MTH401 Midterm Solved MCQs by Junaid

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

1. z dy»dx + (sinx)y = cosx (page48) (100% Sure)
2. y dx»dy + (siny)x = cosy
3. y dx»dy + (siny)x = cosx
4. y dx»dy + (sinx)x = cosy

Q2. Which of the following function would satisfy: dy»dx = d2y» dx2 = ------

= dny» dxn?

1. y = Aex (Confirm) (100% Sure)
2. y = Axex
3. y = Aexx
4. y = Axx exx

Q3. y= 2 + x

, then which of the following is true for it?

1. Its annihilator is D
2. Its annihilator operator is D2 (pag159) (100% Sure)
3. Its annihilator operator is D3
4. 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:

1. function of x also (page40) (100% Sure)
2. function of y
3. constant
4. multi-variable function of both x and y

Q5. Which of the following are explicit solution of the differential

1. y = ± √ 4 + x
2. y = ± √ - 4 + x2
3. y = ± √ 4 - x2 (page16) (100% Sure)
4. y = ± √ - 4 - x2

Q6. For f(x,y) = 2x»3y + 7, f(tx, ty) = - - -

1. f(x,y)
2. t f(x,y) (page26) (100% Sure)
3. t2 f(x,y)
4. t3 f(x,y)

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

1. (D2 - 1)
2. (D2 + 4)
3. (D2 - 4)
4. (D2 + 1) (100% Sure)

Q8. The differential equation dy»dx - y = y 3

1. Bernoulli's (page55) (100% Sure)
2. Homogeneous
3. Cauchy
4. Bessel

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

1. sinx (100% Sure)
2. cosx
3. esin x
4. ecos x

Q10. In exponential model for the population growth: P(t) = P0ekt If k>0, then lim t→∞ P(t) =

1. 0
2. 1
3. ∞ (page97) (100% Sure)
4. - ∞

Q11. The hook's law states that the force F is proportional to the

1. Length
2. Elongation (page197) (100% Sure)
3. Weight
4. None of these

Q12. Separable form of the differential equation: dy»dx = y - 1 is ________, where v = y - 1.

1. dx»x = dv
2. dx = vdv
3. dy»v = dx (page17) (100% Sure)
4. dv»v = dx»x

Q13. For f(x,y) = 2x»3y + 7, f(tx, ty) = - - -

1. f (x, y)
2. t f(x, y) (page26) (100% Sure)
3. t2 f(x,y)
4. t3 f(x,y)

Q14. Which of the following is an equivalent form of the exact differential equation: ydx + xdy = 0?

1. d x»y = 0
2. d y»x = 0 (page33) (100% Sure)
3. d (xy) = 0
4. d (x + y) = 0

Q15. In the general solution of a separable differential equation is sin-1y = cos-1x + c, provided that y (1»√2) = 1»√2, then c = - - - .

1. Π»2