# 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 ✔

# 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