MTH401 GRAND QUIZ SOLVED FILE 1|| 100% VERIFIED|| VURANK

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

Q1: Which of the following is the first order linear equation in unknown variable y?

A) z ^dy⁄_dx + (sinx)y = cosx (page48) (100% Sure)

D) y ^dx⁄_dy + (siny)x = cosy

A) y ^dx⁄_dy + (siny)x = cosx

A) y ^dx⁄_dy + (sinx)x = cosy

Q2: Which of the following function would satisfy: ^dy⁄_dx = ^d2y⁄ _dx² = ------ = ^dny⁄ _dxⁿ?

A) y = Ae^x (Confirm) (100% Sure)

B) y = Axe^x

B) y = Ae^xx

B) y = Ax^x e^xx

Q3: If
        y= 2 + x
        , then which of the following is true for it?

A) Its annihilator is D

C) Its annihilator operator is D² (pag159) (100% Sure)

B) Its annihilator operator is D³

B) Its annihilator operator is D + 1

Q4: For the non-exact differential equation M(x,y)dx + N(x,y)dy =0, if ^{∂M⁄_∂y - ∂N⁄_∂x} ⁄ _N $ is a function of x, then the integrating factor is:

A) function of x also (page40) (100% Sure)

D) function of y

D) constant

D) multi-variable function of both x and y

Q5: Which of the following are explicit solution of the differential equation: ^dy⁄_dx = - ^x⁄_y

A) y = ± √ 4 + x

A) y = ± √ - 4 + x²

D) y = ± √ 4 - x²   (page16) (100% Sure)

D) y = ± √ - 4 - x²

Q6: For f(x,y) = ^2x⁄_3y + 7, f(t_x, t_y) = - - -

A) f(x,y)

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

A) t² f(x,y)

D) t³ f(x,y)

Q7: What is the annihilator operator of the function g(x) = 4sinx ?

A) (D² - 1)

D) (D² + 4)

D) (D² - 4)

D) (D² + 1) (100% Sure) Click here for detail

Q8: The differential equation ^dy⁄_dx - y = y ³

A) Bernoulli's (page55) (100% Sure)

A) Homogeneous

A) Cauchy

D) Bessel

Q9: The integrating factor for the first order linear differntial equation: ^dy⁄_dx + ycotx = sin²x is ______.

C) sinx (100% Sure) Click here for detail

D) cosx

D) e^{sin x}

D) e^{cos x}

Q10: In exponential model for the population growth: P(t) = P₀e^kt   If k>0, then lim t→∞   P(t) =

A) 0

B) 1

B) ∞ (page97) (100% Sure)

B) - ∞