Download JNTU Kakinada B.Tech 1-1 2014 Feb MATHEMATICS II Question Paper

Subject Code: R13107/R13

Set No - 1

I B. Tech I Semester Regular Examinations Feb./Mar. - 2014

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MATHEMATICS-II (MATHEMATICAL METHODS)

(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)

Time: 3 hours

Max. Marks: 70

Question Paper Consists of Part-A and Part-B

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Answering the question in Part-A is Compulsory,

Three Questions should be answered from Part-B

*****

PART-A

1. (i) Write the sufficient condition for the convergence of Newton-Raphson method? 1

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2. (ii) Show that µd = (? + ?)? 2
3. (iii) Write the merits and demerits of Euler Modified method?
4. (iv) Write the Dirichlet's conditions of f(x)?
5. (v) State Initial and Final value theorems of Z-transforms?
6. (vi) Write the statement of Fourier integral theorem?

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[3+4+4+3+4+4]

PART- B

1. (a) Using Runge-Kutta method of fourth order solve dy/dx = xy, y(1) = 2 at x = 1.2 with h = 0.2 [8+8]
2. (b) Find the Fourier transform of f(x) = x^n-1

1. For the following data estimate f (1.720) using forward, f (2.68) using backward and f (2.36) using central difference formula.

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[16]

1. (a) Solve the differential equation dy/dx = x + y subject to y(0) = 1 by Picard's method and hence find y(0.2). [8+8]
2. (b) Using Regula Falsi method find a real root of f(x) = 2x⁷ + x⁵ + 1 = 0 correct upto two decimal places.

1. (a) Find the Fourier series for f (x) = 2lx - x² in (0, 2l), hence show that 1/1² + 1/2² + 1/3² + 1/4² = p²/12 [8+8]
2. (b) Find the inverse Z transform of (3z²+z)/((5z-1)(5z-2))

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Page 1 of 2

Subject Code: R13107/R13

Set No - 1

1. (a) Find the Fourier transform of f(x) = {1 - x², |x| < 1; 0, |x| > 1} [8+8]
2. (b) Find a real root of f (x) = x + log x - 2 using Newton-Raphson method.

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1. (a) Find Z-transform of (i) aⁿn² + bn + c (ii) sin (3n + 5) [8+8]
2. (b) Find the half range Fourier sine series for f (x) = x in (0,p)?

Subject Code: R13107/R13

Set No - 2

I B. Tech I Semester Regular Examinations Feb./Mar. - 2014

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MATHEMATICS-II (MATHEMATICAL METHODS)

(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)

Time: 3 hours

Max. Marks: 70

Question Paper Consists of Part-A and Part-B

--- Content provided by FirstRanker.com ---

Answering the question in Part-A is Compulsory,

Three Questions should be answered from Part-B

*****

PART-A

1. (i) State Intermediate Value theorem?

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2. (ii) Show that?(e^ax log bx)?
3. (iii) Write the second order Runge-Kutta formula?
4. (iv) Give any one application of Fourier Series with example?
5. (v) State the convolution theorem of inverse Z-transforms?
6. (vi) Write the formulas Fourier cosine and sine transform?

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[4+3+4+3+4+4]

PART- B

1. (a) Using modified Euler's method to find the value of y at x = 0.2 with h = 0.1 where y' = 1 - y, y(0) = 0 [8+8]
2. (b) Find the Fourier transform of f(x) = {x, |x| {"less than or equal to"} a; 0, |x| > a} FirstRanker.com

1. (a) Prove the relation ?² f_k = ? ⁿ_k=0 [4+12]

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2. (b) Use Lagrange's interpolation formula to calculate f(3) from the following table.

1. (a) Solve the differential equation dy/dx = x²y subject to y(0) =1 by Taylor series method and hence find y(0.1), y(0.2). [8+8]
2. (b) Using bisection method find a root of f(x) = x - cos x = 0.

1. (a) Obtain the Fourier series for f(x) = |x| in [-p,p], hence show that 1/1² + 1/3² + 1/5² +… = p²/8 [8+8]
2. (b) Solve U_n+2 + 4U_n+1 + 3u_n = 3ⁿ with u₀ = 0; u₁ = 1 using Z transforms

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Page 1 of 2

Subject Code: R13107/R13

Set No - 2

1. (a) Using Fourier integral, prove that e^-ax = (2a/p) ?₀⁸ (cos ax)/(a²+?²) da, a > 0, x > 0 [8+8]
2. (b) Find a real root of f(x) = xlog₁₀x = 1.2 using Newton-Raphson method.

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1. (a) Find the Z transform of (i) cos(n + 1)? (ii) sinh (np/2) [8+8]
2. (b) Obtain the Fourier series for spectrum of a periodic function with example?

Subject Code: R13107/R13

Set No - 3

I B. Tech I Semester Regular Examinations Feb./Mar. - 2014

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MATHEMATICS-II (MATHEMATICAL METHODS)

(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)

Time: 3 hours

Max. Marks: 70

Question Paper Consists of Part-A and Part-B

--- Content provided by​ FirstRanker.com ---

Answering the question in Part-A is Compulsory,

Three Questions should be answered from Part-B

*****

PART-A

1. (i) Write the sufficient condition for the convergence of Newton-Raphson method? 1

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2. (ii) Show that µd = (? + ?)? 2
3. (iii) Write the advantages & disadvantages of Taylor series method?
4. (iv) Write the Fourier series when the given function f(x) is an even?
5. (v) Write the properties of multiplication by n and division by n of Z-transforms?
6. (vi) Write the complex form of Fourier integral theorem?

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[3+3+4+4+4+4]

PART- B

1. (a) Using iteration method find a real root of f(x) = x² - 3x + 1 correct upto three decimal places starting with x=1. [8+8]
2. (b) Solve U_n+2 — 2U_n+1 + U_n = 3ⁿ + 5 using Z-Transforms?

1. (a) Evaluate ?(e^ax log bx) [4+12]

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2. (b) By using Lagrange's interpolation formula, fit a polynomial data

1. (a) Using modified Euler method solve numerically the equation dy/dx = 2 +v(xy) with y(1) = 1 to find y(2) [8+8]
2. (b) Find f(x) if its Fourier sine transform is s/(1 + s²)

1. (a) Obtain the Fourier series for f(x) = (p - x)² in 0 < x < 2p, hence deduce that 1/1² + 1/2² + 1/3² +… = p²/6 [8+8]
2. (b) Using convolution theorem, evaluate Z^-1[z²/(z²-4z+3)]

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Page 1 of 2

Subject Code: R13107/R13

Set No - 3

1. (a) Using Parseval's identities, prove that [8+8]
2. (b) Using Runge-Kutta method of third order, find the values of y(x)for x = 0.1, 0.2 where y' = x – 2y, y(0) = 1.

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1. (a) Find the half range sine series for f(x) = x(p – x) in (0,p) [8+8]
2. (b) Find a real root of f(x) = x³ – 19 correct upto three decimal places using Newton- Raphson method

Subject Code: R13107/R13

Set No - 4

I B. Tech I Semester Regular Examinations Feb./Mar. - 2014

--- Content provided by‍ FirstRanker.com ---

MATHEMATICS-II (MATHEMATICAL METHODS)

(Common to ECE, EEE, EIE, Bio-Tech, EComE, Agri.E)

Time: 3 hours

Max. Marks: 70

Question Paper Consists of Part-A and Part-B

--- Content provided by​ FirstRanker.com ---

Answering the question in Part-A is Compulsory,

Three Questions should be answered from Part-B

*****

PART-A

1. (i) Show that µd = (? + ?)? 1

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2. (ii) Write the merits and demerits of Iteration method? 2
3. (iii) Write the merits and demerits of Euler Modified method?
4. (iv) Write the Dirichlet's conditions of f(x)?
5. (v) State convolution theorem of Z-transforms?
6. (vi) Write the statement of Fourier integral theorem?

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[3+4+4+3+4+4]

PART- B

1. (a) Find the Fourier sine and cosine transforms of (2.e^-5x +5.e^-2x). [8+8]
2. (b) Given f(x)= {1-x, -p = x = 0; 1+x, 0 = x = p}. Is the function even or odd? Find the Fourier series for f(x).
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1. (a) Prove the relation between E and D? [4+12]

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2. (b) For the following data estimate K (0.25) using backward difference formula.

1. (a) Solve the differential equation dy/dx = 1+ xy subject to y(0) = 1 by Taylor series method and hence find y(0.2). [8+8]
2. (b) Solve the difference equation y_n+2+3y_n+1+2y_n = 0, y₀= 1, y₁ = 2 by z – transform.

1. (a) Find the Fourier series of f(x)=x+x²,- p < x < p and hence deduce the series 1/1² - 1/2² + 1/3² = p²/12 [8+8]
2. (b) Apply Runge - Kutta Method to find y(0.1) and y(0.2) where dy/dx = x²y and y(0) = 1.

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Page 1 of 2

Subject Code: R13107/R13

Set No - 4

1. (a) Find the Fourier transform of e^-|| [8+8]
2. (b) Using Regula Falsi method find a real root of f (x) = 2x⁷ + x⁵ + 1 = 0 correct upto two decimal places.

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1. (a) Find z(1/n!) and hence evaluate z((1/(n+1)!)) and z((1/(n+2)!)) [8+8]
2. (b) Find a real root of f(x) = x + log x - 2 using Newton-Raphson method.