MTH401-Differential Equations Quiz MCQs Lecture 23-45 Finalterm Objective Questions | SUPERSTARWEBTECH

MTH401-Differential Equations Quiz MCQS #Objective #Questions #FinalTerm

1. The non-trivial solution of the system of differential equation exist only when

  • det(X-λI)=0
  • det(A-λI)≠0
  • det(A+λI)=0
  • det(A-λI)=0 ✔

2. Vectors

( -1 ) and ( 2 ) are linearly ___
0 0

  • Dependent ✔
  • Independent 

3.

[ b11 ] is a
b21
  • Row matrix
  • column matrix ✔

4. Vectors

( -2 ) and ( -66 ) are linearly ___
3 99
  • Dependent ✔
  • Independent 

5. Matrix form of the following system of non-homogenous differential equations is
dy/dx = -2x +4y + et -4t
dy/dx = 3x-4y+11t

  • X’ = [ -2  4 ] [ x ] + [ 1 ]et + [ -4 ]t ✔
    3 -4 y 0 11

6. If A is a m X n matrix and A=AT which of the following must always be true?

  • m ≠ n
  • m = n ✔

7. A matrix is defined as

A = [ a  b ], k is a constant then
c  d
  • A = kA
  • Ak = kA ✔
  • -Ak = Ak
  • Ak ≠ kA

8. If

K = [ 1 ]
-1

is an eigenvector of the given matrix

A = [ 1  0 ] then AK is
0  1

  • 1K ✔
  • -1K
  • 1
  • -1

9. Let

A = [ a  b ] and B = [ u v ] then A + B is
c  d x y
  • A + B = [ a + u   b + v ]
    c + x   d + y

10. The equation form of a non-homogenous system of differential equations

X’ = [ -2  4 ] [ x ] + [ 1 ]et + [ -4 ]t
3 -4 y 0 11
  • X’ = -2x + 4y + et – 4t,     X’ = 3x – 4y + 11t ✔

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MTH401-Differential Equations Quiz MCQs Lecture 1-7 Objective Questions | SUPERSTARWEBTECH

MTH401-Differential Equations Quiz  MCQS #Objective #Questions

1. Which of the following would be a general solution of the differential equaion: dy/dx = 4?

  • y = 4x+a
  • y = ax+4
  • y = 4x+4
  • y = ax+a

2. The order of the differential equation: d²y/dx²+5(dy/dx)³-3y = esin x is___.

  • 0
  • 1
  • 2
  • 3

3. ydx-y(sin x)dy = 0, is an example of ___ differential equation.

  • Exact
  • Non-Exact
  • Non-linear
  • Non-homogeneous

4. Which of the following substituton will transform the differential  equation: dy/dx = (x+y+1)/(x+2y+1), in to separable form?

  • y = v+x
  • y = vx
  • x = vy
  • x = X+h, y = Y+k

5. For the non-exact differential equation ydx-(y-3x-3)dy = 0, if (∂N/∂x-∂M/∂y)/M = 2/y, then the integrating factor is:

  • -1/y²
  • 1/y²
  • -y²

6. For f(x,y) = x²y-xy²,f(tx,ty) =…

  • f(x,y)
  • tf(x,y)
  • t²f(x,y)
  • t³f(x,y)

7. Which of the following is first order linear equation in unknown variable y?

  • x(dy/dx)+(sin x)y = cos x
  • y(dx/dy)+(sin y)x = cos y
  • y(dx/dy)+(sin y)x = cos x
  • y(dx/dy)+(sin x)x = cos y

8. Which of the following is the integrating factor for the 1st order linear differential equation: x(dy/dx)+y = f(x)

  • ex
  • lnx
  • x
  • 1/x

9. Which of the following are explicit solutions of the differential equation: dy/dx = -x/y

  • y = ±√(4+x)
  • y = ±√(-4+x²)
  • y = ±√(4-x²)
  • y = ±√(-4-x²)

10. A differential euation M(x,y)dx+N(x,y)dy = 0 is exact if there exists a multi-variable  function (x,y) such that ___

  • df(x,y) = (∂f/∂x)dx+(∂f/∂y)dy
  • ∫f(x,y)dx = ∫(∂f/∂x)dx+∫(∂f/∂y)dy
  • f(x,y) = (∂f/∂x)dx+(∂f/∂y)dy
  • f(x,y) = ∫(∂f/∂x)dx+∫(∂f/∂y)dy

11. The differential equation dx/dy+(1/y)x=2siny is first order linear in unknown___

  • variable x
  • variable y
  • multi-variables x and y
  • dy/dx

12. If the non-exact differntial equation M(x,y)dx+N(x,y)dy = 0 is homogeneous and xM(x,y)+yN(x,y) ≠ 0, then the integrating factor is:

  • (∂N/∂x-∂M/∂y)/M
  • (∂M/∂y-∂N/∂x)/N
  • 1/(xM-yN), xM-yN ≠ 0
  • 1/(xM+yN), xM+yN ≠ 0

13. The integrating factor for the first order linear differential equation: dy/dx+y cot x = sin² x is

  • sin x
  • cos x
  • e sin x
  • e cos x

14. Which of the following is an example of Homogeneous function?

  • f(x,y) = sin (1/x)
  • f(x,y) = sin (x/y)
  • f(x,y) = sin x
  • f(x,y) = sin xy

15. Which ofthe following would be a constantsolution of the separable differential equation: dy/dx = cos x sin y?

  • x = nπ,n∈ℤ
  • x = 2nπ,n∈ℤ
  • y = nπ,n∈ℤ
  • y = (n+1/2)π,n∈ℤ

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