No.
of Printed Pages : 8 MEC-003
MASTER OF ARTS (ECONOMICS)
Term-End Examination
June, 2022
MEC-003 : QUANTITATIVE TECHNIQUES
Time : 3 hours Maximum Marks : 100
Note : Answer questions from both the sections as per
instructions.
SECTION A
Answer any two questions from this section. 220=40
1. Explain how differential equations are applied in
economics. Discuss the role of initial condition in
solving a differential equation. Give appropriate
examples.
2. Consider the following utility function :
u = f(x1, x2, ... xn)
where xi is the quantity of ‘n’ goods consumed.
Let the price of good xi be pi for i = 1, 2, ... n. Let
the income of the consumer be M. Show that the
Lagrangian multiplier of utility maximisation
problem equals the marginal utility of income.
MEC-003 1 P.T.O.
3. (a) Describe the properties of standard normal
distribution.
(b) The impurities in a chemical are normally
distributed with mean 127 parts per
million (ppm) and standard deviation
22 ppm. The chemical is acceptable only if
its impurities are below 150 ppm. What is
the proportion of chemicals that is
acceptable ? [The area under standard
normal curve for the value z = 1·5 is 0·668.]
4. A revenue maximising monopolist requires a
profit of at least 1500. His demand and cost
functions are :
D = 304 – 2 Q and
C = 500 + 4 Q + 8 Q2.
Determine the equilibrium level of output and
price. If the monopolist opts for profit
maximisation, what will be his output and price ?
MEC-003 2
SECTION B
Answer any five questions from this section. 512=60
5. Given that :
1 1 1 1 2 3
A = 2 3 4 , B= 6 12 6
3 2 3 5 10 5
Find the rank of the matrices AB, BA and A + B.
6. The correlation coefficient between the nasal
length and stature of 20 persons was found to be
0·203. Test whether the correlation is
statistically significant.
7. A linear programming problem is given as :
Maximize z = 30x1 + 50x2
subject to x1 + x2 9
x1 + 2x2 12
x1 0, x2 0.
Find its optimal solution.
8. Find the extreme values of
z = 2 x 12 – x1 x2 + 4 x 22 + x3 + x 32 + 2.
Verify whether it is a case of maximum or
minimum.
MEC-003 3 P.T.O.
9. Show that in a Poisson distribution, the mean
and the variance are equal.
10. State and explain Bayes’ theorem.
11. Explain the method of maximum likelihood
method for estimation of parameters.
12. Write short notes on any two of the following :
(a) Eigenvalues
(b) Taylor’s expansion
(c) Kuhn-Tucker conditions
MEC-003 4
E_.B©.gr.-003
E_.E. (AW©emñÌ)
gÌm§V narjm
OyZ, 2022
E_.B©.gr.-003 : n[a_mUmË_H$ à{d{Y`m±
g_` : 3 KÊQ>o A{YH$V_ A§H$ : 100
ZmoQ> : XmoZm| ^mJm|> go {ZX}emZwgma àíZm| Ho$ CÎma Xr{OE &
^mJ> H$
Bg ^mJ> go {H$Ýht Xmo àíZm| Ho$ CÎma Xr{OE & 220=40
1. ì`m»`m H$s{OE {H$ AW©emñÌ _| {d^oXH$ g_rH$aU H¡$go
bmJy hmoVo h¢ & {d^oXH$ (AdH$b) g_rH$aU H$mo hb H$aZo
_| àma§{^H$ eV© H$s ^y{_H$m na MMm© H$s{OE & C{MV
CXmhaU Xr{OE &
2. {ZåZ Cn`mo{JVm \$bZ na {dMma H$s{OE :
u = f(x1, x2, ... xn)
Ohm± Cn^moJ H$s JB© ‘n’ dñVwAm| H$s _mÌm h¡ & _mZm
xi,
i = 1, 2, ... n Ho$ {bE pi dñVw xi H$s H$s_V h¡ & Cn^moº$m
H$s Am` H$mo M _mZVo h¢ & Xem©BE {H$ Cn`mo{JVm
A{YH$V_rH$aU g_ñ`m H$m b¡J«opÝO`Z JwUH$ Am` H$s
gr_m§V Cn`mo{JVm Ho$ ~am~a h¡ &
MEC-003 5 P.T.O.
3. (H$) _mZH$ àgm_mÝ` ~§Q>Z H$s {deofVmAm| H$m dU©Z
H$s{OE &
(I) EH$ agm`Z _| Aew{Õ`m± 127 ^mJ à{V {_{b`Z
(ppm) _mÜ` Am¡a 22 ^mJ à{V {_{b`Z (ppm)
_mZH$ {dMbZ Ho$ gmW gm_mÝ` ê$n go ~§{Q>V h¢ &
agm`Z V^r ñdrH$m`© hmoJm O~ CgH$s Aew{Õ`m±
150 ^mJ à{V {_{b`Z (ppm) go H$_ hm|Jr &
ñdrH$m`© agm`Zm| H$m AZwnmV Š`m h¡ ?
[z = 1·5 Ho$ {bE _mZH$ gm_mÝ` dH«$ Ho$ A§VJ©V joÌ
0·668 h¡ &]
4. amOñd (Am`) A{YH$V_ H$aZo dmbo EH$m{YH$mar H$mo
H$_-go-H$_ 1500 Ho$ bm^ H$s Amdí`H$Vm h¡ & CgHo$ _m±J
\$bZ Am¡a bmJV \$bZ h¢ :
D = 304 – 2 Q Am¡a
C = 500 + 4 Q + 8 Q2.
CËnmXZ Am¡a H$s_V H$m g§Vb
w Z ñVa kmV H$s{OE & `{X
EH$m{YH$mar bm^ A{YH$V_ H$aZm Mmho, Vmo CgHo$ CËnmXZ
Am¡a H$s_V Š`m hm|Jo ?
MEC-003 6
^mJ> I
Bg ^mJ> go {H$Ýht nm±M àíZm| Ho$ CÎma Xr{OE & 512=60
5. {X`m J`m h¡ {H$ :
1 1 1 1 2 3
A = 2 3 4 , B= 6 12 6
3 2 3 5 10 5
Amì`yh AB, BA Am¡a A + B H$s Om{V (H$mo{Q>) kmV
H$s{OE &
6. 20 bmoJm| H$s Zm{gH$m H$s bå~mB© Am¡a D±$MmB© Ho$ ~rM
ghg§~§Y JwUm§H$ H$m _yë` 0·203 àmßV hþAm & narjU
H$s{OE {H$ Š`m `h ghg§~§Y gm§p»`H$s` ê$n go _hÎd
aIVm h¡ &
7. EH$ a¡{IH$ àmoJ«m_Z g_ñ`m Bg àH$ma h¡ :
A{YH$V_ H$s{OE z = 30x1 + 50x2
~eV} x1 + x2 9
x1 + 2x2 12
x1 0, x2 0.
Bï>V_ hb kmV H$s{OE &
8. z = 2 x 12 – x1 x2 + 4 x 22 + x3 + x 32 + 2
Ho$ Ma_ _yë`m|
H$mo kmV H$s{OE & gË`m{nV H$s{OE {H$ `h A{YH$V_ H$s
pñW{V h¡ `m Ý`yZV_ H$s &
MEC-003 7 P.T.O.
9. Xem©BE {H$ EH$ ßdmgm| ~§Q>Z _| _mÜ` Am¡a àgaU ~am~a
hmoVo h¢ &
10. ~oµO à_o` ~VmBE Am¡a BgH$s ì`m»`m H$s{OE &
11. àmMbm| Ho$ AmH$bZ Ho$ {bE A{YH$V_ g§^m{dVm {d{Y H$s
ì`m»`m H$s{OE &
12. {ZåZ _| go {H$Ýht Xmo na g§{jßV {Q>ßn{U`m± {b{IE :
(H$) A{^bj{UH$ _mZ (AmBJoZ_mZ)
(I) Q>oba H$m {dñVma
(J) Hw$hZ-Q>H$a eV]
MEC-003 8
