Download PTU B-Tech ECE 2020 Dec 2nd Sem 76255 Mathematics Ii Question Paper

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Roll No. ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ Total No. of Pages : 03

Total No. of Questions : 18

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B.Tech. (Electrical Engg./ECE) (2018 & Onwards) (Sem.-2)

MATHEMATICS-II

Subject Code : BTAM-202-18

M.Code : 76255

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

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SECTION-A

Answer briefly :

1. Is this differential equation x²(d²y/dx²) + y(dy/dx) +y²=0 linear?
2. Is this differential equation (e^x + 1) cos x dx + e^xsin xdy = 0 exact?
3. Write the solution of the Clairaut’s equation y = px + cos^-1(p + 1).

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4. Find complete solution of ?²z/?x² - 4 ?²z/?x?y + 4 ?²z/?y²=0.
5. Find particular integral of ?²z/?x² - ?²z/?x?y +12 ?²z/?y²=e^x-y.
6. Give geometric interpretation of Newton Raphson method.
7. Give the Gauss’s forward interpolation formula.
8. Write the formula for Simpson’s ? rule.

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9. Give the Adam’s predictor corrector formula.
10. Write the one dimensional heat equation.

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SECTION-B

11. Solve:
    1. dy/dx = (2xycos x² - 2xy +1)/(x²—sinx² -3)

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    2. tany dy/dx - y +tan x = cos y cos²x.
12. 1. Solve (D²- 2D—4)y=x²
    2. Solve using method of variation of parameters (d²y/dx²) - 6(dy/dx) +9y = e^3x/x

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13. 1. Solve yzp +zxq = xy.
    2. ?²z/?x² - 6?²z/?x?y + ?²z/?y²=cos(3x+y).
14. 1. Solve the PDE (D+D'-1)(D+2D' —3)z=4+3x +6y.
    2. Using method of separation of variables, solve 3?u/?x +2?u/?y =0 with u (x, 0) = 4e^-x.

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SECTION-C

15. 1. Find a root of cos x =xe^x using regula falsi method correct upto three decimal places.
    2. Using interpolation, find missing values in the following table :

    X	45	50	55	60	65
    	3	30	-	20	-	24

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16. 1. Estimate f(38), using Gauss backward difference formula :

    x	20	25	30	35	40	45
    f(x)	354	332	291	260	231	204

17. 1. Estimate ?₀² e^xdx, using Trapezoidal rule by taking 10 intervals.
    2. Use Taylor’s series method to find the value of y at x = 0.2 upto 3 decimals, where dy/dx =x²-y, y(0)=1.

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18. 1. Use Runge-Kutta method of order 4 to find the value of y at x = 0.1 upto 3 decimals, where y (0) =1, dy/dx =x+y.
    2. Using Crank-Nicholson method, solve the PDE ?²f/?x²=?f/?t; 0 < t <15 0<x<4 subject to conditions f(x, 0) =50 (4 —x),f(0,t)=0, f(4,t)=0.

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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