Download SGBAU B-Tech 4th Sem Applied Mathematics Question Paper

Download SGBAU (Sant Gadge Baba Amravati university) B-Tech/BE (Bachelor of Technology) 4th Sem Applied Mathematics Previous Question Paper

B.?l?ech. F ourth Semester (Chem. / Poly / Food / Pulp & Paper / Oil & Paint / Petro) (01d)
P. Pages :
7
Applied Mathematics - II : 4 SCT 1
AW - 3553
" I l L1}
T ime : Three Hours ?my?lzm?llnsmll Max. Marks :
Notes : 1. Assume suitable data wherever necessary.
1.
2.
3 a)
b)
C)
4 a)
b)
C)
5 a)
b)
6 a)
b)
AW - 3553 1 P.T.O
2. Use of calcu1at0r normal distribution table signi?cance table is permitted.
3. Use of pen Blue/Black ink/re?ll only for writing the answer book.
A tightly stretched string with ?xed end point x ?? 0 and x = L, is initially in a position
given by y(x, 0) = Yo sin3 (?1. If it is released from rest from this position. ?nd the
displacement y at any distance x from one end and at any time t.
OR
A rod of length I. has its ends A and B kept at 0?Cgand 100?C respectively until steady
state conditions prevail. If the temperature at B is reduced suddenly to 0?C and kept so.
while that of A is maintained. Find the temperature u(x, t) at a distance x from A and at
any time t.
. ~ 7 . . . . . . . .
Show that the function u = x? -3xy? IS harmonic. Find its harmomc conjugate function
and corresponding analytic function in terms ofz.
7 .
Prove that cosh" 2?5th2 2 = l .
Find all values of 2, which satis?es the equation 24 +1: 0.
OR
2 2 L
a 8 .
1f F(z) is regular function, provc that [7+7 |f(2)|2=4|F'(z)12
5X 0:!
m/n
Prove that (x+iy)m/" +(x?iy)m/n = 2( x2 +y2) -cos(?nltan_'(y/x))
n
Prove that log? + i tana) = logseca + i 0..
Find the root of the equation x3 +X?l =0 by iterative method.
1
Evaluate J x3 dx by using Trapezoidal rule, with ?ve sub intervals.
0
0R
1f y(l)= ?3, y(3) =9, y(4) : 30, y(6)=132 ; ?nd the Lagrangc's interpolation
polynomial that takes the same values as y at the given point.
Given that
x 1.0 1.1 1.2 1.3 1.4 1.5 1.6
y 7.99 8.40 8.78 9.13 9.45 9.75 10.03
Find 1?? atx=1.1.
dx
13
13

10.
ll.
12.
AW - 3553
b)
b)
b)
b)
Solve the LPP graphically -
Maximize Z = 2x| + x2
subject to x, $252 _:: o
\l ' X: H C)
3| A- 2x2 5 I
with x120, x3 20
Solve the I_PP by using simplex method :
Maximize Z = 3x1 + 4x;
subjec: to 2x1 +3x;3 S 0
4x] +3313 5 12
?1th X120. x3 >0
()R
Prove that "the feasible region ot'LPP is convex". _
Solve the following LPP using simplex method and comment on the solution.
Minirrize f : ?3X3 -- 2x:
subjcc: to x] ?x; S I.
3x. ?2x2 i (i
with x120, x3 20
For the following distribution. coxm?ute the mean and 5.1). of 100 students.
[ ?,7,
|
yjssmkg 60-62 63-65 66-88E69-7t_ 72-74
3 N.E.fsmdgt???c-5" _ '_ 19 "?"1: ivy? ; 08
The mean and variance ofzt binomial distribution are 4 and 5:. respectively; ?nd P(x a |).
OR
Ifthe probability that an iudit iduttl suffers a bad reaction from a certain injection is
0.001, determine the prohnhiiity that out 01?2000 individuals -
i) ex actly 3 ii) at least 2 iii) none will suffer a bad reaction.
Students ofa class were given an aptitude test. Their marks were found to be normally
distributed with mean 60 um: SD. of 5. What is the percentage of students scored more
than 6C marks ??
Using samples of sizes 10 :md 16 with variance: SE _ 50 and S, = 30 ; assuming
. ? . . 3 . .
nonnallty 01 the populutton. test the hypothesns 110 26'2 :02? agams?t the altematlvc
7 I
o" > 0?22. Choose (1: 590.
Find the regression line 01'} an x for the data.
x L4 _5
.,
.37 _ V
y .? 5
'l.43
_.
F.) b.)
OR
Distinguish between -
i) Null and Altematixe hyymthesis. ii) Type - | and l?ype - 1] errors.
In a sample of 600 men from u certain city. 450 are found smokers. In another sample of
900 men from another city 450 are smokers. Do the data indicate that the cities are
signi?cantly different wnh re meet to the habit ot?smoking among men ?
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