ECO/V/07 Student's Copy
2 0 1 8
Pre-CBCS
5th Semester
ECONOMICS
SEVENTH PAPER
Quantitative Techniques—I
Full Marks 75
Time 3 hours
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. How many subsets are there altogether in the set S
4
8
12
16
/258 1 Contd.
2. Which of the following pairs of sets are disjoint?
and f
and
10, 12} and
16} and
3. The derivative of xn-1 is
nxn-1
n xn-1
n xn-2
nxn-2
4. A monopolist's demand curve is given by p =100 2q. Identify the slope
of AR.
50 q
50
-2q

5. What is the value of ò1dx?
6. Integration of any given marginal revenue functions will yield
total revenue function
average revenue function
demand function
supply function
7. Identify the singular matrix.
9. The feasible region of a linear programming problem is
a concave set
a convex set
a null set
a singleton set
10. Regarding non-negativity constraints, the constrains remain unchanged in
primal
dual
both primal and dual
None of the above
ECO/V/07/258 3 Contd.
SECTION—B
Marks 15
Answer the following questions 3×5=15
1. Define finite and infinite sets.
2. What is meant by elasticity of demand?
3. If MC 5 X then find the total cost function.
4. Define rank of a matrix.
5. Write a note on the concept of dual.
ECO/V/07/258 4 Contd.
PART B—DESCRIPTIVE
Marks 50
The figures in the margin indicate full marks for the questions
1. Define dependent and independent variables. 4
Verify the associative law of union and intersection by using the
following sets 4
A B and C
Let the demand function of a commodity is D 24 2P and its supply
function is S 7P. Find the equilibrium price. 2
OR
2. Distinguish between logarithimic and exponential functions. 4
Given A B and C verify the distributive
law of union and intersection. 4
Enumerate all the subsets of the set c}. 2
3. Evaluate the limits of the following
Find the relative extrema of the function y x 3 3x2 2. 3
Given the supply function S -100 2P, find the elasticity of supply
with respect to price at P =10. 3
OR
4. Find the derivatives of the following
y (x2 2x 5)10
y x
1
The total cost function of a firm is given by TC 200Q 5Q2 0 × 05Q3,
where Q is the quantity produced. Find the marginal cost function
and the output level at which marginal cost is equal to average
cost
5. Evaluate the following 2×3=6
ò 3 x dx
(5e x x 2 3)dx
If the demand curve is p 85 4x x2, where p and x are respectively
the price and the amount demanded of a commodity, what will be
the consumers surplus when p 64? 4
OR
6. If MR =16 x2, find the total revenue function and the average revenue
function. Calculate the total revenue when x =10. 6
If the demand and supply functions for a commodity are
Pd 3x2 20x 5 and Ps =15 9x respectively, find the producer's
surplus at equilibrium price. 4
ECO/V/07/258 6 Contd.
7. State and prove the basic properties of determinants. 6
Given that
Find A 2B I where I is an identity matrix of 2 ´ 2. 4
OR
8. What is column matrix? 2
Solve the following equations by using matrix inversion method or
Cramer's rule 8
x y z
x y z
x y z



4
3 8
2 0
9. Use graphical method to solve the linear programming problem. Also
indicate the feasible region.
Minimize C 3x1 2x2
subject to
5 10
6
4 12
1 2
1 2
1 2
x x
x x
x x
³
³
³
and x1, x2 ³ 0 8+2=10
OR
10. Explain the meaning of linear programming. What are the main
assumptions of the technique of linear programming? 2+8=10