Saurastra University 2006 M.B.A Quantitative Methods - Question Paper

M.B.A. (Sem. I) exam
April / May – 2006
Quantitative Methods
Time : three Hours] [Total Marks : 70
1 (a) Solve completely the subsequent equations using 7
matrices.
5x - 6y + 4z = 15, 7x + 4y - 3z = 19, 2x + y + 6z = 46.
(b) If A
a b
c d
= L
N M
O
Q P
and I = L
N M
O
Q P
1 0
0 1
, show that 7
A2 - ba + dgA = bbc - adgI .
OR
1 (a) describe the subsequent terms : (any three) 7
(i) Explicit functions
(ii) Monotone functions
(iii) Periodic functions
(iv) Rational functions.
(b) If f bxg = x2 + x - 1, then simplify f x  one  3f x  2f x  one b g bg b g.7
2 (a) discuss the method of exponential smoothing. 4
(b) Fit a parabola y = a + bx + cx2 to the subsequent data, 10
estimate prince of the commodity for the year 1997.
Year 1991 1992 1993 1994 1995 1996
Prices 100 107 128 140 181 192
OR
2 (a) discuss the method of moving avg. with its 4
advantages and limitations.
(b) Using the method of exponential smoothing taking 10
initial estimate as 100 and a = 0.4, prepare forecast.
Time period t
true sales xt
b g
b g
1985 1986 1987 1988 1989 1990
110 120 121 125 124 122
3 (a) State assumptions and requirement of linear 4
programming.
(b) Solve using simplex method maximum 10
Z = 200x + 300y
Subject to 5x + 2y £ 180
3x + 3y £ 135
y £ 2x, x, y, ³ 0.
OR
3 Attempt any 2 : 14
(i) obtain the 3 numbers in A.P., where the sum of the
numbers is 24 and the sum of their cubes is 1968.
(ii) If ba - bg, bb - cg, bc - ag are in G.P., then
ba + b + cg = bab+ bc + cag 3
3 .
(iii) Prove that AH = G2, A > G > H.
4 Attempt any 2 : 14
(i) obtain the correlation coefficient ranging from the age and the
playing habit of the people from the subsequent
information.
Age group
No of people
No of players
:
. :
. :
15 20 20 25 25 30 30 35 35 40 40 45
200 270 340 360 400 300
150 162 170 180 180 120
     
(ii) elaborate the regression coefficients ? State their
properties.
(iii) From the data provided below, obtain
(i) The 2 regression equations.
(ii) The most likely marks in statistics when marks in
economics are 30.
Marks in Eco
Marks in Stat
.
.
25 28 35 32 31 36 29 38 34 32
43 46 49 41 36 32 31 30 33 39
SQ–6742] two [Contd...
5 (a) There are 50 workers in a factory. The data provided 8
in the subsequent table.
Category
Sex
Male Female
Technician seven 3
Non - technician 23 17
One worker is opted at random. What is the prob.
that (1) worker is male provided that he is a technician
(2) worker is male provided that is non-technician
(3) worker opted is technician provided that he is male
(4) worker is non-technician provided that she is a female.
(b) describe subsequent : 6
(i) Sample space
(ii) Union set
(iii) Equally likely event.
OR
5 (a) For a Binomial variate n=8 and 16Pb2g = Pb6g . 4
obtain the probability of success.
(b) 50 patients are admitted every day in a hospital. 5
Out of 100 patients, three patients demand for special
room. In a particular morning three special rooms are
available in the hospital. Assuming that 50 patients
are admitted, obtain the probability that
(i) No patient will demand for special room
(ii) Hospital will not meet the demand of patients.
(c) In AEC company, the amount of light bill follows 5
normal distribution with S.D. 60. 11.31% of customers
pay light bill less than Rs. 260. obtain avg. amount
of light bill.

Earning:   Approval pending.