Deemed University 2010 B.B.A University: Lingayas University Term: I Title of the : Business Mathematics-I - Question Paper

Roll No. ..

 

Lingayas University, Faridabad

BBA-MBA (Integrated) 1^st Year (Term-I)

Examination Nov 2010

Business Mathematics-I (BA-1102)

[Time: 3 Hours] [Max. Marks: 100]

 

Before answering the question, candidate should ensure that they have been supplied the correct and complete question paper. No complaint in this regard, will be entertained after examination.

 

Note: Attempt five questions in all; picking up any two from Section A, any two from Section B and the last Section C question 8 is compulsory.

 

SECTION A

Q-1. (a) Evaluate (x) for the following function at the given point.

at x=-1 (5)

(b) Differentiate the following function w.r.t. x.

(5)

(c) Verify that the points (0,2) and (3,0) lie on the line 2x+3y=6. Hence find the slope of the line. Is the line uphill, downhill or horizontal. (10)

Q-2. (a) If the demand function is; P=100-4Q. Find expression for TR and MR in terms of Q. Hence estimate the change in TR brought about by a 0.3 unit increase in output from a current level of 12 units. (10)

(b) If the consumption function is, C=0.01y²+0.2y+50. Calculate MPC and MPS when y=30 and interpret the result. (10)

Q-3. (a) Determine the elasticity of demand when the price falls from 136 to 119, given the demand function, P=200-Q². (10)

(b) Given the demand function P=50-2Q. Find the elasticity when the price is 30. Is demand inelastic, unit elastic or elastic at this price? (10)

 

SECTION B

Q-4. Given the supply function P=10+find the price elasticity of supply

(a) average along an are between Q=100 and Q=105

(b) at the point Q=100. (10x2=20)

Q-5. A firms short run production function is given by Q=6L²-0.2L³ where L denotes number of workers.

(a) Find the size of the work force that maximizes output.

(b) Find the size of the work force that maximizes the average product of labour. Calculate MP_L and AP_L at this value of L. What do you observe? (10x2=20) Q-6. The demand function of a good is P+Q=30 and total cost function is TC=

(a) Find the level of output that maximizes total revenue.

(b) Find the level of output that maximizes profit. Calculate MR and MC at this value of Q. What do you observe? (10x2=20)

Q-7. If evaluate at the point (2,6).

(a) Use the small increments formulae to estimate the changes in Z as x decreases from 2 to 1.9 and y increases from 6 to 6.1.

(b) Confirm your estimate of part (a) by evaluating Z at (2,6) and (1.9,6.1). (10x2=20)

SECTION C

 

Q-8. A firms production function is Q=50L-0.01L² where L denotes the size of the workforce. Find the value of MP_L in the case when (a) L=1, (b) L=10, (c) L=100, (d) L=1000. Does the law of diminishing marginal productivity apply to this particular function? (20)

Roll No. ..

 

Lingayas University, Faridabad

BBA/MBA (Integrated) 1^st Year (Term-I)

Examination Nov, 2010)

Business Mathematics-I (BA-1102)

[Time: 3 Hours] [Max. Marks: 100]

 

Before answering the question, candidate should ensure that they have been supplied the correct and complete question paper. No complaint in this regard, will be entertained after examination.

 

Note: Attempt five questions in all; picking up any two from Section A, any two from Section B and the last Section C question 8 is compulsory.

 

SECTION A

Q-1. (a) Evaluate (x) for the following function at the given point.

at x=-1 (5)

(b) Differentiate the following function w.r.t. x.

(5)

(c) Verify that the points (0,2) and (3,0) lie on the line 2x+3y=6. Hence find the slope of the line. Is the line uphill, downhill or horizontal. (10)

Q-2. (a) If the demand function is; P=100-4Q. Find expression for TR and MR in terms of Q. Hence estimate the change in TR brought about by a 0.3 unit increase in output from a current level of 12 units. (10)

(b) If the consumption function is, C=0.01y²+0.2y+50. Calculate MPC and MPS when y=30 and interpret the result. (10)

Q-3. (a) Determine the elasticity of demand when the price falls from 136 to 119, given the demand function, P=200-Q². (10)

(b) Given the demand function P=50-2Q. Find the elasticity when the price is 30. Is demand inelastic, unit elastic or elastic at this price? (10)

 

SECTION B

Q-4. Given the supply function P=10+find the price elasticity of supply

(a) average along an are between Q=100 and Q=105

(b) at the point Q=100. (10x2=20)

Q-5. A firms short run production function is given by Q=6L²-0.2L³ where L denotes number of workers.

(a) Find the size of the work force that maximizes output.

(b) Find the size of the work force that maximizes the average product of labour. Calculate MP_L and AP_L at this value of L. What do you observe? (10x2=20) Q-6. The demand function of a good is P+Q=30 and total cost function is TC=

(a) Find the level of output that maximizes total revenue.

(b) Find the level of output that maximizes profit. Calculate MR and MC at this value of Q. What do you observe? (10x2=20)

Q-7. If evaluate at the point (2,6).

(a) Use the small increments formulae to estimate the changes in Z as x decreases from 2 to 1.9 and y increases from 6 to 6.1.

(b) Confirm your estimate of part (a) by evaluating Z at (2,6) and (1.9,6.1). (10x2=20)

SECTION C

 

Q-8. A firms production function is Q=50L-0.01L² where L denotes the size of the workforce. Find the value of MP_L in the case when (a) L=1, (b) L=10, (c) L=100, (d) L=1000. Does the law of diminishing marginal productivity apply to this particular function? (20)