Download JNTUA B.Tech 1-1 R13 2019 Dec 13A54102 Mathematics II Question Paper

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Code: 13A54102

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B.Tech I Year (R13) Supplementary Examinations December 2019

MATHEMATICS – II

(Common to EEE, ECE, EIE, CSE & IT)

Time: 3 hours Max. Marks: 70

PART - A

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(Compulsory Question)

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1 Answer the following: (10 X 02 = 20 Marks)

(a) Find the Eigen values and the corresponding of is Hermitian.

(b) Show that A =

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(c) Define algebraic and transcendental equations with example each.

(d) The value of dx by Simpson's 1/3 rule (taking n = 4) is

(e) If dy/dx = -y, y(0) = 1, h = 0.01 then by Euler's method the value of y1 is

(f) Write the Fourier series of f(x) in [C, C+2L].

(g) Find the Fourier cosine transform f(x) = e^-ax .

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(h) Define convolution theorem.

(i) Write the two dimensional Laplace equation.

(j) Form a partial differential equation by eliminating the arbitrary constants a and b from the equation: z = ax + by.

PART - B

(Answer all five units, 5 X 10 = 50 Marks)

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UNIT - I

2 Reduce the matrix A = into its normal form and hence find its rank.

OR

3 Reduce the quadratic form 3x² + 5y² + 3z² + 2xy + 2xz - 2yz into canonical form using orthogonal transformation and find its rank, index and signature.

UNIT - II

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4 (a) Using Newton-Raphson method compute v41 correct to four decimal places.

(b) Find the root of an equation 2x - log x = 6 by Regula-falsi method.

OR

5 (a) Evaluate x³dx with five sub-intervals by Trapezoidal rule.

(b) Evaluate dx using Simpson's rule for n = 4.

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UNIT - III

6 Using Euler's method, solve for y at x = 0.1 from dy/dx = x + y + xy, y(0) = 1 taking step size h = 0.025.

OR

7 Find the Half range cosine series of f(x) = x(1 - x) in [0, 2].

UNIT - IV

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8 Find the Fourier series for f(x) =

Hence deduce that 1/1² + 1/3² + 1/5² + ...= p²/8

OR

9 (a) Find Z(n sin n?).

(b) Find Z^-1 ,|z|>3.

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UNIT - V

10 Form the PDE by eliminating arbitrary function f (x² + y² +z², xyz) = 0 .

OR

11 A bar of length 7 with insulated sides is initially 0°C temperature throughout the end x = 0 is kept at 0°C for all time and heat is suddenly applied such that ?u/?x = 10 at x = l for all time. Find the temperature function u(x, t).

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