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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 CO3 K2
Y 7 11 14 18 24 32
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 o3 Kl
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(OR)
2.a) Using Gauss backward formula, find f(42), from the following table
X 20 25 30 35 40 45 CO4 K2
f(x) 354 332 291 260 231 204
b) Using Lagrange’s interpolation formula find Y (10) from the following table
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X 5 6 9 11 CcO4 K3
Y 12 13 14 16
UNIT-II
3.a) Find the cube root of 41 using Newton-Raphson method. CO5 K2
b) Evaluate ?oz X3ii+1 by using Simpsons 1/3™ rule with h = 0.25 CO5 K2
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(OR)
4.a) Find a real root of the equation x log10x=1.2 by Regula-false method CO5 K2 correct to three decimal places
b) Evaluate y(0.8) using Runge Kutta method given
y' =(x+y)2, y(0.4) =0.41 COS 3
UNIT-III
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5.a) If U=tan-1 (x3+y3)/(x-y) and prove that x Ux +y Uy =sin 2U, col K2
b) If u=x2-2y2, v=2x2-y2 where x=rcos?, y=rsin? then show that ?(u,v)/?(r,?) =6r2 sin 2?. col K2
(OR)
6.a) Expand x2y + 3y -2 in powers of (x-1) and (y+2) using Taylor's theorem. Co1 K2
b) By using the method of differentiation under the integral sign prove that ?08 tan-1(ax)/x dx = p/2 log(1+a), a=0. COl1 K3
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UNIT-1V
7.a) Solve x(y-z)p+y(z-x)q=z(x-y). CO2 K2
b) solve (D2-DD' -2D'2)z=(y-1)ex. co2
(OR)
8.a) Solve x(y-z)p+y(z-x)q=2z(x-y). CcO2
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b) solve (D2+D D' -D-2D'2 -3)z=3x+6y+4. CcO2 K2
UNIT-V
9.a) Obtain the solution of ?u/?t = c2 ?2u/?x2 by the method of separation of CO6 K2 variables.
b) A tightly stretched elastic string of length L, fixed at its end points is initially in a position given by u(x, 0) = µsin(3px/L). If it is released from CO6 K3 rest, find the displacement at any subsequent time.
(OR)
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10.a) Obtain the solution of ?u/?t = c2 ?2u/?x2 by the method of separation of co6 K2 variables.
b) A bar of conducting material of length l units is initially kept at a temperature sin x. Find the temperature at any subsequent time if the CO6 K3 ends of the bar are held at zero temperature.
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This download link is referred from the post: JNTUK B.Tech R19 2020 Model Question Papers || JNTU kakinada (All Branches)
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