Download JNTUK B-Tech 2020 R19 IT 1102 Mathematics II Model Question Paper

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[B19 BS 1102]

I B. Tech I Semester (R19) Regular Examinations

MATHEMATICS - 11

(Common to CSE, ECE & IT)

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MODEL QUESTION PAPER

Answer ONE Question from EACH UNIT

All questions carry equal marks

Max. Marks: 75 M

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UNIT-I CO KL

1. a) Using Newton’s forward difference interpolation formula find Y (3), from the following table
   

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   X	0	5	10	15	20	25
   Y	7	11	14	18	24	32

   CO3 K2
   Find the interpolating polynomial f(x) for the data of the following table
   
2. b)

   X	0	1	4	5
   f(x)	4	3	24	39

   o3 Kl

(OR)

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1. a) Using Gauss backward formula, find f(42), from the following table
   

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

   CO4 K2
   
2. b) Using Lagrange’s interpolation formula find Y (10) from the following table
   

   X	5	6	9	11
   Y	12	13	14	16

   CcO4 K3

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UNIT-II

1. a) Find the cube root of 41 using Newton-Raphson method. CO5 K2
2. b) Evaluate ?₀¹ X³ii+1 by using Simpsons 1/3™ rule with h = 0.25 CO5 K2

(OR)

1. a) Find a real root of the equation x log₁₀x=1.2 by Regula-false method CO5 K2 correct to three decimal places

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2. b) Evaluate y(0.8) using Runge Kutta method given y' =(x+y)², y(0.4) =0.41 COS 3

UNIT-III

1. a) If U=tan^-1 (x³+y³)/(x-y) and prove that x U_x +y U_y =sin 2U, col K2

U_xx+ 2xy U_yy + y²U_yy =2cos 3U sin U.

1. b) If u=x²- 2y²,v=2x²—y² where x=rcos?, y=rsin? then show that ?(u,v)/?(r, ?) =6r² sin 2?. col | K2

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(OR)

1. a) Expand x²y + 3y -2in powers of (x—1) and (y+2) using Taylor's theorem. Ccol1 K2
2. b) By using the method of differentiation under the integral sign prove that ?₀⁸ tan^-1(ax)/x dx = log(a), a>0. COl1 K3

UNIT-IV

1. a) Solve x(y-z)p+y(z-x)q=z(x-y). CO2 K2

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2. b) solve (D²-DD' -2D'²)z=(y-1)e^x. co2

(OR)

1. a) Solve x(y-z)p+y(z-x)q=2z(x-y). CcO2
2. b) solve (D²+D'² -1)(D+2D' -3)z=3x+6y+4. co2 K2

UNIT-V

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1. a) Obtain the solution of ?²u/?x?t = 0 by the method of separation of variables. CO6 K2
2. b) A tightly stretched elastic string of length L, fixed at its' end points is initially in a position given by u(x, 0) = µsin3(px/L). If it is released from rest, find the displacement at any subsequent time. CO6 K3

(OR)

1. a) Obtain the solution of x ?u/?x + y ?u/?y = 0,by the method of separation of variables. co6 K2
2. b) A bar of conducting material of length l units is initially kept at a temperature sin(px/l). Find the temperature at any subsequent time if the ends of the bar are held at zero temperature. CO6 K3

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