No.
of Printed Pages : 10 MEC–203
MASTER OF ARTS (ECONOMICS)
(MAEC)
Term-End Examination
June, 2024
MEC-203 : QUANTITATIVE METHODS
Time : 3 Hours Maximum Marks : 100
Note : Answer questions from each Section as per
instructions.
Section—A
Note : Answer any two questions from this Section.
1. (a) Use Cramer’s rule to find the solution of
the following system of equations : 8
X1 4X2 3X3 2
2X 2 2X3 1
X1 3X2 5X3 0
P. T. O.
[2] MEC–203
(b) Discuss the properties of orthogonal matrix
and idempotent matrix. 6
(c) Define the terms eigen value, eigen vector
and characteristic equation. 6
2. (a) Explain Taylor’s approach to polynomial
approximation. 8
(b) Let F = R3 R such that x ( x1 , x 2 , x3 ) .
Let F( x ) ex1 x2 x3 . Find Taylor’s third
order polynomial in the neighbourhood of
(0, 0, 0). 12
3. (a) What do you understand by sample
design ? List the advantages of sample
survey. 7
(b) Briefly explain different types of sampling
methods. 8
(c) What are the different sources of bias in
sample survey ? 5
[3] MEC–203
4. Find the time path and investigate the
behaviour of price in a market when demand
and supply functions are : 20
Dt 86 0.8 Pt
St 10 0.8Pt 1
Section—B
Note : Answer any five questions from this Section.
5. (a) Find the norm of vectors (5, – 2, 3) and
(– 2, 2). 4
(b) Find the inner product of the following
vectors : 4
(i) (2, 3, 4) and (4, 5, 5)
(ii) (– 2, – 3, 4) and (4, 5, – 6)
(c) Define linear independence of vectors. 4
6. (a) Find the total differential coefficient of the
function x2y with respect to x, where
x 2 xy y2 1 . 6
P. T. O.
[4] MEC–203
(b) Find out the concavity and convexity of the
following function over this set of real
numbers that are non-negative : 6
(i) f (u) 2u13 6u22
(ii) f (u ) 8u2
7. (a) Find the limit of the following : 8
x3 8
(i) lim
x 2 x 2 4
x 5 3
(ii) lim
x 4 x 4
(b) What are the properties of a continuous
function ? 4
8. (a) What is meant by improper integral ? 4
2
(b) Determine if the integral x ex dx is
convergent or divergent. If it’s convergent,
find its value. 8
9. Differentiate between the following : 4+4+4
(a) Parameter and Statistics
(b) Type I and Type II errors
[5] MEC–203
(c) Normal distribution and Standard normal
distribution
10. (a) Let f : R2 R2 be defined as : 8
f ( x , y ) ( e2xy , 2x 2 3 y2 )
Find the Jacobian Jf at the point (2, 1).
(b) Explain mean value theorem. 4
11. (a) Derive the mean of the Binomial
distribution. 8
(b) Prove that Poisson distribution is a
limiting case of Binomial distribution. 4
P. T. O.
[6] MEC–203
MEC-203
2024
-203
&
X1 4X2 3X3 2
2X 2 2X3 1
X1 3X2 5X3 0
[7] MEC–203
& ]
F = R3 R
x ( x1 , x 2 , x3 )
F( x ) ex1 x2 x3 (0, 0, 0)
12
(biases)
P. T. O.
[8] MEC–203
Dt 86 0.8 Pt
St 10 0.8Pt 1
&
(5, – 2, 3) (– 2, 2)
(i) (2, 3, 4) (4, 5, 5)
(ii) (– 2, – 3, 4) (4, 5, – 6)
4
[9] MEC–203
x x2y
]
x 2 xy y2 1
]
(i) f (u) 2u13 6u22
(ii) f (u ) 8u2
x3 8
(i) lim
x 2 x 2 4
x 5 3
(ii) lim
x 4 x 4
2
x ex dx
P. T. O.
[ 10 ] MEC–203
4+4+4
I II
f : R2 R2
f ( x , y ) ( e 2 xy , 2x 2 3 y2 )
(2, 1) Jf
(Poisson)
(Binomial)
MEC–203
