MTH401 Midterm MCQs 2024 by Miss Mehwish

Past Papers for Mids./Finals are also Available

Sure, here's a summary of the MCQs with their options and the correct answers you selected:

1. MCQ: Equivalent form of the exact differential equation: ydx + xdy = 0.

• a) d(x/y) = 0
• b) d(xy) = 0
• c) d(y/x) = 0
• d) d(x + y) = 0

Correct option: b) d(xy) = 0

2. MCQ: For f(x,y) = x^2y - xy^2, f(tx,ty) is...

• a) t^3 f(x, y)
• b) f(x, y)
• c) t^2 f(x, y)
• d) tf(x, y)

Correct option: c) t^2 f(x, y)

Q3. MCQ: Which function would satisfy: dy/dx = d^2y/dx^2 = ... = d^n y/dx^n?

• a) y = Ax^n e^x
• b) y = Axe^x
• c) y = Ae^x^2
• d) y = Ae^x

Correct option: d) y = Ae^x

4. MCQ: Order of the differential equation: d^2y/dx^2 + 5(dy/dx)^3 - 3y = e^sin x.

• a) 3
• b) 0
• c) 1
• d) 2

Correct option: d) 2

5. MCQ: Integrating factor for a non-exact differential equation ydx - (y - 3x - 3) dy = 0.

• a) -y^2
• b) y^2
• c) 1/y^2
• d) -1/y^2

Correct option: c) 1/y^2

Q6. MCQ: Constant solution of the separable differential equation: dy/dx = e^x+y?

• a) y = 0
• b) y = 1
• c) No constant solution exists
• d) y = a ∈ ℝ

Correct option: a) y = 0

7. MCQ: Integrating factor for the first-order linear differential equation: (x - 1)^3 dy/dx + 4(x - 1)^2 y = cos x.

• a) e^(1/(x-1))
• b) e^(x-1)
• c) (x - 1)^4
• d) ln(x - 1)

Correct option: b) e^(x-1)

8. MCQ: Integrating factor for the non-exact differential equation M(x,y)dx + N(x,y)dy = 0.

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

Correct option: d) 1/(xM + yN), xM + yN ≠ 0

9. MCQ: The differential equation dx/dy + x/y = 2 sin y is first-order linear in unknown ___.

• a) variable x
• b) multi-variables x and y
• c) variable y
• d) dy/dx

Correct option: c) variable y

10. MCQ: General solution of the separable differential equation: dy/(1+y^2) = 2xdx.

• a) y = cot^(-1)(x^2 + c)
• b) y = tan(x^2 + c)
• c) y = tan^(-1)(x^2 + c)
• d) y = cot(x^2 + c)

Correct option: c) y = tan^(-1)(x^2 + c)