Download PTU B.Tech 2020 March CSE-IT 3rd Sem BTAM 301 18 Mathematics Iii Question Paper

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Roll No. : Total No. of Pages : 02

Total No. of Questions : 09

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

MATHEMATICS-III

Subject Code : BTAM-301-18

M.Code : 76393

Time : 3 Hrs. Max. Marks : 60

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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.

SECTION-A

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1. Write briefly :
   1. Show that the function f(x, y) = x²y / (x⁴ + y²) has no limit as (x, y) approaches (0, 0).
   2. Find the local extreme values of the function f (x, y) = x³ + y³ - 2x²y + 6.
   3. Sketch the region of integration for the integral ?₀¹?_arcsinx^p/2 y dydx and write an integral with the order of integration reversed.
   4. Define convergence of a series and give an example of a convergent series.
   5. Explain the limit comparison test.

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   6. By inspection obtain the integrating factor and solve the differential equation : xdx = ydy + 2(x² + y) dx = 0
   7. Check whether the following differential equation exact. 2x+e^ydx+xdy=0
   8. Find the general solution of the differential equation y''' +2y' +y =0
   9. Verify whether the linear combination of f₁ and f₂ is a solution of the differential equation Y''+2y=0
   10. Find the Wronskian of the functions x, x² and x³.

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SECTION-B

Solve the following integral

?₀^ln2 ?₀^v(ln2)2-y2 e^-x2-y2 dxdy

by converting it into an equivalent polar integral.

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For what values of x does the following power series converge ?

?_n=1⁸ (xⁿ / n)

Solve the differential equation (3x²y²e^x +y² +1) dx + (x³y²e^x — x) dy = 0.

Solve the differential equation y'" + 4y" + 4y = e^-2x.sin x by using method of variation of parameters.

Check the convergence of the following series

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1. ?_n=1⁸ (2n)! / (3ⁿn!)

SECTION-C

1. a) Find the maximum and minimum values of the function f(x, y) = 3x + 4y on the circle x²+y² =1
2. b) Find the volume in the first octant bounded by the coordinate planes and the surface z=4-x²-y²
3. State and prove Leibniz’s test for alternating series.

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4. Find the general solution of the equation x³y''' - 3x²y' + 3y = 16x + 9x² In 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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