SYLLABUS AND SAMPLE QUESTIONS FOR MS(QE) 2012 Syllabus for ME I (Mathematics), 2012 Algebra: Binomial Theorem, AP, GP, HP, Exponential, Logarithmic Series, Sequence, Permutations and Combinations, Theory of Polynomial Equations (up to third degree). Matrix Algebra: Vectors and Matrices, Matrix Operations, Determinants. Calculus: Functions, Limits, Continuity, Differentiation of functions of one or more variables. Unconstrained Optimization, Definite and Indefinite Integrals: Integration by parts and integration by substitution, Constrained optimization of functions of not more than two variables. Elementary Statistics: Elementary probability theory, measures of central tendency; dispersion, correlation and regression, probability …show more content…
The probability of using 2 2 transports A, B, C, D by an individual is 1 , 9 , 4 , 9 respectively. The 9 9 probability that he arrives late at work if he uses transportation A, B, 4 C, D is 5 , 7 , 6 , and 6 respectively. What is the probability that he 7 7 7 used transport A if he reached office on time? A B C D 1 , 9 1 , 7 3 , 7 2 . 9 19. What is the least (strictly) positive value of the expression a3 +b3 +c3 − 3abc, where a, b, c vary over all strictly positive integers? (You may use ( ) the identity a3 +b3 +c3 −3abc = 1 (a+b+c) (a−b)2 +(b−c)2 +(c−a)2 .) 2 A 2, B 3, C 4, D 8. 20. If a2 + b2 + c2 = 1, then ab + bc + ca is, (A) −0.75, (B) Belongs to the interval [−1, −0.5], (C) Belongs to the interval [0.5, 1], (D) None of the above. 21. Consider the following linear programming problem: Maximize a + b subject to a + 2b ≤ 4, a + 6b ≤ 6, 5 a − 2b ≤ 2, a, b ≥ 0. An optimal solution is: (A) a=4, b=0, (B) a=0, b=1, (C) a=3,b=1/2, (D) None of the above. ∫ −1 1 22. The value of −4 x dx equals, (A) ln 4, (B) Undefined, (C) ln(−4) − ln(−1), (D) None of the above. 23. Given x ≥ y ≥ z, and x + y + z = 9, the maximum value of x + 3y + 5z is (A) 27, (B) 42, (C) 21, (D) 18. 24. A car with six sparkplugs is known to have two malfunctioning ones. If two plugs are pulled out at random, what is the probability of getting at least one malfunctioning plug. (A) 1/15, (B) 7/15, (C) 8/15, (D) 9/15. 25. Suppose there is a multiple choice test which has 20 questions.
The economy of Brazil is in the top ten largest economies along with the United States. It is the biggest in Latin America. Actually it is the seventh largest in the world. Brazil has used its newly found economic mechanism to syndicate its outcome in South America and show more of a role in the Global Businesses. The Obama Administration’s National Security Strategy recognizes Brazil as a developing center of effect, and greets the management of the country’s joint and global issues. The United States and Brazil associations mostly have been good in the recent years. But Brazil has other strengthening relations with neighboring countries and expanding ties with nontraditional partners in the South that’s developing.
3. Questions 3a through 3d are based on a distribution of scores with and the standard Draw a small picture to help you see what is required.
Consider the production schedules for two fictional countries, Ying and Tai. Both countries can only produce two types of goods, Lychees and Teacups. The rows a to e depict the possible combinations of these two goods that each country can produce. Ying Number of Number of Lychees Teacups 0 12 2 Tai Number Lychees 4
The statement, "John buys more of good X as his income increases, Ceteris paribus," means:
In his cartoon, “Welcome to Economics 101, Kid”, Jeff Parker demonstrates a frustrated tone using an exaggerated symbolism and ironic background to highlight the unjustly overpriced costs of college tuition fees.
Problems #65 - #94 from page 311. Please provide your answer after each problem and submit the file with your answers through Blackboard.
Unauthorized immigration has been a major political issue at least for the past 30 years, and is one of the most difficult to resolve. The problem relates to both economic and business realities of the U.S. and Mexico. There may be anywhere between 4 to 12 million undocumented immigrants living in the United States. For undocumented immigrants from Mexico, population experts have discovered that there is a constant flow of both immigrants into the US and leaving the US . This is the primary reason why the exact number remains unknown.
2. Inferential statistics refers to generalizing from a sample to a population, estimating unknown parameters, drawing conclusions, and making decisions.
1. SteamScot face a ‘basic economic problem’ what is this ‘problem’ and what is the opportunity cost of the replace and repair programme?
Standard: A1.4. Linear functions, equations, and inequalities (Algebra) Students understand that linear functions can be used to model situations involving a constant rate of change. They build on the work done in middle school to solve sets of linear equations and inequalities in two variables, learning to interpret the intersection of the lines as the solution. While the focus is on solving equations, students also learn graphical and numerical methods for approximating solutions to equations. They use linear functions to analyze relationships, represent and model problems, and answer questions. These algebraic skills are applied in other Core Content areas across high school courses.
Question #6 has the options 1 to 4, 4 to 6 and 6 to 10. These are examples of non-mutually exclusive responses. I would recommend changing the options to 1 to 4, 5 to 6 and 9 to 10.
Once these situations have been accepted, we can use the Solver function in Excel to answer the three questions.
In the United States, minimum wage has remained at a low number for several years. Minimum wage is defined as the lowest possible income that an employer can legally pay an employee. This ensures that all people are fairly paid and not defrauded by companies or businesses. Minimum wage is considered a price floor and the minimum wage laws determine the lowest price possible that any employer must pay for labor. In an economic model, the quantity of supplied is greater than the quantity demanded and the minimum wage is above equilibrium price and quantity. Minimum wage prevents labor supplied and labor demanded from moving
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