ECO/V/CC/07 Student's Copy
2 0 1 8
CBCS
5th Semester
ECONOMICS
SEVENTH PAPER
Quantitative Techniques—I
Full Marks 75
Time 3 hours
Simple calculator can be used in this paper
PART A—OBJECTIVE
Marks 25
The figures in the margin indicate full marks for the questions
SECTION—A
Marks 10
Tick the correct answer in the brackets provided 1×10=10
1. One variable expressed directly in terms of the other variables is a/an
explicit function
implicit function
rational function
2. If there is a one-to-one correspondence between the elements of the two
sets, then the sets are said to be
equal sets
equivalent sets
disjoint sets
ECO/V/CC/07/84 1 Contd.
3. If dy/dx> then
the curve rises from left to right
the curve remains stationary
the curve falls from left to right
4. Total revenue is maximum, when
MR 0
MR 0
MR 0
5. If MC 4q 3 6q2 4q, then TC is
q4 3q 3 4
q4 2q 3 2q2
6q2 +12q 4
6. ò dx
1
x2
x c
7. If any two rows/columns of a determinant are interchanged, then
the value of the determinant remains unchanged
the value of the determinant is zero
the sign of the determinant changes
8. A special type of matrix in which there is only one row or one column
is a/an
vector
indentity matrix
singular matrix
ECO/V/CC/07/84 2 Contd.
9. In a linear programming problem, if the given constraints fail to define a
feasible region, then
multiple optimal solution will exist
there will be no feasible solution
None of the above
10. The set of constraints in LP problem defines
a feasible region
an optimal solution
the objective function
SECTION—B
Marks 15
Answer the following questions 3×5=15
1. Distinguish between linear and quadratic equations.
OR
Define cartesian product.
2. If y x 3 5x2, find f when x 2.
OR
Mention the relationship between marginal cost and average cost.
3. Define consumer's surplus.
OR
If MR 50 7q, then calculate the total revenue function.
4. Define rank of a matrix.
OR
Explain singular matrix.
ECO/V/CC/07/84 3 Contd.
5. What is linear programming?
OR
Formulate the dual of the given linear programming problem
Maximize Z 2x1 3x2
subject to
The figures in the margin indicate full marks for the questions
1. Define exogenous and endogenous variables. 3
Enumerate all the proper subsets of set A a c 3
State and verify associative laws of union and intersection by using the
following sets
A 4 B 6 and C 7 4
OR
2. Distinguish between finite and infinite sets. 3
If E a c d e and A c e then find the complement of A. 2
In a survey of 100 students, it was found that 50 passed in Economics,
40 in Mizo, 55 in Geography, 15 in Economics and Mizo, 20 in
Economics and Geography, 16 in Mizo and Geography and 3 in none
of these subjects. How many students passed in all the three subjects? 5
3. State the condition for optimization of a function. 2
Find the point elasticity of demand for the demand function
q 7 2p, when p 2. 4
ECO/V/CC/07/84 4 Contd.
Find the derivatives for the following functions (any two) 2×2=4
y 3x e2x log x
y (7x2 3x
OR
4. Find the partial derivatives of Z x 5y 2
The total revenue and total cost functions of a firm are given by
R 30q q2 and C 20 4q respectively. Find the profit maximizing
output level. 3
If C 2Q3 -Q2 4Q, where Q is the output—
find MC;
verify that at a minimum of average cost, AC MC.
5. Evaluate the following functions (any two) 3×2=6
ò (5x 3)3 dx
xe xdx ò
2 2
0
2 ò x x dx
If MR =16 q2, then find the total and average revenue functions.
OR
6. The demand and supply functions are given by Pd 3q2 20q 5 and
Ps =15 9q respectively, determine the producer's surplus under pure
competition. 6
The marginal cost function of a firm is given by MC 5 2x, where x is
the output. Find the total cost function, if the fixed cost is R 200. 4
ECO/V/CC/07/84 5 Contd.
7. Find the inverse of the matrix A é
verify whether (AB A¢B where A¢ and
B ¢ are transposes of the matrices A and B respectively. 6
OR
8.
Find the values of c and if A B C. 3
Solve the following equations by Cramer's rule
x y z
x y z
x y z



2 3 1
3 4 3
2 2 1
7
9. Discuss the various basic assumptions for the application of linear
programming problems. 10
OR
10. Solve the following linear programming problem by graphical method and
indicate the feasible region in the diagram 8+2=10
Maximize Z 3x1 4x2