IGNOU BECC-102 June 2022 Previous Year Question Paper

Q1.(a) Given that demand function is of the form P = a — bQ, show that the value of price elasticity of demand ¢ ‘a is not influenced by the value of the slope.

(b) A firm faces a demand function P = 180e°6 @ Determine the price elasticity of demand when p = 10. Calculate the response to a 5% increase in price when p = 10.

Q2.A fish population increases by 5% each generation but a catch of 9000 is lost from each generation. If P, represents the size of the population for generation t, write the difference equation which expresses P, in terms of P,_,.

Q3.By using the condition that the point (x, y) is equidistant from the points (3, 1) and (-1, 2), obtain the equation of the line which is the perpendicular bisector of the line joining these points.

Q4.<A firm can produce quantity x of a product at cost ; x3 — 6x? + 160x + 15 The firm faces the demand function : x=144-p where p is the price of the product.

(a) Show that the marginal cost is positive at all levels of production.

(b) Find the profit maximising level of output.

Q5.Explain the properties of reflexivity, symmetry, antisymmetry and transitivity with regard to a relation. In this context, what do you understand by an order relation ?

Q6.(a) Explain the concept of a quantifier. Why are quantifiers needed ? What is an existential quantifier ?

(b) Distinguish between the inverse and converse of an implication.

Q7.(a) Find the equation of the circle

(i) with centre (8, — 4) and radius 7.

(ii) with centre at the origin and radius 5.

(b) Write down the equation of the parabola with focus (0, 2) and directrix x = 2.

Q8.(a) Define a discontinuous function. Distinguish between irremovable discontinuity and removable discontinuity.

(b) Explain the Intermediate-Value Theorem.

Q9.(a) Differentiate x°+2x4+1

(b) The cost function for a manufacturer is given by: 10 ge C=100q- — q+ + 4 3 q 9 where C is the cost of production and q is the level of output. Find the level of output at which the marginal cost is equal to the average cost.

Q10.A monopolist’s demand function is x = 210 — 3p, where p = price and x = quantity demanded. The total cost function is x? + 6x + 10. Find the consumer surplus at the equilibrium.

Q11.Differentiate between the following :

(a) Correspondence and Set function

(b) Exponential function and Power function

Q12.Explain the following :

(a) Homogeneous difference equation

(b) Intersection of sets P=180e°6Q BECC-102 6 ; x? — 6x2 4+ 160x+ 154 | x=144-p

Q13.aaa & det F wages (reflexivity), सममिति (converse) & aa seat Fae AIT | 2 ak fram (directrix) x = 22 | BECC-102 8 x” +2x41