PTU B.Tech ECE 2nd Semester May 2019 76255 MATHEMATICS II Question Papers

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Roll No.

Total No. of Pages : 02

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Total No. of Questions : 09

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

MATHEMATICS-II

Subject Code : BTAM-202-18

M.Code : 76255

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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

1. Answer briefly :
   1. Check whether the given equation is exact and obtain the general solution :
      (1+x²)dy + vvdx = 0

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   2. Solve the differential equation (x -a)dy/dx + 3y = 12 (x-a)³ ; x > a > 0.
   3. Find the solution of the differential equation y'' + 2y' + 2y = 0.
   4. Find a differential equation of the form ay" + by' + cy = 0, for which e^-x and xe^-x are solutions.
   5. Solve the differential equation y"" + 32y" + 256y = 0
   6. Write a short note on initial value problems.

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   7. Find the interval in which the root of equation x³ – x – 11 = 0 lies.
   8. Write a short note on Bisection method.
   9. Define transcendental equation.
   10. Find the polynomial which takes following data (0, 1), (1, 2) and (2, 1).

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SECTION-B

2. i) Find the integrating factor and hence solve (5x³ + 12x² +6y²) dx + 6xy dy = 0
   ii) Solve the differential equation dy/dx – y = y² (sin x + cos x).
3. i) Find a homogeneous linear differential equation with real coefficients of lowest order which has the xe^x + e^2x as the particular solution.
   ii) Using differential operator, find general solution of (D² + 9) y = xe^2x cosx.

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4. Find the general solution of the equation y"+16y = 32 sec 2x, using the method of variation of parameters.
5. Find the general solution of the equation x²y"+5xy' – 5y = 24xlnx.

SECTION-C

6. Use Newton iterative method to find the root of equation 3x – cos(x) + 1, by taking initial guess 0.6.
7. Solve the following equations by elimination method 2x + y + z = 10, 3x + 2y + 3z = 18 and x + 4y + 9z = 16.

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8. Using Newton's forward formula, find value of f (1.6), if :
   

   X	1	1.4	1.8	2.2
   f(x)	3.49	4.82	5.96	6.5

9. Using Runge-Kutta method of order 4, find y(0.2) for the equation y' = (y – x)/(y + x), y(0) = 1, take h = 0.2.

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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