Download AKTU B-Tech 3rd Sem 2015-2016 NAS 301 Engineering Mathematics Iii Question Paper

Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 3rd Semester (Third Semester) 2015-2016 NAS 301 Engineering Mathematics Iii Question Paper

Printed Pages: 6 I4 NAS-301
(Following Paper ID and Roll No. to be filled-in your
Answer Book)
Roll No;
. B.Tech. ? _,
(SEM. III) THEORY EXAMINATION 2015-16
ENGINEERING MATHEMATICSrlH:
[Time:3 hours] [MaximumMark? 100
. I SediiohJ I
Q.1 Attempt. all parts. 'All 'partszcan'y equal gmarks.? Write
answer of each part in shorts. (lOXZ=20)
8 4- 3 7?
(a) Findinverse Z-?agsfggmation of (j z)!
. _ z
(b): If u(x,y)= x2 ? yz, prove that the? u ?sj?tis'ffiie's'
Laplace euqations.
zz+l
2?
1
Z
(0) Evaluate]. dthereCis circle |z|=3/ 2. ?
C _ . _: , .
(d) Expand mm the" regions |z| ?< 1" *
43509 (4):" ._ P.T.O

(6) Estimate the production for 1954' and 1966 from
the following data :
Year: 1961 1962 1963 1969 1355,1966 1957
~ Prodmtion: 200 220 260 -" 39 7'- 430
(f) State Newton - Gregory backward interpolation
formula.
1,k=_0
(g). Find Z-u?ansformauon of f (k) = ( 0 , k g: 0
(b) State Cauchy?s integral theorem
6) 970% that: Alog f (x): 10%? 32(5)]
(j) Dp?nc regression lines.
Section-B
Note: Attempt-any ?ve Questions from this section:
' (1 OXS-S?)
1, H???
_ Q2 FindmeFourieru'ansfomof F(x)={0, M)"
0.3 Exmnine?wnatureofthe?mction
f(0}=?
In the region including the origin.
(2) NA$301
Q.4 Solve the following system of linear equations by Cmut?s
Method:
x+y+z=3;2x-y+3z= 16; 3x+y-z=-3
Q.5 Find the rank comalation coef?cient of marks of A and
B from me following data :
MaksAfls 20 L217 13 45 60 20 75
'MarksB .so 30 55 30 25 10 30 7o
Q.6 A survey of 240 families with 4 children. slim the
following distribution: 1
Nabfboys "?4 3' 2 '1 o
No. of families: 10, 55 105 58 12
Tostthehypothxismmegndfanalebinhsmequal
probab? ? le.? ? > '
(Given z?o.os=9.49 and 11.! for 4 d.f and 5- cl]?
respectively)
Q.7 Solve the following differential equation using Rungc-
Ku?a method:
Given that g = with y(0) = 1, ?nd y(2).
x+y
48500 (3) P.T.O.

Q.8 Use the method of least squares to obtain the normal
C
equations and ?t the curve for y = 7?+clJE to the
following table of values :
x 0.1 0.2 0.4 0.5 l 2
21 ll 7 ...6 5 6
, Q9 The table given below reveals the velocity ?v? ofa body
during the time ?t? speci?ed. Find its acceleration at
t=l'.l.
t : 1.0 1.1 1.2 1.3 L ? 1.4
v : 43.1 47.7 52.1 56.4 60.8
? Section-C
Attem?t any two questions from this sectioh: (15X2=30)
Q10 a) Using Lagrange?s interpolation formula, ?nd y( 10)
from the following table.
x : 5 6 9 l l
y : 12 13 14 ?16
b) The ?rst four moments about the working mean
28.5 of a distribution are 0.294, 7.144, 42.409 and
454.98. Calculate the moments about the mean.
Also evalute ,6'1 and ?62 and comment upon the
skewness and kurtosis of the distribution.
(4) NAS-301
Q.11a)
b)
Q.12 a)
b)
48500
Using the Fourier integral transformation, show
_ 2a?? cossx
thatea"=?JI??--2 2ds,a>0,x20
7! 0s +a
Evaluate by Cauchy integral formula
f z ? 2 dz Where C is the circle |z| :3,
C (2+1)2 22+4
Solve x3_5x+3=0 by using Regula - Falsi
method.
Using the Z-transform solve the following
differenee equations :
_ k
yk+2 + 4Yk+1 + 3)?k = 3
given y(0) = 0, y(l) =1
From the data given below, ?nd the number of items 11 :
rxy = 0.52XY =120,ZX2 = 90, ay = 8 where
x and y are deviations from the arithmetic mean.
If f(z)=u+iv is analytic function and
u ? v = ex(cosy ? sin y) , ?nd f(z) in terms ofz.
(5) P.T.O.

ex
c) Find rwdx approximately using Simpson?s
? 1 + x . ,
3/8 rule on integration.
-.s_)(._.
(6) NAS-301