Download PTU B-Tech ME 2020 Dec 2nd Sem 76256 Mathematics Ii Question Paper

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Roll No. :

Total No. of Pages : 02

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Total No. of Questions: 18

B.Tech. (Mechnical Engg) (2018 & onwards) (Sem.-2)

MATHEMATICS-II

Subject Code: BTAM-203-18

M.Code: 76256

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Time : 3 Hrs.

Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION - B & C have FOUR questions each.

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3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.

SECTION-A

Answer briefly :

1. Solve y (log y) dx + (x - log y)dy = 0.

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2. Solve p = log (px - y).
3. Find the particular integral of (D² - 2D + 4)y = cos x.
4. Solve (D²+1)y = 0.
5. What is the necessary and sufficient condition for a differential equation to be exact?
6. Define analytic function.

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7. Evaluate ? (x² - xy + y)dz where C is the contour |z| = 1.
8. State maximum modulus theorem.
9. Find all zeros of sin z.
10. What is the principal value of iⁱ?

SECTION-B

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11. Solve:
    1. x dy/dx + y = x²y⁶.
    2. Solve (xy³ + y) dx + 2(x²y²+x+y²) dy = 0.
12. Solve y = 2px + y²p³
13. a) Using method of variation of parameters, solve d²y/dx² +4y = tan 2x.
    

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    b) Solve y" - 2y' + 5y = 0 if y (0) = -3, y' (0) = 1.
14. Solve x²d²y/dx² - 3xdy/dx + y = log x sin (logx)+1 / x

SECTION-C

15. Show that the function u = e^-2x sin (x²- y²) is harmonic. Find conjugate function v and express u + iv as an analytic function of z.
16. Derive Cauchy Riemann equations for analytic functions.

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17. a) Evaluate ? (z+z) dz along the line joining the points (1,-1) and (2, 3).
    b) By integrating around a unit circle evaluate ? 2 cos 3? / 5-4cos? d?.
18. Evaluate 1 / z²-3z+2 in the region.
    a) |z|<1 b) 1<|z|<2 c) |z|>2 d) 0<|z-1|<1

NOTE: Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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