Exam Details
| Subject | Quantitative Methods | |
| Paper | ||
| Exam / Course | Master of Arts in Economics | |
| Department | School of Social Sciences (SOSS) | |
| Organization | indira gandhi national open university | |
| Position | ||
| Exam Date | June, 2016 | |
| City, State | new delhi, |
Question Paper
1. A revenue maximising monopolist requires a profit of at least 1500. His demand and cost functions are D=304-2Q and C=500 4Q 8Q^2
Determine his price and level of output. Contrast these values with those that would be achieved under profit maximisation.
2.(a) Write a linear first-order differential equation and work out its general solution. How will you solve Harrod-Domar formulation of steady growth through differential equations
3. A production function is given by y where y is the output and xl and x2 are the two inputs. If price of output Py= 15 and prices of inputs PXl Px2 then Derive profit maximising inputs; and Verify that these inputs are profit maximising.
4. If x1, x2 and x3 are a random sample of size 3 from a population with mean u and variance and T1, T2, T3 are the estimators used to estimate the mean value J.L where T1 =xl x2
T2=2xl-4x2 3x3 and T3= 1/3 (axl x2 x3) Are Tl and T2 unbiased estimators of u For what value of T3 will be unbiased estimator of u For what value of will T3 be a consistent estimator? Which of the 3 is the best estimator?
Answer any five questions from this section
5. <img src='./qimages/11921-5.jpg'>
Find ranks of AB, BA and A B.
6. A subcommittee of 6 is to be formed out of a group of 7 men and 4 ladies. Calculate the probability that the subcommittee will have: exactly 2 ladies at least 2 ladies
7.(a) Find dy/dx when
y=log(e^x
(ii) 1 sqrtx^2 a^2 Find the total differential given
y= Xl Xl X2
8. Suppose <img src='./qimages/11921-8-1.jpg'> be the technology
matrix. Let <img src='./qimages/11921-8-2.jpg'> be the final demand vector.
Find the level of production of the three goods.
9. Suppose a die is rolled. We are told that the number is even. What is the probability that it
10. The standard deviation of the distribution of income of a sample of 100 household was RS 6970. Test the hypothesis that the standard deviation of the distribution of income for all households is Rs 4700. (Use large sample test).
11. Solve the following Linear Programming Model
Max z=45x1 55x2
Sub. to 6x1 4x2 120
3x1 10x2 180
Xl x2 0
12. What is Poisson Distribution? Find its mean and variance.
Determine his price and level of output. Contrast these values with those that would be achieved under profit maximisation.
2.(a) Write a linear first-order differential equation and work out its general solution. How will you solve Harrod-Domar formulation of steady growth through differential equations
3. A production function is given by y where y is the output and xl and x2 are the two inputs. If price of output Py= 15 and prices of inputs PXl Px2 then Derive profit maximising inputs; and Verify that these inputs are profit maximising.
4. If x1, x2 and x3 are a random sample of size 3 from a population with mean u and variance and T1, T2, T3 are the estimators used to estimate the mean value J.L where T1 =xl x2
T2=2xl-4x2 3x3 and T3= 1/3 (axl x2 x3) Are Tl and T2 unbiased estimators of u For what value of T3 will be unbiased estimator of u For what value of will T3 be a consistent estimator? Which of the 3 is the best estimator?
Answer any five questions from this section
5. <img src='./qimages/11921-5.jpg'>
Find ranks of AB, BA and A B.
6. A subcommittee of 6 is to be formed out of a group of 7 men and 4 ladies. Calculate the probability that the subcommittee will have: exactly 2 ladies at least 2 ladies
7.(a) Find dy/dx when
y=log(e^x
(ii) 1 sqrtx^2 a^2 Find the total differential given
y= Xl Xl X2
8. Suppose <img src='./qimages/11921-8-1.jpg'> be the technology
matrix. Let <img src='./qimages/11921-8-2.jpg'> be the final demand vector.
Find the level of production of the three goods.
9. Suppose a die is rolled. We are told that the number is even. What is the probability that it
10. The standard deviation of the distribution of income of a sample of 100 household was RS 6970. Test the hypothesis that the standard deviation of the distribution of income for all households is Rs 4700. (Use large sample test).
11. Solve the following Linear Programming Model
Max z=45x1 55x2
Sub. to 6x1 4x2 120
3x1 10x2 180
Xl x2 0
12. What is Poisson Distribution? Find its mean and variance.
Other Question Papers
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- Actuarial Economics: Theory and Practice
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- Economics of Growth and Development
- Economics of Social Sector and Environment
- Financial Institutions and Markets
- Indian Economic Policy
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- Macroeconomic Analysis
- Microeconomic Analysis
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- Quantitative Methods
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