Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 3rd Semester (Third Semester) 2016-2017 NAS 301 Mathematics Iii Question Paper
(Following Paper ID and Roll No. to be filled in your
Answer Book)
I?upcr ll): 20|4073 Roll No.
B. TECH,
Regular Theory ExaminatiOn,(Odd Sem-III) 2016-li7
MATHEMATICS - III
_ Time : 3 Hours ? Max. Marks : I00
SECTION-A ?
?1. Attempt all parts of this question. Each question
carries two marks. ' (10XZ=20)
V ??
??d
a) Evaluate [4% 22 +1 2
b) . Find the residue of f(z) = cot 2 at its pole.
c) Find the Z-transform of the sequence {an}.
d). State the convolution?theorem for inverse Z-
transform. '
e) Discuss in brief the types of correlation.
f) What do you understand by measures of Kurtosis,
discuss in brief.
301/12/2016/49420 (1) (p.110.
. NAS-301
g) De?ne order of convergence for ?nding out the
root of an transcendental equation.
h) For the data [a, f(a)], [a+h, f(a+h)] and [a+2h,
f(a+2h)], ?nd A2 f (a).
- i) _ De?ne a diagonal system of simultaneous linear
a1 gebraic equations. -
j) Write_the formula for solving the differential
equation 3- = f (x,y), y(xo.) = yo by Runge-Kutta
fourth order method.
SECTION - B
Attempt any three parts of the _following:- (3XI0=30)
_ a) Us'evCalculus of Residue to evaluate the follOwing
integral
cosx'
b) Find the Fourier transform ofthe following ?mction
de?ned for a > O by f (t) = e?
301/12/2016/49420 (2)
NAS-301
c) Find the coef?cient of correlation (r) and obtain -
the?equation to the lines of regression for the
following data:
x 6 2 10 h 4 8
y - 9 ll 5 8 7
(1) Using method of least squares; derive the normal
equation to ?t a parabola y = a '+ bx + cx2 from the
following data:
xi 2 3 . 4 5 6
y 14 17 20 24 29
e) Describe Picard?s method for solving differential I
equation and hence solve the differential equation.
dy ' . . ?
E = 1 + x}? upto thlrd approx1mation, when y(OFO
SECTION - C
Attempt any two parts of the following : (2 x5=10)
a) Find the values of C and C2 such that the function
f(z)= x2+c y 2-2xy + i (02 x2- y2 + 2xy) IS analytic.
Also ?nd f(lz).
301/12/2016/49420 (3) ' [P.T._O.
. NAS-301
b) Find the peles (with its order) and residue at each
poles of the following function:
1?22
f(Z)= z(z?1)(z?2)2 . .
c) Find the Laurent series expansion of
72 ? 2
f(z) =Win the regiOn l< |z+1I < 3
Attempt any two parts ofthe following:- (2x5=10)
a) Fihd the root of the equation 2x - lOgl'qx = 7 which
lies between 3.5 and 4.0, using method of false
position (?ve iterations only).
- b) Using Newton?s forward interpolation formula, ?nd
a polynomial function for f(x) and hence evaluate
f(0.5), from the following data:
x 0 '1 2 3 4
f(x) ?1 0 13 50 123
c) Using Lagrange?s meth'ed for interpolation, ?nd
. y(10) from the following data:
x, 5 6 9 11
y 12 ? 13 14 " 16,
301/12/2016/49420 - (4)
N AS-30'1
Attempt any tWo parts of the following:- (2 X5=10)
a) Evaluate the following integral, using Simpson?s
three - eight rule:
0 dx
J.01+x12
Taking 12 intervals.
b) Apply Gauss-Seidal iteration method to solve the
following equations (three iterations only)
20x+y~2z=17
3x+20y?z=_18
2x?3y+202=25
c) Find f ' (1.1) from the following data:
x 1.0 '1 1.2 1.4 1.6. 1.8 2.0
f(x) 0.0 0.12 30.55 1.29 2.43 4.00
Attempt any two parts of the following: (2X5=10).
a) If for two random variables, x and y with same mean,
the two regression lines are
301/12/2016/49420 (5) [PTO
NAS-301
NAS-301
? , . b 1_ a c) Using Z-transform, solve the followi '
y = ax + b andx = ay + ,3, then show that :3? : 1 equation. ng dlfference
" a
u + 2 + " = ' _ _
Also ?nd the common mean. "*2 um un n Wlth uo ? ?1 _ 0
b) The ?rst four moments of a distribution about the
value 4 of the variable are -1.?, .17, -30 and 108. W
Fmd the moments about the orlgm.
c) Out of 800 families with 5 children?each, how many
families would be expected to have
i) Three boys and two girls
ii) At the most two girls.
Assume that probabilities for boys and girls axe equal
7. Attetnpt any two parts of the following:- (2X5=10)
a) Find the inverse Z-transform of
2(2) =V?, |z| >1
b) Find the ?nite Fourier sine transform of
This post was last modified on 29 January 2020