Download PTU B-Tech CSE-IT 2020 Dec 3rd Sem 76393 Mathematics Iii Question Paper

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B.Tech. (IT) (2018 Batch) (Sem.-3)

MATHEMATICS-III

Subject Code : BTAM-304-18
M.Code : 76393

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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 contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

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SECTION-A

Write briefly :

1. Find the first order derivative of f'(x, y) = tan^-1(y/x) w.r.t. X
2. Evaluate the integral ? (x to 1) (0 to 1) dy dx / (2 + y²)
3. Give examples of the convergent and divergent sequences.

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4. State Cauchy Root test for convergence of a positive term infinite series.
5. Write down the Taylor's series expansion for sinh x about x = 0.
6. Write down the Clairaut's equation and find its solution.
7. Solve the differential equation : 3e^x tan y dx + (1 + e^x) sec² y dy = 0
8. Check whether the given equation is exact or not, if yes then find solution 2xy dx + x² dy = 0

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9. Solve the differential equation d²y/dx² - 6 dy/dx + 11y = 0
10. Find Particular integral for d²y/dx² - 6 dy/dx + 9y = e^3x

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SECTION-B

11. Find the dimensions of the rectangular box, open at the top of maximum capacity whose surface is 432 sq. cm.
12. Find the area bounded by the parabola y = x² and the line y = 2x + 3.
13. For what value(s) of x does the series converge (i) conditionally (ii) absolutely?
    S (xⁿ / (n * 2ⁿ)) Also find the interval of convergence (n=1 to 8)

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14. Solve the differential equation : (2xy + y² + 3) dx - 2xydy = 0
15. Solve the differential equation d²y/dx² - 3 dy/dx + 2y = xe^x

SECTION-C

16. a) Check the convergence of the series S (1 / (n (ln n)²)) (n=2 to 8)
    b) Find the volume of the ellipsoid x²/a² + y²/b² + z²/c² = 1

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17. a) Solve the differential equation dy/dx + y/x sin2y = x³ cos²y
    b) Solve the differential equation p² + xp + py + xy = 0, where p = dy/dx
18. a) Solve by Method of Variation of parameters d²y/dx² + 2 dy/dx + y = e^-xcosx
    b) Solve x² d²y/dx² - x dy/dx + 4y = sin(ln x)

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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