Download JNTUK B-Tech 2020 R19 CE 1201 Mathematics II Model Question Paper

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TIME : 3 Hrs. Max. Marks: 75 M

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[B19 BS 1201]

SAGI RAMA KRISHNAM

I B. Tech II Semester (R19) Regular Examinations

MATHEMATICS -11

(Common to CE, EEE & ME)

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MODEL QUESTION PAPER

Answer ONE Question from EACH UNIT

All questions carry equal marks

UNIT-I CO KL

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

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

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

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

   CO3 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

UNIT-II

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1. a) Find the cube root of 41 using Newton-Raphson method. CO5 K2
2. b) Evaluate ?oz 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
2. b) Evaluate y(0.8) using Runge Kutta method given y' =(x+y)²,y(0.4) =0.41 COS 3

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UNIT-III

1. a) If U=tan?¹(x/y) and x U? +y U? =sin 2U, prove that x²U? + 2xy U? + y²U? =2cos 3U sinU. col K2
2. b) If u=x²-2y², v=2x²-y² where x=rcos?, y=rsin? then show that ?(u,v)/?(r,?) =6r³ sin 2?. col K2

(OR)

1. a) Expand x²y + 3y -2 in powers of (x-1) and (y+2) using Taylor's theorem. Co1 K2

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2. b) By using the method of differentiation under the integral sign prove that ?0^8 tan?¹(ax)/x dx = p/2 log(1+a), a>=0. COl1 K3

UNIT-IV

1. a) Solve x(y-z)p+y(z-x)q=z(x-y). CO2 K2
2. b) solve (D²-DD'-2D'²)z=(y-1)e?. co2

(OR)

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

UNIT-V

1. a) Obtain the solution of ?u/?t = c² ?²u/?x² 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) = µ0sin³(px/L). If it is released from rest, find the displacement at any subsequent time. CO6 K3

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(OR)

1. a) Obtain the solution of ?u/?t = c² ?²u/?x² 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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