Roll No………
Total No. of Questions: 07
MBA/MBA (IB)
(Sem.-1st)
QUANTITATIVE
TECHNIQUES
Subject Code:
MB-104 (2008 & onward Batches)
Paper ID:
[C0167]
Time:
3 Hrs. Max.
Marks: 60
Instruction
to Candidates:
1. Section-A is Compulsory.
2. Attempt any Four questions from Section-B.
SECTION-A
1.
(a) Discuss the
use of Regression Analysis in Business Management.
(b) Using Principle of
Mathematical Induction, check that
2+6+10+14+…………+2[2n-1]=
2n2+1; nN.
(c) Discuss Trend
Method in Time Series Analysis.
(d) If A= and A+2B=,
find x and y.
(e) List the relevance
of selecting Base Period in Index Numbers.
(f) A & B are 2
independent events. The probabilities that both occur simultaneously is 1/6 and
the probability that neither occurs in 1/3. Find the probabilities of
occurrence of A & B respectively.
(g) Discuss utility of
Spearman’s Rank Correlation method.
(h) Discuss
Significance Level and Degrees of Freedom in Hypothesis Testing.
(i) What are the
difference errors in Hypothesis Testing?
SECTION-B
2.
The prices (in
Rs.) of three commodities X, Y, and Z are x, y and z respectively. A purchases
4 units of Z and sells 3 units of X and
5 units of Y. B purchases 3 units of Y and sells 2 units of X and 1 unit of Z, C purchases 1 unit of X
and sells 4 units of Y and 6 units of Z. In the process A, B and C earn Rs.
6000, Rs. 5000 and Rs. 13000 respectively.
Using matrices, find
the prices per unit of the three commodities.
3.
By Mathematical
Induction principle, prove that for all positive integers in.
4.
Construct the consumer
price index number for 2010 on the basis of data of 2000 from the following
data using.
(a) Family Budget Method
(b) Aggregative Expenditure Method
Commodities
|
Rice
|
Wheat
|
Pulses
|
Ghee
|
Oil
|
Weights
|
40
|
20
|
15
|
20
|
5
|
Price
(per Unit) In 2000(Rs.)
|
16.00
|
40.00
|
0.50
|
5.12
|
2.00
|
Price
(per Unit) In 2010 (Rs.)
|
20.00
|
60.00
|
0.50
|
6.25
|
1.50
|
5.
The data in the
following table related to the weekly maintenance cost (in Rs.) to the age (in
months) of 10 machines in a company. Using regressional analysis, estimate the
maintenance cost for the machine which is 72 months old.
Machine
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
Age
(Months)
|
5
|
10
|
15
|
20
|
30
|
30
|
30
|
50
|
50
|
60
|
Cost
(Rs.)
|
190
|
240
|
250
|
300
|
310
|
355
|
300
|
300
|
350
|
395
|
6.
In order to test
whether declaration of dividends has had any effect on the market price of
shares of companies, a random sample of 8 companies was taken, from companies
which have declared at least 15% dividends.
The data regarding the share prices of the sample companies is given as
below.
|
|
|
|
|
|
|
|
|
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
Market
Price 10 days before dividends were declared
|
70
|
65
|
112
|
58
|
25
|
147
|
95
|
68
|
Market
Price 10 days after dividends were declared
|
80
|
85
|
110
|
64
|
32
|
159
|
100
|
70
|
Can we say that the increase in the average market price
after declaration of dividends is significant (at 5% significance level)?
7.
A progressive
farmer uses 3 types of fertilizers on 4 different fields. The yield figures per
field are given below.
|
YIELD
|
TOTAL
|
|||
Fertilizers
|
Field
A
|
Field
B
|
Field
C
|
Field
D
|
|
Nitrogen
|
6
|
4
|
8
|
6
|
24
|
Potash
|
7
|
6
|
6
|
9
|
28
|
Phosphates
|
8
|
5
|
10
|
9
|
32
|
TOTAL
|
21
|
15
|
24
|
24
|
84
|
Test whether the 4
fields are materially different in fertility? Also find out whether the three
different fertilizers make any material difference in the yields?
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