# Numerical Methods and Computer Programming 3

Electrical Engineering MCQ Question Papers: Campus Placement

Subject: Numerical Methods and Computer Programming 3

Part 3: List for questions and answers of Numerical Methods & Computer Programming

Q1. Which of the following equations is an exact DE?

a) (x^2 + 1) dx – xy dy = 0

b) x dy + (3x – 2y) dx = 0

c) 2xy dx + (2 + x^2) dy = 0

d) x^2.y dy – y dx = 0

Q2. Which of the following equations is a variable separable DE?

a) (x + x^2 y) dy = (2x + xy^2) dx

b) (x + y) dx – 2y dy = 0

c) 2y dx = (x^2 + 1) dy

d) y^2 dx + (2x – 3y) dy = 0

Q3. The equation y^2 = cx is general solution of:

a) y’ = 2y / x

b) y’ = 2x / y

c) y’ = y / 2x

d) y’ = x / 2y

Q4. Solve the differential equation: x(y – 1) dx + (x + 1) dy = 0. If y = 2 when x = 1

a) 1.80

b) 1.48

c) 1.55

d) 1.63

Q5. If dy = x^2 dx; what is the equation of y in terms of x if the curve passes through (1, 1)

a) x^2 – 3y + 3 = 0

b) x^3 – 3y + 2 = 0

c) x^3 + 3y^2 + 2 = 0

d) 2y + x^3 + 2 = 0

Q6. Find the equation of the curve at every point of which the tangent line has a slope of 2x

a) x = -y^2 + C

b) y = -x^2 + C

c) y = x^2 + C

d) x = y^2 + C

Q7. Solve (cox x cos y – cotx) dx – sin x sin y dy = 0

a) sin x cos y = ln (c cos x)

b) sin x cos y = ln (c sin x)

c) sin x cos y = -ln (c sin x)

d) sin x cos y = -ln (c cos x)

Q8. Solve the differential equation dy – x dx = 0, if the curve passes through (1, 0)?

a) 3x^2 + 2y – 3 = 0

b) 2y^2 + x^2 – 1 = 0

c) x^2 – 2y – 1 = 0

d) 2x^2 + 2y – 2 = 0

Q9. What is the solution of the first order differential equation y(k + 1) = y(k) + 5

a) y(k) = 4 – 5/k

b) y(k) = 20 + 5k

c) y(k) = C – k, where C is constant

d) The solution is non-existence for real values of y

Q10 .Solve (y – root of (x^2 + y^2)) dx – x dy = 0

a) Root of(x^2 + y^2 ) + y = C

b) root of(x^2 + y^2 + y) = C

c) Root of(x + y) + y = C

d) root of(x^2 – y) + y = C

Q11. Find the differential equation whose general solution is y = C1x + C2ex

a) (x – 1) y” – xy’ + y = 0

b) (x + 1) y” – xy + y = 0

c) (x – 1) y” + xy’ + y = 0

d) (x + 1) y” + xy’ + y = 0

Q12. Find the general solution of y’ = y sec x

a) y = C (sec x + tan x)

b) y = C (sec x – tan x)

c) y = C (sec x tan x)

d) y = C (sec2 x + tan x)

Q13. Find the differential equations of the family of lines passing through the origin

a) y dx – x dy = 0

b) x dy – y dx = 0

c) x dx + y dy = 0

d) y dx + x dy = 0

Q14. What is the differentia equation of the family of parabolas having their vertices at the origin and their foci on the x-axis

a) 2x dy – y dx = 0

b) x dy + y dx = 0

c) 2y dx – x dy = 0

d) dy / dx – x = 0

Q15. Determine the differential equation of the family of lines passing through (h, k)

a) (y – k) dx – (x – h) dy = 0

b) (y – h) + (y – k) = dy / dx

c) (x – h) dx – (y – k) dy = 0

d) (x + h) dx – (y – k) dy = 0

Q16. Determine the differential equation of the family of circles with center on the y-axis

a) (y”)3 – xy” + y’ = 0

b) y” – xyy” + y’ = 0

c) xy” – (y’)3 – y’ = 0

d) (y’)3 + (y”)2 + xy = 0

Q17. Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of radium decomposes to 96 mg. How many mg will be left after 100 years?

a) 88.60

b) 95.32

c) 92.16

d) 90.72

Q18. The population of a country doubles in 50 years. How many years will it be five times as much? Assume that the rate of increase is proportional to the number inhabitants

a) 100 years

b) 116 years

c) 120 years

d) 98 years

Q19. Radium decomposes at a rate proportional to the amount present. If the half of the original amount disappears after 1000 years, what is the percentage lost in 100 years?

a) 6.70%

b) 4.50%

c) 5.35%

d) 4.30%

Q20. A nominal interest of 3% compounded continuously is given on the account. What is accumulated amount of P10,000 after 10 years

a) P13,620.10

b) P13,500.10

c) P13,650.20

d) P13,498.60

Part 3: List for questions and answers of Numerical Methods & Computer Programming