Download AKTU B-Tech 4th Sem 2016-17 NAS401 Engineering Mathematics Iii Question Paper

Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 4th Semester (Fourth Semester) 2016-17 NAS401 Engineering Mathematics Iii Question Paper

Printed Pages:2 Roll N0.I I I I I I I I I I I NAS401
B. TECH.
THEORY EXAMINATION (SEM-IV) 2016-17
ENGINEERING MATHEMATICS-III
Time : 3 Hours Max. Marks : 100
SECTION ? A
1. Attempt all parts of the following question: (2 x 10 = 20)
Z
e
(3) Evaluate I dz , where C is the circle IZI = 2
Cz+1
(b) Prove that f(Z) = sinh z is analytic
1
(c) Prove that Modulation theorem F {f(x) cos ax} = EI f (s+ a) + f (s? a)]
(d) Solve the Z?transform: yk+2 + yk+1 ? 237k = 09 yo =4 3?1 2 0
(e) What is the meaning of Skewness?
(f) Write Normal equation of y = a + B
x
A V
(g) Prove that A + V = ? ? ?
V A
(h) Find first approximation value of (17)?3 by using Newton Raphson method
(i) Using Picard?s method ,find the solution of g 2 1+ xy upto the third approximation
when x(0) = 0
(j) Find y(0. 1) using Euler?s method given that% =10g(x + y) y(0) = 1.0
SECTION ? B
2. Attempt any five parts of the following question: (5 x 10 = 50)
3 ~ 3 .
x 1+1 ? 1?1
?( 2) y2( ) ?t0 is continuous
x +y
0 z=0
and the CR. equations are satisfied at the origin, yet f ?(0) does not exist.
(a) Prove that the function f (z) defined by f(z) =
2z
(b) Using Cauchy Integral formula to evaluate e?4dz ,where C is the circle |z| = 3.
c(z+1)
(c) Find the Fourier cosine transform of 2 and then find Fourier sine transform of
1 + x
x
1+ x2 .
((1) Find the multiple linear regression of X1 0n X2 and X3 from the data relating to three
variables:
X1 7 12 17 20
X2 4 7 9 12
X3 1 2 5 8

(e) Find the root of the equation xe" = cos x by using Regula-Falsi method correct to four
decimal places.
2x+3y+z=9
(f) Apply Crout?s method and solve the system of equations x + 2y + 3z = 6
3x+y+2z=8
(g) Find the value y(1.1) using Runge?Kutta method of fourth order, given that
dy
Attempt any two questions of the following:
3. (i)
(ii)
(iii)
4. (i)
(ii)
(iii)
(ii)
(iii)
= y2 + xy, y(1) = 1.0, take h = 0.05
SECTION ? C
(2 X 15 = 30)
Show that the function defined by f (z) =?|xy| is not regular at the origin,
although Cauchy-Riemann equations are satisfied
27r
Evaluate: I + if a>|b|
0 a + b Sln 6?
Solve by Z?transform: Yk+2 ?4yk+1 + 3Yk = 5k
Using the convolution theorem, evaluate Z ?1 {
2
Z?
(z?1)(z 4)}
If the 6 is the acute angle between the two regression lines in the case of two
2
1? r O'XO'y
.? ,where r, ax, 0'y have
r ax + o-y
variables x andy, show that tan6=
their usual meanings. Explain the significance of the formula when r = 0 and
r = :1
By using zz?test, find out whether there is any association between income
level and type of schooling :
Social status Health Poor Rich Total
Below Normal 130 20 150
Normal 102 108 210
Above Normal 24 96 120
Total 256 224 480
Find the missing figure in the following table
x 2 3 4 6
f(x) 45 49.2 54.1 67.4
Find a cubic polynomial which approximates the data:
x ?2 ?1 2
y(x) -12 -8 3
Find an approximate value of the loge 5 by calculating to four decimal places
. 1 . 5
by Slmpson?s g rule, given I
4x+5