MTH401 GRAND QUIZ SOLVED FILE 2|| 100% VERIFIED|| VURANK

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

Q1: The hook's law states that the force F is proportional to the _________.

A) Length

B) Elongation (page197) (100% Sure)

C) Weight

D) None of these

Q2: Separable form of the differential equation: ^dy⁄_dx = y - 1 is ________, where v = y - 1.

A) ^dx⁄_x = dv

B) dx = vdv

C) ^dy⁄_v = dx (page17) (100% Sure)

D) ^dv⁄_v = ^dx⁄_x

Q3: For f(x,y) = ^2x⁄_3y + 7, f(tx, ty) = - - -

A) f (x, y)

B) t f(x, y) (page26) (100% Sure)

C) t² f(x,y)

D) t³ f(x,y)

Q4: Which of the following is an equivalent form of the exact differential equation: ydx + xdy = 0?

A) d ^x⁄_y = 0

B) d ^y⁄_x = 0 (page33) (100% Sure)

C) d (xy) = 0

D) d (x + y) = 0

Q5: In the general solution of a separable differential equation is sin^-1y = cos^-1x + c, provided that y (¹⁄_√2) = ¹⁄_√2, then c = - - - .

A) ^Π⁄₂  

B) ^Π⁄₄

C) - ^Π⁄₂

D) 0 (Confirm Solved) (100% Sure)

Q6: The differential equation of orthogonal trajectory to the family of curves x - 2y = c is:

A) ^dy⁄_dx = - ¹⁄₂

B) ^dy⁄_dx = ¹⁄₂

C) ^dy⁄_dx = 2

D) ^dy⁄_dx = -2 (Confirm) (100% Sure)

Q7: Classify the following differential equation e^{x dy}⁄_dx + 2y = 3xy

A) Separable and not linear

B) Linear and not sparable

C) Both sparable and linear

D) Neither sparable nor linear (Confirm Solved) (100% Sure)

Q8: The periodic time is given by:

A) ^w⁄_2Π

B) ^2Π⁄_w (page201) (100% Sure)

C) 2Π + w

D) ^Π⁄_w

Q9: If x²y³dx + x³y²dy = 0 has the equivalent form as d (¹⁄₃ x³y³) = 0, then its solution is _____ .

A) x³ + y³ = c

B) x³ - y³ = c

C) x³y³ = c

D) ^x3⁄_y³ = c

Q10: The family of parabolas y² = 4ax are solutions of the differential equation: ^dy⁄_dx = ^2a⁄_y for ------- value(s) of a.

A) infinite

B) finite

C) unique

D) no (Confirm) (100% Sure)