[2] MEC-003
(b) Give a geometrical interpretation of
No. of Printed Pages : 10 MEC-003
derivatives.
M. A. (ECONOMICS) 2. Find out the extreme for the following
(MEC) function :
Term-End Examination z x12 3 x1 x 2 3 x 22 4 x 2 x3 6 x32
December, 2021 Determine whether it is a maximum or
MEC-003 : QUANTITATIVE METHODS minimum value.
Time : 3 Hours Maximum Marks : 100 3. (a) Bring out the salient features of normal
distribution.
Note : Answer the questions from each Section as
(b) The height of 10000 persons is distributed
directed.
normally with mean 64.5 inch and
Section—A standard deviation of 4.5 inch. Find the
Note : Answer any two questions from this number of persons whose height is between
55.5 inch and 69 inch [P (z = 2) = 0.4772
Section. 2×20=40
and P (z = 1) = 0.3413].
1. (a) What is meant by continuity in a function ?
4. Explain how the method of maximum
State the properties of a continuous likelihood can be used to estimate a regression
function. model.
P. T. O.
[3] MEC-003 [4] MEC-003
Section—B 7. Find the inverse of the following matrix :
Note : Answer any five questions from this 4 1 –1
A 0 3 2
Section. 5×12=60
3 0 7
5. Solve the following linear programming
8. Estimate the regression model y a bx for the
problem :
following data :
Maximize :
x y
z 5 x1 10 x2
1 3
Subject to : 2 7
3 5
x1 3 x2 50
4 11
4 x1 2 x2 60 5 14
x1 5 9. Explain the procedure of applying difference
equation for solving a cobweb model.
x1 0, x2 0 .
10. Consider the matrices :
6. Explain the process of drawing inferences and
1 1 – 1 –1 – 2 3
testing hypothesis for the difference between A 2 –3 4 , B 6
12 6
two population means, when the population 3 –2 3 5 10 5
variances are known. Find the rank of the matrices A, B and [A + B].
P. T. O.
[5] MEC-003 [6] MEC-003
11. Solve the following equation : MEC-003
x 2 dy y ( x y ) dx 0
12. Write short notes on any two of the following :
6×2=12 2021
-003
(a) Kuhn-Tucker condition
(b) Input-output table
(c) Chain rule of differentiation
&
2 × 20 = 40
(function)
(continuity)
(continuous function)
P. T. O.
[7] MEC-003 [8] MEC-003
(derivatives) (Regression)
(geometrical) ] (maximum
(function) likelihood)
(extreme)
z x12 3 x1 x 2 3 x 22 4 x 2 x3 6 x32 &
5×12=60
(Normal distribution) (linear programming)
] :
] (mean)
z 5 x1 10 x2
64.5 (standard :
derivation) 4.5 x1 3 x2 50
4 x1 2 x2 60
x1 5
[P (z = 2) = 0.4772 P (z = 1) = 0.3413] x1 0, x2 0 .
P. T. O.
[9] MEC-003 [ 10 ] MEC-003
(population) (Cobweb)
(variances) ] (difference equation)
(means) ]
(changing inferences) ª
(hypothesis testing)
1 1 – 1 –1 – 2 3
A 2 –3 4 , B 6
12 6
3 –2 3 5 10 5
ª (inverse)
A, B [A + B] ª (rank)
4 1 –1 (equation)
A 0 3 2
3 0 7
x 2 dy y ( x y ) dx 0
(Regression)
y a bx
6×2=12
x y (Kuhn-Tucker condition)
1 3 (Input-output table)
2 7
(Chain rule of
3 5
differentiation)
4 11
5 14 MEC–003
P. T. O.
