)

18. Which of the following is true?

a) b)

c) d)

19. If the system of non-homogeneous simultaneous equations are given by

where and A= and then the trial solution for the

particular integral of above system is given by (Where )

a) b) c) d) None of above

20. If satisfy the equations =0, =0 and is the

second order differential equation satisfied by then what is the value of b

a) 5 b) c) 3

d)

21. When the given system of linear differential equation

are expressed into a matrix form

where then what is the value of A

a) (b) (c) (d)

22. For a given system of linear differential equation , the

second order linear differential satisfied by the is

a) b) c) (d)none

23. The general solution of system of simultaneous equations given by , where

and A= is

a ) , where are corresponding vectors of eigen values.b) , where are corresponding vectors of eigen values

c) , where are corresponding vectors of eigen values

d) , where 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 bya) 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 bya) 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 , then what will be the Complementary Factor?

a) b) c) d)

29. If , then Particular Integral will be written as

a) b) c) d)

30. The auxiliary equation of

a)

b)

c)

d)

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

a) -3, 2 b) 3, 2c) -3 ± 2i d) 3 ± 2i

32. The characteristic equation of 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 then general solution is(a) (b) (c) (d)

34. The Wronskian of the functions f(x)=secx and g(x)=tanx is (a) 1 (b) -1 (c) secx (d) tanx

35. If and are solutions of 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 is

(a) (b) (c) (d)

37. The general solution of is

(a) (b)

(c) (d)

38. The general solution of is

(a) (b)

(c) (d)

39. If D is a differential operator then value of

(a)

(b) (c)

(d)

40. Particular Integral of is

(a) (b) (c) (d)

41. Particular Integral of is

(a) (b) (c) (d)

42. If D is a linear differential operator then

(a) , (b)

(c)

, (d)

, 43. In method of undetermined coefficients if complimentary function

of equation then choice of particular

integral will be(a) (b) (c) (d)

44. In method of undetermined coefficients. If complementary function

of equation then choice of particular integral

(a) c1 xCos2x+ c2Sin2x (b) c1Cos2x+ c2xSin2x (c) x[c1Cos2x+ c2Sin2x] (d) c1Cos2x+ c2Sin2x

45. General solution of (a) (b) (c)

(d)

46. General solution of

(a) (b)

(c) (d)

47. General solution of system of simultaneous equations

(a) (b)

(c) (d)

48. General solution of system of simultaneous equations

(a)

(b)

(c)

(d)

49.The equation is normal in any of the subintervals of a) b) c) d)

50. A2x+B(6x+3)+C(3x+2)=0 will be linearly independent whena) A=B=C b) A=B=C=0 c) Wronskian(A,B,C)=0 d) A=B=C=1

51. General solution of is

a) b) c) d)

52. General solution of is given by

a) b) c) d)

53. Particular integral for is

a) b) c) d) None of these

54. The diff. equation of has P.I.

a) b) c) d) None of these

55.By method of undetermined coefficient , the choice of particular integral for isa) b) c) d)

56. By variation of parameters ,the value of wronskian isa)1 b) 2 c) 4 d) none of these

57. General solution of is

a) b) c) d) none of these

58. The solution of diff. equation is

a) b) c) d) None of these

59.By elimination, solution of in the simultaneous system

will be

a) b) c) 0 d) Does not exist

60. 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 area)3,3 b) c) d)

62. By matrix method , Eigen values for 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