Roll No…….
Total No. of
Questions: 07
Paper
ID [MB104]
MBA
(Sem.1^{st})
QUANTITATIVE
TECHNIQUES (MB104)
Subject Code: MB104
Time: 3 Hrs. Max.
Marks: 60
Instruction to Candidates:
1.
SectionA is
Compulsory.
2.
Attempt any Four
questions from SectionB.
SECTIONA
Q1. (a)
Are the following sets equal A={x ; x is a letter in the word ‘LOYAL’}
(b) If log_{10}y=x_{2
}find the value of 10^{2x} in terms of y.
(c) Without expansion prove
that xyz=1,
If
(d) Using binomial theorem,
compute the value of (99).
(e) If x_{1}=50, x_{2}=27,
n_{1}=9, n_{2}=5, find the combined mean.
(f) Write a note on kurtosis
of distribution.
(g) Find the chance of a non
leap year having 53 Wednesday.
(h) If in a Poisson
distribution P(I)=P(2), find the value of P(4).
(i) Write conditions for the
application of x^{2} test.
(j) Define probable error of
coefficient of correlation.
SECTIONB
Q2. (a) The present population of a country is 9261000. If it has been increasing at the rate of 3%
annually, using log tables find the population 3 years ago.
(b)
Prove by mathematical induction that n<2”, for all nN.
Q3. (a)
Product of first three terms of a G.P. is 1000. If 6 is added to its second
term and 7 added to its third term, it becomes an A.P. Find the G.P.
(b) Score obtained by
two batsmen in 10 matches are as follows:
A

30

44

66

62

60

34

80

46

20

38

B

34

46

70

38

55

48

60

34

45

30

Determine who is the
most consistent batsman.
Q4. (a)
Find the coefficient of correlation between industrial production and export
using
Production

55

56

58

59

60

60

62

Export

35

38

38

39

44

43

44

(b)
If is the angle between two regression lines,
then show that
tan
Explain the significance of
the formula when r=0, r=1.
Q5. (a) Fit a straight line trend by least squares method to the
following data and calculate short time fluctuations:
Year

1985

1986

1987

1988

1989

1990

Production(‘000 tons)

75

83

109

129

134

148

(b) The average whole sale prince in rupees per 20
seers of wheat sold in U.P. is given below. Using 1956 as base year find the price relatives (simple index
numbers) corresponding to all the years.
Year

1953

1954

1955

1956

1957

1958

Price

14.95

14.94

15.10

15.65

16.28

16.53

Q6. (a)
A and B throw alternately with a pair of dice. A wins if he throws 6 before B
throws 7 and B wins if he throws 7 before A throws 6. If a begins, find his
chances of winning.
(b) The marks obtained in a certain examination are
found to be normally distributed. If
12.5% of the candidates obtain 60% or more marks, 39% obtain less than 30
marks, find the mean number of marks obtained by candidates. (Given that for
A=0.125, x/0=1.15 and for A=0.61, x/0=0.279)
Q7. (a)
If T is an unbiased estimator of show that T^{2} and are the unbiased estimators of ^{2} and respectively.
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