Download SGBAU (Sant Gadge Baba Amravati university) B-Tech/BE (Bachelor of Technology) 4th Sem Engineering Mathematics II Previous Question Paper
P. Pages : 3
Time : Three Hours
11010 : Engineering Mathematics - II
4 CT 01
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lugljl?sl! Max. Marks : 80
Notes :
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7.
All question carn' marks as indicated.
Answer threg question from Section A and three question from Section B.
Due credit will be given to neatness and adequate dimensions.
Assume suitable data wherever necessary.
Illustrate you: answer necessary with the help of neat sketches.
Use of slide rule logarithmic tables, Steam tables, Mollier's Chart, Drawing
instrument, Thermodynamic table for moist air, Psychrometn'c Charts and
Refrigeration charts is permitted.
Use of pen Blue/Black ink/re?ll only for writing the answer book.
1. a) A tightly stretched string of lengtht with ?xed ends is initially in equilibrium position. It 7
is set vibrating by giving each point a velocity v0 sin3 (?25).
Find the displacement y(x, t).
b) Using the method of separation of variables, solve gil- = 2%+ u where u(x, 0) = 6E3" 7
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2 a) au azu 7
Solve the equation E? = ?2 with boundary conditions u(x, 0) = 3 sin nnx u(O, t) = 0
6x
and u(1.t)=0 where0
b) Find the de?ection of a vibrating string of unit length having ?xed ends with initial ?7
velocity zero and initial deflection f (x) = k(sin x ? sin 2x).
3. a) If f(z) is an analytic function with constant modulus, show that f(z) is constant. 5
b) If (a + ib)b = mx+iy , prove that one of the values of y/x is 2tan'](b / a) / log (a2 + b2) i 4
c) Find the analytic function, whose real part is sin 2x / (cosh 2y - c052 x) . 4
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4' 3) 'Find the conjugate harmonic of v(r,9) = r2 cos 26? most) + 2 and show that v is 5
hannonic.
13)
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l l x 4
Prove that tanh' x = sinh?
_ :11? x2
] P.T.O
b)
a)
b)
b)
a)
Find the orthogonal trajectories of the family of the curves.
x4 + y4 ? 6x?7'y2 = constant
Find the positive root of x4 ~? x :10 correct to three decimal places, using Newton-
Raphson method.
From the following table the number of students who obtained marks between 40-45.
Marks 7?? i 30-40 1 40-50 50-60
60-70
70-80
No. of students 31 Y 42 51
35
31
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Solve the system of non?linear equations x2 + y = I l. y2 + x = 7 by Newton's - Raphson
method.
06
' 2
Use Simpson's 1?3?d rule to ?nd I e? (b; by taking seven ordinates.
0
Using simplex method. solve lhc LPP.
Minimize : Z = (1*3X: +3x3
subject to : 3x1~-x2 +sz3 _<_ 7
2x1 + 4x: 2 ?12
?4xv>_ +3x2 +3X3 $10
x1, x3. X3 20
Solve graphically the following LPP
Maximize : Z:4xl +3x2
subject 10 : xl ~ X2 S?l
?,\'l + x2 $0
XI. ?(2 20
OR
Using simplex method, solve following LPP
Minimize I Z = 3X1+5X2 +4X3
subject to : 2x, + 3x2 3 8
2x2 +5X3 s10
3X1+2X2 +4X3 515
x1, x2, X3 20
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10.
ll.
12.
b)
a)
b)
b)
a)7
b)
b)
Solve graphically the following LPP
Maximize : Z = 2x1+3x2
Subject to : x1 -x2 3 2
x1 + x2 2 4
X] , X2 2 0
Two cards are drawn in succession from a pack of 52 cards ?nd the chance that the ?rst is
a king and the second is a queen, if the ?rst card is
i) replaced ii) not replaced
A skilled typist on routine work kept a record of mistakes made per day during 300
working days.
Mistake/day 0 1 2 3 4 5 6
No. of dajs 143 90 42 12 9 3 1
OR
A certain screw making machine produces on average of 2 defective screws out of 100 and
packs them in boxes of 500 ?nd the probability that a box contains 15 defective screws.
If the variance of Poisson's distribution is 2. F ind the probabilities for r = l, 2, 3, 4, from
the recurrence relation of the Poisson's distribution. Also ?nd p (r 2 4).
Fit a straight line to the data._
x12345
y 5 7 91011
The regression equation of two variables x & y are
x = 0.7y + 5.2
y = 0.3x + 2.8
?nd the mean ofx & y
OR
The regression equation calculated from a given set of observation two random variables
are
x = ?0.4y + 6.4 y = ?0.6x +4.6 calculate Y, Y & r.
Fit 3 straight line to the data.
x 0 S 10 15 20 25
y 12 15 17 22 24 30
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This post was last modified on 10 February 2020