MTH401 GRAND QUIZ SOLVED FILE 4|| 100% VERIFIED|| VURANK

MTH401 GRAND QUIZ SOLVED 100% VERIFIED BY ADMIN (MID TERM SYLLABUS)

Q1: The family of curve x² + y² = C² represents a family of circles centered at ___________.

A) (1, 0)

D) (0, 1)

D) (0, 0) (page84) (100% Sure)

D) (1, 1)

Q2: The differential equation: (x + 2y³) ^dy ⁄ _dx = y is linear in unknown:

A) variable y

B) multi- variable x and y

B) variable x (100% Sure)

B) ^dy ⁄ _dx

Q3: For a system in simple harmonic motion which of the following is the time required to complete a cycle of motion?

A) Frequency

B) Amplitude

B) Period (page201) (100% Sure)

B) Revolution

Q4: Suppose that y₁, y₂ ....... y_n are n solution of the homogeneous nth order differential equation. Then the solution is linearly dependent on an interval if and only if _________ .

A) W(y₁, y₂, ....... ,y_n) = 0 (page120) (100% Sure)

B) W(y₁, y₂, ....... ,y_n) = ∞

C) W(y₁, y₂, ....... ,y_n) ≠ 0

D) W(y₁, y₂, ....... ,y_n) = -∞

Q5: If we substitute u = ^y ⁄ _x is differential equation.

A) ue^u du = dx

B) ue^(-u) du = dx (page61) (100% Sure)

C) ue^u du = dy

D) ue^(-u) du = dy

Q6: Which of the following would be a particular solution of the differential equation: ^dy ⁄ _dx = 4?

A) y = 4x + a

B) y = ax + 4

B) y = ax + a

B) y = 4x + 4 (Solved Confirm) (100% Sure)

Q7: A set of functions {f₁(x),f₂(x),f₃(x),......,f_n(x)} is said to be __________ on an interval I if there exist constants.

A) Linear dependent (page111) (100% Sure)

B) Linear independent

Q8: Separable form f(y)dy + g(x)dx = 0, of the differential equation x sinydx + (x² + 1) cosydy = 0 is ________.

A) tanydy + ^x ⁄ _{x² + 1} dx = 0

B) cotydy + ^x ⁄ _{x² + 1} dx = 0 (Solved Confirm) (100% Sure)

B) tanydy + ^x ⁄ _{x² - 1} dx = 0

B) cotydy + ^x ⁄ _{x² - 1} dx = 0

Q9: The differential equation is (1 + lnxy)dx + (1 + ^x ⁄ _y) dy = 0 is exact because __________.

A) ^∂M ⁄ _∂y = ^∂N ⁄ _∂x = ¹ ⁄ _x

B) ^∂M ⁄ _∂x = ^∂N ⁄ _∂y = ¹ ⁄ _y

B) ^∂M ⁄ _∂y = ^∂N ⁄ _∂x = ¹ ⁄ _y (Confirm Solved) (100% Sure)

B) ^∂M ⁄ _∂x = ^∂N ⁄ _∂y = ¹ ⁄ _x

Q10: We can derive a differential equation governing the motion of a mass attached to spring when the Newton's second law combined with _________.

A) Hook's law (page197) (100% Sure)

B) Newton's 3rd law