Download VTU BE 2020 Jan Question Paper 17 Scheme 17MAT21 Engineering Mathematics II First And Second Semester

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CBCS SCHEME

17MAT21

Second Semester B.E. Degree Examination, Dec.2019/Jan.2020

Engineering Mathematics - II

Time: 3 hrs.

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Max. Marks: 100

Note: Answer any FIVE full questions, choosing ONE full question from each module.

Module-1

1. a. Solve ^d3y/_dx³ - 6 ^d2y/_dx² + 11 ^dy/_dx - 6y = 0 (06 Marks)
2. b. Solve (D² - 4)y = Cosh (2x - 1) + 3^x (07 Marks)

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3. c. Solve (D² + 1)y= Secx by the method of variation of parameters. (07 Marks)

OR

1. a. Solve (D³ - 9D² +23D -15)y = 0 (06 Marks)
2. b. Solve y" - 4y' + 4y = 8 (Sin2x + x²) (07 Marks)
3. c. Solve ^d2y/_dx² + 2 ^dy/_dx + 4y = 2x² by the method andetermined coefficients. (07 Marks)

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Module-2

1. a. Solve (x²D² + (xD) + 1)y= sin (2logx) (06 Marks)
2. b. Solve x²p² + 3xyp + 2y = 0 (07 Marks)
3. c. Find the general and singular solution of Clairaut's equation y = xp + p². (07 Marks)

OR

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1. a. Solve (2x + 1)² y" - 2 (2x + 1) y' - 12y = 6x (06 Marks)
2. b. Solve p² + 2py cot x - y² = 0 (07 Marks)
3. c. Find the general solution of (p - 1)e^x + p³ e^2x = 0 by using the substitution X =e^x, Y = e^y. (07 Marks)

Module-3

1. a. Form the partial differential equation by eliminating the function from Z = y² + 2f(^y/_x + log y) (06 Marks)

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2. b. Solve ^?2z/_?x?y = sin x siny for which z = -2siny when x = 0 and z = 0 when y is an odd multiple of ^p/₂ (07 Marks)
3. c. Derive one dimensional wave equation ^?2u/_?t² = c^{2 ?2u}/_?x² (07 Marks)

OR

1. a. Form the partial differential equation by eliminating the function from f(x + y+z, x² +y² + z²) = 0 (06 Marks)
2. b. Solve ^?z/_?y + z = 0 given that z = cosx and ^?z/_?y = sin x when y = 0. (07 Marks)

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3. c. Obtain the variable separable solution of one dimensional heat equation ^?u/_?t = c^{2 ?2u}/_?x² (07 Marks)

Module-4

1. a. Evaluate ?(x² + y² )dx dy (Limits not specified) (06 Marks)
2. b. Evaluate ? dydx by changing the order of integration. (Limits not specified) (07 Marks)
3. c. Drive the relation between Beta and Gamma function as B(m, n) = ^G(m)G(n)/_{G(m + n)} (07 Marks)

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OR

1. a. Evaluate ?(x² + y² + z²)dx dy dz (Limits not specified) (06 Marks)
2. b. Find the area between the parabolas y² = 4ax and x² = 4ay. (07 Marks)
3. c. Prove that ?₀^p/2 Sinⁿ ? d? = ^{vp G(n+1/₂)}/_{G(ⁿ/2 + 1)} (07 Marks)

Module-5

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1. a. Find the Laplace transform ^{Cosat - Cosbt}/_t (06 Marks)
2. b. Express the function f(t) = { Sin t, 0 < t < p; 0, t > p } in terms of unit step function and hence find its Laplace transform. (07 Marks)
3. c. Find L^-1 [^s+2/_s²-2s+5] (07 Marks)

OR

1. a. Find the Laplace transform of the periodic function f(t) = t², 0 < t < 2 (06 Marks)

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2. b. Using convolution theorem obtain the Inverse Laplace transform of ¹/_{s² (s² + 1)} (07 Marks)
3. c. Solve by using Laplace transform y" + 4y' + 4y = e^-t. Given that y(0) = 0, y'(0) = 0. (07 Marks)

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