University of Lucknow 2006 B.A Economics , Third - Question Paper
B.A ( Part III) exam 2006
Economics
3rd Paper
X
A-253
B. A. (Part III) Examination, 2006 ECONOMICS Paper III (Quantitative Methods)
Time Allowed : Three Hours Maximum Marks : 50
Note: Answer Five questions in all. Question No. 1
is compulsory. Attempt one question from each Unit. Marks are indicated against each question.
ft? jpftI % tex i srft i I I pit * w I I
1. Answer the following in brief : 20
Pwtfifcf % *%? 5 3=pr 'IPfs :
.......' dv &y , civ
(i) Distinguish among and
dX A X Cvv
' -v- r?ei % #3 I
ax ' is. x dx
1 \
- ;
(ii) Show that the following is a linear homogeneous function :
Z = .
WT I :
Z = vTy? .
(iii) Locate the focus and the directrix of the parabola :
x2 + 20y + 4 x ~ 56 - 0.
PrMsrt #r Pm\ srt
:
x2 + 20 y -t- 4x - 56 = 0. _____
(iv) Explain the meaning of positive and negative skewness.
(v) Graphically explain the kinds of kurtosis.
(yi) Find the maximum and minimum values of the function :
y ~ xs - 3 x 1.
'X -* -j
y jr - - 1.
(vii) In a survey of 25 fax ..lies, the number
of children reported were :
5, 4, 4, 5. 5, 5, 7, 6, 6, 6, 5, 5S 7, 4, 5,
7, 5, 9, 7, 2. 3, 4S 1, 2,
Find mean and mode.
25 W
f? Sfff # :
5, 4, 4, 5, 5, 5, 7, 6, 6, 6, 5, 5, 7, 4, 5,
fIRR WT #1 WR! !
r
jl 2 j4 == 13 6
firid/W?!
(ix) What are the components of a Time Series ? w % Pci w I ?
(;<) Distinguish between primary and secondary data.
Unit I Wff I
(a) Obtain the equation and slope of the line
joining two points (1, 2) and (3, 4). .
m Pppft (1, 2) cWT (3, 4) Wt
jm fFiRoi m sra m. #4 1
(b) If 7 sin2 6 + 3 cos' = 4, then prove that:
trn f) = +
:
1
tan 8 - -7=-v i
(c) Find the sum of n terms *.,f the series : M % n 3>T % STRT :
3 + 33 + 333 + ...,.......
1111 2~
(a) Find the value of the determinant :
. b a
a + b
b + c-
c
b
e =
nxl
to i v-
then obtain e'e and ee', 3+4=7
cTt e'e dEff ee' !
Unit II f5Bff II
Differentiate the following functions :
1111 2.+?--+o-7
2 2 2 2
, x 5 + tan*
(a) v=.-277y-
(b) y - x5 log (2 x)
(c) Find second derivative of the function :
Find total revenue, marginal revenue and elasticity of demand at p 3, if demand curve is given by D = 30 ~ 4p - p1. 7~
*&
Unit III TO# III
Calculate median and quartiies Q} and Q~ from
1 i i 1
the following data : 2;f2;r*-2~-~7~
J. I I. L
PNIifef #is5t % m qgpfo Q, <mr
Q? Wf? :
Wages (Rs.) fro} |
Pei sons sftS |
30-40 |
1 |
40-50 |
3 |
50-60 |
11 |
60-70 |
21 |
70-80 |
43 |
80 90 |
32 |
90-100 |
9 |
la a Football session, the goals scored by two teams A and B in different matches are given below. Explain that which of the two teams is more consistent in its performance : 7
rftm m n % a m b sm ftps M t[ t wii #1. $ ijf | . mm p Nt 3 % #t~# m -am % c#pr tm I :
Number of Goals |
Number of Matches Played 'R 4! iiw Team A c&_ A 2? 9 >5 5 4 Team B |
9
6
5
3
Unit IV
(a) Explain the use of scatter diagram lo determine the direction and degree of correlation between two variables.
fnTffkw || sq#? mwm i
(b) From the following data, calculate the coefficient of correlation by any method :
2Jr-+S~l1-
2 7
X |
25 |
26 |
27 |
27 |
1 00 ! |
28 |
! k> VO 1 1 |
29 |
30 ! 31 | |
Y |
10 |
14 |
12 |
9 |
i 1 13 |
17 |
20 |
14 |
13 | 18 |
9. Name some applications of Index numbers in Economics. / \
STsfeTTM if % mm % fS TO sfcffftr |
From the following data, calculate (i) Fisher's c r
index number for the year 1980 and (ii) Show, \ \
whether the Time Reversal Test and Factor ' .4 4
1
Reversal Test are satisfied or not : 7
PiHlRslcl #55ft % WfT (i) fW\ 3JT
Year |
1975 |
Year |
1980 | |
Commodity |
1975 |
M 1980 | ||
Wg |
Price |
Quantity |
Price |
Quantity |
Hl=fi | ||||
A |
A "A |
20 |
6 |
10 |
B |
3 |
15 |
5 |
20 |
C |
7 |
25 |
3 |
15 |
D |
10 |
4 |
40 |
A-253-8-10000
Attachment: |
Earning: Approval pending. |