Mathematics

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The sub-subject “differential equations” is a branch of Mathematics that involves the function and its derivatives. The function represents the physical quantity and the derivative represents the rate of change. The differential equation established a relationship between them.

A differential equation is known by its order and the order is determined by their derivative. A first derivative equation is a first order differential equation, the second derivative equation is a second order differential equation. Differential equation has several types: Ordinary differential equation, partial differential equation, linear or non-linear differential equation.

The sub-subject “Partial differential equations” is a branch of Mathematics that involves an equation which contains the function of several variable and its partial derivatives. A partial derivative of a function is a derivative of the function of two or more variable with respect to the more than one variable.

A partial differential equation is known by its order and the order is determined by their derivative. A first derivative equation is first order partial differential equation, the second derivative equation is second order partial differential equation. A partial differential equation has several types: Linear PDE, Quasi-linear PDE, Nonlinear PDE.

Abstract algebra is also known as modern algebra. The most common divisions of abstract algebra are, commutative algebra, representation theory, and homological algebra. Abstract algebra includes study of group theory, ring theory, vector spaces, lattices and algebras. Real life applications of abstract algebra are medical imaging (algebraic topology is used to convert 3D information from the data out of a scanner), coordination between robots etc.

Topology is the mathematical study of the properties of the object that are preserved under some transformations (deformation, twisting, stretching etc.) called as homeomorphism. For instance, a circle can be transformed into an ellipse by stretching. Thus, making them topologically equivalent. The most common branches of topology are, algebraic topology, differential topology and low-dimensional topology. Applications of topology are in many fields. It is used in computer science to encode the data set in the form of a specific version of Betti number called as a barcode. Under cosmology, topology can be used to determine the shape of the universe (known as space-time topology).

Numerical analysis is a vast subject that includes analysis of techniques in order to get approximate solutions to difficult problems and the study of algorithms & design. Numerical analysis includes, interpolation, extrapolation, regression, optimization, evaluating integrals, computing values of function etc. Numerical analysis is used in solving difficult engineering problems (solution of higher order differential equations, evaluations of integrals).

Functional analysis is the branch of mathematics that is derived from the study of vector spaces equipped with some limitations (example, inner product, norm, topology, etc.) Functional analysis includes, Normed vector spaces which further includes Hilbert spaces and Banach spaces. Hahn-Banach theorem one of the important theorems in functional analysis is used in financial mathematics in the Fundamental theorem of asset pricing. Another important application is signal analysis and data compression.

Example 1. What is bank reconciliation statement?
Example 2. Explain the importance of Bank Reconciliation Statement and give real examples explaining all possible items that make differences between cash balance in general ledger and bank statement balance.
Example 3. When Cash is presented on a Balance Sheet, what are the details of the Cash A/C? How does a Bank Reconciliation Statement factor into the Cash Balance? Please be specific in your details.
Example 4. A firm’s bank reconciliation statement shows a book balance of $32,740, an NSF check of $1,350, and a service charge of $95. Its adjusted book balance is

- $31,485.
- $34,185.
- $33,995.
- $31,295.

Complex analysis is a category of analysis that deals with the complex numbers. In simpler terms it is the study of complex functions of a complex variable and their algebra, geometry dealing with derivatives, integration, and other practical applications. Various important results include Cauchy Integral theorem, Morera’s Theorem, Liouville’s Conformality Theorem etc. Complex analysis has its real-life applications in mainly engineering, specifically nuclear, electrical, mechanical and aerospace engineering.

The sub-subject “Differential geometry” is a branch of mathematics that uses the performances of differential & integral calculus and multilinear algebra. The concepts that are mainly covered in differential geometry are the geometry of plane curves, curvature of curves and surfaces etc. An important application of differential geometry is in the field of economics. It is used to investigate the geometrical structures. Also, it is applied in engineering to solve the problems related to digital signaling processes.

Real analysis is a subdivision of pure mathematics that sets the ground work for numerous other subfields, such as probability, calculus and differential equations.Consecutively, real analysis is grounded on fundamental concepts from number theory and topology. A strong experience in calculus, logical reasoning and proofs is needed to study real analysis.

Engineering mathematics is one major sub-subject in Mathematics which is the building block of all the streams and lays foundation of the concepts for all the students of graduates studying in the sciences and engineering. Engineering mathematics consists of all the topics in differential calculus, integral calculus, linear algebra and differential equations with applications to various engineering problems.

1. Apply the product rule for exponents, if possible. 25) (-2×3)(9x10y6) 26) 5 5 -3 -3 0 4

2. A recipe calls for 1/2 cups of sugar. You find that you only have 1/18 cups of sugar left. What fraction of the recipe can you make? Your answer must be a fraction written in simplest terms. If your answer is a whole number, then give your answer as a fraction with 1 in the denominator. Cups of sugar

1. Apply the product rule for exponents, if possible. 25) (-2×3)(9x10y6) 26) 5 5 -3 -3 0 4

2. A recipe calls for 1/2 cups of sugar. You find that you only have 1/18 cups of sugar left. What fraction of the recipe can you make? Your answer must be a fraction written in simplest terms. If your answer is a whole number, then give your answer as a fraction with 1 in the denominator. Cups of sugar

1. Write the following in terms of sin e and cos θ; then simplify if possible. (Leave your answer in terms of sin θ and/or cos θ.) csc θ tan θ Need Help?

2. Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if po log

1. Congruent Inscribed Angles Proof.How would you prove that two angles in a circle that inscribe the same arc are congruent?Is it possible to prove it without using the “Congruent Inscribed Angles Theorem”

2.a. fx,y)-(e,cos(xy Let c(t) be a path with c(0) (0,0) and c'(0) 1,2). What is the tangent vector to f o clt) at t 0 b. fr,y)-esinx-y Let c(t) be a path with c(0) (0,0) and c'(0) (2,-3). What is the tangent vector to fo clt) at t0

1. Why is the magnitude of the sum of two vectors less than or equal to the sum of the magnitudes of each vector? Please be as detailed as possible.
2. 1)Explain why you will get an error for cos-1(-1.008). Specific.2) Solve algebraically, 2sin(3x)-1=0, give the first exact positive solutions.

Single variable calculus is a branch of calculus that deals with functions of a single variable. The topics which are involved within single variable calculus are limits and continuity, applications of graphing, rates and approximations, differentiation and integration of functions in a single variable.

Multi variable itself defines its meaning that more than one variable. Multi variable is the extended form of calculus of single variable to more than one variable. It studies the function of more than one variable. It deals with so many topics such as Gradient, flux, vector field, surface integral Jacobian, Differential operator, Contour integral etc. There are lots of applications of multi variable calculus in day to day life, such as, in the stock market, in engineering, social science, to analyse deterministic systems etc.

The sub-subject “Vector calculus” is a branch of Mathematics that disturbed with differentiation and integration of vector fields, primarily in 3 – dimensional. Sometimes {\displaystyle \mathbb {R} ^{3}.}Sometimes vector calculus is used as an alternative of multivariable calculus, which includes partial differentiation and multiple integration along with calculus. Vector calculus plays a crucial part in differential geometry as well as study of partial differential equations.

Advanced calculus is the further advanced extension of calculus that deals with the functions of one variable together with the linear algebra. Main topics included in advanced calculus are vector spaces, Differential calculus, Reiman integration etc. Advanced calculus has its main applications in field like statistics majorly.

Discrete Math Discrete mathematics is a category of mathematics that deals with the objects discretely or rather distinctly. Unlike the term ‘continuous’ used in real analysis, the values in discrete are treated separately. The study of Discrete mathematics involves the concepts like sets, relations and functions, graph theory, Boolean algebra, probability, counting theory etc. The main applications of Discrete mathematics are in the computer science field for computing, programming languages, algorithms, cryptography, etc.

Finite mathematics is the part of calculus. It is concerned with limits, finite number of variables, linear programming, elementary matrix algebra, introduction to probability, mathematics of finance etc. Finite mathematics gives a survey of mathematical techniques and has many applications in day to day life, such as linear programming is used for transportation optimization, Probability is used in weather prediction, sports strategies etc.

Applied Mathematics is concerned with mainly focused on the applications of Mathematics. It deals with the applications of calculus, differential equations. etc. Important applications of applied part are in the field of business, life sciences, social science, computer science, etc.

Biology is a category of mathematics that deals with the study and theoretical analysis of living organisms. The mathematical problems that require the knowledge of biology comes under this division of mathematics. Main topics that come under this are Mainly related to real life problems that relates to cell biology, ecology, evolution, molecular biology, etc. One of the most common and well-known problem it deals with is Cancer-Inspired Free Boundary Problem.

1. A drug is given at an infusion rate of 50 mg/h. The drug concentration value determined at 3.2 h after the start of the infusion is 8 mg/L. Assuming the patient has 5.4 L of blood, estimate the half-life of this drug. Round your answer to two decimal places.

2. In a sorority with 40 members, 18 take Mathematics, 5 take both Mathematics and biology, and 8 take neither Mathematics nor Biology. How many take Biology but not Mathematics.

3. What is the difference between discrete and distributed time delay in mathematical biology? advantage and disadvantage?

4. (a) Why Is Mathematical Biology So Hard?

(b) What is one example of a biological question to solve using mathematics?

Business mathematics is the arithmetic used by profitable firms to evident and accomplish corporate maneuvers. Commercial organizations make use of mathematics in financial analysis, forecasting, inventory management, accounting and marketing. Business management can be done more efficiently by making use of more advanced mathematics like linear programming, calculus and matrix algebra.

1. What did you learn in business mathematics class especially related to payroll?

2. John invested $15,000 in a mutual fund for 4 years ago. If the fund grew at the rate of 9.8%/year compounded monthly, what would John’s account be worth today?

3. Determine the utilization and the efficiency for each of these situations: A. A loan processing operation that processes an average of 7 loans per day. The operation has a design capacity of 10 loans per day and an effective capacity of 8 loans per day. B. A furnace repair team that services an average of four furnaces a day if the design capacity is six furnaces a day and the effective capacity is five furnaces a day. C. Would you say that systems that have higher efficiency ratios than other systems will always have higher utilization ratios than those other systems? Explain.

4. WDH Incorporation has borrowed $1,000,000 to purchase new factory equipment and the company must repay the loan in 5 years, quarterly at 7% interest rate and interest rate per period is 1.75%. Find the quarterly payment to be made by the company to discharge the loan in time.

OR is signifies research on operations. OR is a scientific method of providing explicit quantitative understanding and assessment of complex situations for better decision making. In operation research, problems are broken down into basic components solved by constructing mathematical models and deriving the solution of the model. Operation research used for solving different types of problems like problem dealing with the waiting line, problem dealing with the allocation of materials etc. Operation research has a several types of methods like linear programming, network flow programming, integer programming, non-linear programming, and dynamic programming.

1. Consider a statistical decision (e, M,, L) with sample space X where Θ-(01, θ2), H and ye [0,0.25)). Find the minimax decision. in R2 plane. Further show that the class of all non-randomized Bayes decisions.

2. In a point estimation problem e-(0,) A (0, and X follows Poisson distribution with parameter 8 and a sample of size one is made available. Show that the estimator T0X) – X is not Bayes but a generalized Bayes under quadratic loss.

Joe Zilch is practicing basketball by repeatedly making attempts (shots) to put the ball in the basket. We label his first shot as random variable (RV) XI , second shot as X2,…, nth shot as X,, etc. When he takes the nth shot, he either makes a basket (X, -1) or misses (X,-0 ). He finds that the result of any shot x, depends on the outcome of his last two shots X -2 and X- as follows:

P(X-1 l he missed both of his last two shots) 1/2

P(X-1 l he made one of his last two shots) 2/3

P(X1 l he made both of his last two shots) – 3/4

a). Show how Joe’s basketball play may be modeled using a Markov chain. How many states are needed? (Hint: Define a state as the outcome of his last two shots). Draw a labeled state transition diagram or trellis describing the process

b). Find the transition matrix P for the process

c). Given that he missed his first two shots, find the joint probability that Joe makes shots number 3 and 4. d). Joe made his first two shots with probability 0.5 and missed his first two shots with probability 0.5. Given these facts, find the joint probability that Joe makes shots number 3 and 4

e). Find the probability that Joe makes any single shot in the long run.

1. A recent article in the Arizona Republic indicated that the mean selling price of the homes in the area is more than $220,000. Can we conclude that the mean selling price in the Goodyear, AZ, area is more than $220,000? Use the .01 significance level. What is the p-value?

1. Let r є N. Let X1,X2, be identically distributed random variables having finite mean m, which are r-dependent, i.e. such that XkXk,.,Xk, are independent whenever kiti > ki +r for each i. (Thus, independent random variables are 0-dependent.) Prove that with probability one, X Xi – m as n -oo. Hint: Break up the sum Ση! Xi into r different sums.

1. Bob, Kevin, and Jack are playing the following game: a single player will toss 5 fair coins. Assume the tosses are independent , and let H = 1 and T 0. Before the coin tosses, without consulting each other, each player chooses some number of the tosses (at least one) and calculates the sum (mod 2) of the tosses. That is the player’s score for example, supposed Kevin chose the second, third and fourth tosses, and Jack chose the first, second, and last toss. If the following coin tossing sequence occurs: HTHHT then Kevin’s score is 0 and Jack’s score is 1. Assume that each player does not select exactly the same subset of tosses.

(a) Show that the scores of the three players are pairwise independent

(b) Show that the scores of Bob, Kevin, and Jack are not always mutually independent. (A counter example when they are not independent is sufficient, but obviously explain your answer.)

1. Which statement about cardiac muscle is FALSE?

- A. Cardiac muscle cells must obey the all-or-none law of contraction. Intercalated disks contain both desmosomes for firm attachment and gap junctions to allow communication.
- B. Calcium-induced calcium release is when extracellular Ca2s stimulates the release of Ca2 from the sarcoplasmic reticulum.
- C. The energy demand of cardiac muscle cells is high because they have many mitochondria.
- D. Cardiac muscle cells use Ca2+ions released from the sarcoplasmic reticulum.

- (A) Abdominal
- (B) Cranial
- (C) Pleural
- (D) Spinal
- (E) Thoracic

- Based on Havighurst’s developmental task theory:
- Explain Susan’s behavior.
- State four (4) priority nursing concerns and related nursing interventions for Susan.

1. Explain briefly about the role of conflict experienced in the psychosexual stages of psychoanalysis.

2. What is the primary difference between acute stress disorder and post-traumatic stress disorder according to the DSM-V criteria?

3. Explain the role of a counselor in an industrial set-up. What are the major challenges experienced in this profession?

4. Describe any two projective tests and their interpretation. What are the limitations of these assessments?

5. Imagine you have a client who has been sexually abused. What is your role as a mental health professional in dealing with this client? Provide a treatment plan and mention about the laws pertaining to this case.

6. Explain correlation and progression analysis and provide examples of research questions where these methods can be used.

Q1. Briefly outline the steps in the formation of our solar system, according to the nebular theory.

Q2. Describe the origin of the Moon.

Q3. Compare and contrast bright and dark nebulae.

Q4. What are three main types of galaxies? What type of galaxy is our Milky Way?

Q1. What would Earth be like without greenhouse effect?
Q2. What is Ozone depletion? What causes Ozone depletion? What is the status of ozone layer recovery?
Q3. What are the human activities that cause acid rain?
Q4. What are the primary objectives of the Kyoto protocol?

Q1. What are two basic wind measurement? What instruments are used to make these measurements?
Q2. Briefly explain how flow aloft aids the formation of cyclones at the surface.
Q3. Name the scale commonly used to rate tornado intensity. How is a rating on this scale determined?
Q4. Why is rainfall easier to measure than snowfall?

Q1. Describe bathymetry.

Q2. List the three major features of active continental margin.

Q3. What is the primary reason for the elevated position of the oceanic ridge system.

Q4. Why are seafloor sediments useful in studying past climates?

Q1. List the seven largest lithospheric plates.

Q2. Describe the process that leads to the formation of deep ocean trenches.

Q3. Describe slab pull and ridge push. Which of these forces appears to contribute more to plate motion?

Q4. How does divergent plate boundaries help in the formation of new oceanic crust?

Example 1. The ________ method allows managers to increase operating income through production by producing more products than needed.

- variable costing
- direct costing
- marginal costing
- absorption costing

- Product Cost under absorption; Product Cost under variable
- Period Cost under absorption; Product Cost under variable
- Period Cost under absorption; Period Cost under variable
- Product Cost under absorption; Period Cost under variable

- both absorption costing and variable costing.
- absorption costing but not variable costing.
- variable costing but not absorption costing.
- neither variable costing nor absorption costing.

- Absorption costing uses (a) and variable costing uses (b).
- Variable costing uses (a) and absorption costing uses (b).
- Variable costing uses (a) and absorption costing uses neither.
- Absorption costing uses (a) and variable costing uses neither.

Example 1. Differential analysis can be used to determine whether to keep or drop a customer. The format is similar to differential analysis used for making product line decisions. What is the difference between differential analysis used to evaluate customer decisions and differential analysis used to make product line decisions? Select one:

- In differential analysis for customer decisions, factor costs, shadow costs, and imputed costs are traced directly to customers rather than to product lines.
- In differential analysis for customer decisions, sales revenue, variable costs, and fixed costs are traced directly to customers, rather than to product lines.
- In differential analysis used customer decisions, discounted prices, increasing costs, and stop/loss costs are traced directly to customers, rather than to product lines.
- In differential analysis for customer decisions, sales predictions, variable input costs, and unallocated overhead costs are traced directly to customers, rather than to product lines.

Example 1. Explain the concept of incremental analysis. Is an incremental analysis often the most direct route to a business decision?
Example 2. What is incremental analysis? In what types of situations is incremental analysis most useful? Discuss
Example 3. Often the most direct route to a business decision is an incremental analysis. What is meant by an incremental analysis?
Example 4. Describe one of the methods of incremental analysis and the outside factors that a manager should consider when performing this type of incremental analysis.

Inorganic chemistry is a branch of chemistry which deals with all main group elements, transition and inner transition elements. It mainly focusses on preparations, properties and structure of inorganic compounds. Group theory, chemical bonding, coordination compounds, atomic structure, periodic properties, acids and bases are major topics in inorganic chemistry. Bioinorganic chemistry deals with biological importance molecules. Different spectral techniques help to understand bonding and structural features in inorganic compounds.

Horizontal Analysis: This involves comparing the financial statements of one year with the past year(s). The comparison is done between the exact line items; for example, comparing the values of the interest income of the current year with the past year(s) and expressing them in terms of the percentage or dollar.

Vertical Analysis: This involves presenting each line item as a percentage of another item. For example, presenting all the items listed under asset side of the balance as a percentage of total assets.

Ratio Analysis: This type of analysis involves comparing two different line items and expressing them in terms of ratios. The two items/accounts may either belong to the same financial statement (say two items of income statement) or it can be from two different statements. Ratio between the net income and the amount of equity is one such example where the accounts belong to different statements. Further, the line items considered for calculating the ratios belong to the same year.

Example 1. Distinguish between horizontal and vertical analysis of financial statement data.
Example 2. Vertical analysis of financial statements is accomplished by preparing common-size statements. True False
Example 3. Example and how to1. Types and purpose of analysis of financial statements and what each indicates
Example 4. Investment Analysis and Portfolio Management (with Thomson ONE – Business School Edition and Stock-Trak Coupon) (10th Edition) Describe briefly two decisions that requires the analysis of financial statements
Example 5. In determining whether a company’s financial condition is improving or deteriorating over time, horizontal analysis of financial statement data would be more useful than vertical analysis.True False

Example 1. Just as we did in chapter two, analyzing transactions is critical to making sure that we understand the transactions prior to recording it in the appropriate account. What are the three steps recommended by the author of your text for analyzing the effects of business transactions? Which step did you find most difficult/easy, and most helpful? Explain!
Example 2. The accounting process involves all of the following except:

- communicating financial information to users by preparing financial reports.
- analyzing and interpreting financial reports.
- identifying economic transactions that are relevant to the business.
- recording nonquantifiable economic events

- Recording adjusting transactions.
- Posting transactions to special journals.
- Accumulating debits and credits
- Collecting detailed listings of amounts

Example 1. Describe the difference and similarities between adjusting and closing entries?

Example 2. What are the major differences between the perpetual inventory system and the periodic inventory system? What are special considerations for each when doing adjusting and closing entries?
Example 3. Van Frank Telecommunications has a patent on a cellular transmission process. The company has amortized the $16.20 million cost of the patent on a straight-line basis since it was acquired at the beginning of 2014. Due to rapid technological advances in the industry, management decided that the patent would benefit the company over a total of six years rather than the nine-year life being used to amortize its cost. The decision was made at the end of 2018 (before adjusting and closing entries).
What is the appropriate adjusting entry for patent amortization in 2018 to reflect the revised estimate? (If no entry is required for a transaction/event, select “No journal entry required” in the first account field. Enter your answers in millions rounded to 2 decimal places (i.e., 5,500,000 should be entered as 5.50).)
Example 4. Van Frank Telecommunications has a patent on a cellular transmission process. The company has amortized the $24.30 million cost of the patent on a straight-line basis since it was acquired at the beginning of 2012. Due to rapid technological advances in the industry, management decided that the patent would benefit the company over a total of six years rather than the nine-year life being used to amortize its cost. The decision was made at the end of 2016 (before adjusting and closing entries).
What is the appropriate adjusting entry for patent amortization in 2016 to reflect the revised estimate. (If no entry is required for a transaction/event, select “No journal entry required” in the first account field. Enter your answers in millions rounded to 2 decimal places (i.e., 5,500,000 should be entered as 5.50).)

Example 1. What is bank reconciliation statement?

Example 2. Explain the importance of Bank Reconciliation Statement and give real examples explaining all possible items that make differences between cash balance in general ledger and bank statement balance.
Example 3. When Cash is presented on a Balance Sheet, what are the details of the Cash A/C? How does a Bank Reconciliation Statement factor into the Cash Balance? Please be specific in your details.
Example 4. A firm’s bank reconciliation statement shows a book balance of $32,740, an NSF check of $1,350, and a service charge of $95. Its adjusted book balance is

- $31,485.
- $34,185.
- $33,995.
- $31,295.

1. You were planning to spend Saturday working at your part-time job, but a friend asks you to go skiing. What is the true cost of going skiing? Now suppose you had been planning to spend the day studying at the library What is the cost of going skiing in this case? Explain.

2. Pat and Kris are roommates. They spend most of their time studying (of course), but they leave some time for their favorite activities: making pizza and brewing root beer. Pat takes 4 hours to brew a gallon of root beer and 2 hours to make a pizza. Kris takes 6 hours to brew a gallon of root beer and 4 hours to make a pizza. ‘’

a. What is each roommate’s opportunity cost of making a pizza? Who has the absolute advantage in making pizza? Who has the comparative advantage in making pizza?

b. If Pat and Kris trade foods with each other, who will trade away pizza in exchange for root beer?

c. The price of pizza can be expressed in terms of gallons of root beet What is the highest price at which pizza can be traded that would make both roommates better off? What is the lowest price? Explain.

3. Maria has decided always to spend one-third of her income on clothing.

a. What is her income elasticity of clothing demand?

b. What is her price elasticity of clothing demand?

c. If Maria’s tastes change and she decides to spend only one-fourth of her income on clothing, how does her demand curve change? What is her income elasticity and price elasticity now?

4. What happens to consumer and producer surplus when the sale of a good is taxed? How does the change in consumer and producer surplus com-pare to the tax revenue? Explain.

5. You are thinking about setting up a lemonade stand. The stand itself costs $200. The ingredients for each cup of lemonade cost $0.50.

a. What is your fixed cost of doing business? What is your variable cost per cup?

b. Construct a table showing your total cost, average total cost, and marginal cost for out-put levels varying from 0 to 10 gallons. (Hint: There are 16 cups in a gallon.) Draw the three cost curves.

1. Give some reasons why gross domestic product is not a suitable measure of the well-being of the nation. (Have you noticed newspaper accounts in which journalists seem to use GDP for this purpose?)

2. Country A and Country B have identical population growth rates of 1 percent per annum, and everyone in each country always works 40 hours per week. Labor productivity grows at a rate of 2 percent in Country A and a rate of 2.5 percent in Country B. What are the growth rates of potential GDP in the two countries?

3. The following table shows real GDP per hour of work in four imaginary countries in the years 2000 and 2010. By what percentage did labor productivity grow in each country? Is it true that productivity growth was highest where the initial level of productivity was the lowest? For which countries?

4. What is a consumption function, and why is it a useful device for government economists planning a tax cut?

5. Comment on the following statement: “Inflationary and recessionary gaps are nothing to worry about because the economy has a built-in mechanism that cures either type of gap automatically.”

1. R.C. had earnings per share of $8 in year 2015, and it paid a $4 dividend. Book value per share at year’s end was $80. During the same period, the total retained earnings increased by $24 million. R.C. has no preferred stock, and no new common stock was issued during the year. If R.C.’s year-end debt (which equals its total liabilities) was $240 million, what was the company’s year-end debt ratio?

2. You are about to borrow $15,000 from a bank at an interest rate of 8% compounded annually. You are required to make three equal annual repayments in the amount of $5,820.50 per year, with the first repayment occurring at the end of year 1. Show the interest payment and principal payment in each year.

3. On October 1, 1970, Walmart first offered 300,000 shares of its common stock to the public at a price of $16.50 per share. Since that time, Walmart has had 11 two-for-one stock splits. So, if you purchased 100 shares in 1970, you would have 204,800 shares as of September 30, 2014. The closing price of the stock on that day was $77.50. What is the compound growth of the Walmart stock over 44 years? (This is equivalent to asking what kind of interest rate you have to earn to match the same growth from your savings account.)

4. Student Emergency Financial Services, Inc., which makes small loans to college students, offers to lend $550. The borrower is required to pay $42 at the end of each week for 16 weeks. Find the interest rate per week. What is the nominal interest rate per year? What is the effective interest rate per year?

5. A local delivery company has purchased a delivery truck for $15,000. The truck will be depreciated under MACRS as five-year property. The truck’s market value (salvage value) is expected to decrease by $2,500 per year. It is expected that the purchase of the truck will increase its revenue by $10,000 annually. The O&M costs are expected to be $3,000 per year. The firm is in the 40% tax bracket, and its MARR is 15%. If the company plans to keep the truck for only two years, what would be the equivalent present worth?

A set of guidelines company managers follow to distribute the earnings of the company to its shareholders. Few companies follow stable dividend policy where few companies follow regular dividend policy. In most of the stance’s companies distribute dividend considering the investment requirement and the sentiment of investors and the market.

1. The indifference policy advocates that –

a. dividend policy is irrelevant.

b. dividend policy is irrelevant as long as the firm’s investment policy is modified for dividend changes.

c. firms are indifferent to dividend policy, but stockholders are not.

d. dividends are irrelevant.

e. stockholders are indifferent to dividend policy only as long as dividends are held constant.

In a swap agreement, the parties agree to pay and receive interest on notional value. The notional value does not transfer from one party to other. The cash flows occur in terms of interest. One party pay at fixed interest rate whereas, the another pay at floating interest rate.

1. Consider the following interest rate swap scenario: notional =$10MM, actual days in quarter=92, annualized floating rate = 2.5400%, and annualized fixed rate = 2.5400%. What is the floating leg payment?

a. $62,088.89

b .$65,0911.89

c. $64,911.11

d. $127,000

2. If the fixed payment is greater than the floating payment, then

a. The net received by the long interest rate swap position will be position

b. The net received by the long interest rate swap position will be negative

c. The net received by the long interest rate swap position will be zero

d. The net received by the long interest rate swap position will be 100% of the notional principal

In general, the price level changes indicate the inflation or deflation in the economy. The changes in price level affect the cost of input and the price of output. Also, it affects the interest rate in the economy and to be demanded by the lenders. This is because lenders are more interested in inflation free interest rate.

Which of the following statements is correct?

a. Along a Marshallian demand curve, the level of utility is held constant and the level of income changes. Consequently, movements along this demand curve illustrate only substitution effects of price changes.

b. Along a compensated (Hicksian) demand curve, the level of utility is held constant and the level of income changes. Consequently, movements along this demand curve illustrate only substitution effects of price changes.

c. Along a Marshallian demand curve, both the level of utility and the level of income are held constant. Consequently, movements along this demand curve illustrate only substitution effects of price changes.

d. Along a compensated (Hicksian) demand curve, both the level of utility and the level of income are held constant. Consequently, movements along this demand curve illustrate both substitution effect and income effect of price changes.

In general, the price level changes indicate the inflation or deflation in the economy. The changes in price level affect the cost of input and the price of output. Also, it affects the interest rate in the economy and to be demanded by the lenders. This is because lenders are more interested in inflation free interest rate.

Which of the following statements is correct?

a. Along a Marshallian demand curve, the level of utility is held constant and the level of income changes. Consequently, movements along this demand curve illustrate only substitution effects of price changes.

b. Along a compensated (Hicksian) demand curve, the level of utility is held constant and the level of income changes. Consequently, movements along this demand curve illustrate only substitution effects of price changes.

c. Along a Marshallian demand curve, both the level of utility and the level of income are held constant. Consequently, movements along this demand curve illustrate only substitution effects of price changes.

d. Along a compensated (Hicksian) demand curve, both the level of utility and the level of income are held constant. Consequently, movements along this demand curve illustrate both substitution effect and income effect of price changes.

A set of guidelines company managers follow to distribute the earnings of the company to its shareholders. Few companies follow stable dividend policy where few companies follow regular dividend policy. In most of the stance’s companies distribute dividend considering the investment requirement and the sentiment of investors and the market.

1. The indifference policy advocates that –

a. dividend policy is irrelevant.

b. dividend policy is irrelevant as long as the firm’s investment policy is modified for dividend changes.

c. firms are indifferent to dividend policy, but stockholders are not.

d. dividends are irrelevant.

e. stockholders are indifferent to dividend policy only as long as dividends are held constant.

In a swap agreement, the parties agree to pay and receive interest on notional value. The notional value does not transfer from one party to other. The cash flows occur in terms of interest. One party pay at fixed interest rate whereas, the another pay at floating interest rate.

1. Consider the following interest rate swap scenario: notional =$10MM, actual days in quarter=92, annualized floating rate = 2.5400%, and annualized fixed rate = 2.5400%. What is the floating leg payment?

a. $62,088.89

b .$65,0911.89

c. $64,911.11

d. $127,000

2. If the fixed payment is greater than the floating payment, then

a. The net received by the long interest rate swap position will be position

b. The net received by the long interest rate swap position will be negative

c. The net received by the long interest rate swap position will be zero

d. The net received by the long interest rate swap position will be 100% of the notional principal

In general, the price level changes indicate the inflation or deflation in the economy. The changes in price level affect the cost of input and the price of output. Also, it affects the interest rate in the economy and to be demanded by the lenders. This is because lenders are more interested in inflation free interest rate.

Which of the following statements is correct?

a. Along a Marshallian demand curve, the level of utility is held constant and the level of income changes. Consequently, movements along this demand curve illustrate only substitution effects of price changes.

b. Along a compensated (Hicksian) demand curve, the level of utility is held constant and the level of income changes. Consequently, movements along this demand curve illustrate only substitution effects of price changes.

c. Along a Marshallian demand curve, both the level of utility and the level of income are held constant. Consequently, movements along this demand curve illustrate only substitution effects of price changes.

d. Along a compensated (Hicksian) demand curve, both the level of utility and the level of income are held constant. Consequently, movements along this demand curve illustrate both substitution effect and income effect of price changes.

Which of the following statements is correct?

Thermodynamics deals with the treatment of solutions or fluids by changing the temperature or heat source. Thermodynamics is the basis for the other chemical engineering subjects (heat and mass transfer and reaction engineering). Thermodynamics includes laws of thermodynamics and their application, concepts of enthalpy and entropy, real and ideal fluids, solution thermodynamics, phase equilibrium, heat engines and heat pumps.

1. We are interested in modelling methane gas with the virial equation of state truncated at the second virial coefficient. The Lennard -Jones potential parameters σ =3.783 Å and ε/k =148.9K.(a) Determine the B(T) at 150, 400 and 600 K in units of cm3/mol.(b) At 150K, what is the constant volume heat capacity if Cv(ideal)= 33.4 and pressure is 1bar?

2. Calculate the relative change in saturation vapor pressure of water at 300 K when it is dispersed in droplets (pore) of 0.1 μm radius. Given: γw = 0.073 N/m.

Mass transfer is the subject which deals with the transfer of a mass (or) substance from one phase to another phase on a molecular scale. The phase may be a solid or fluid (gas or liquid).The mass transfer operations include gas-Liquid operations such as absorption, stripping, distillation and humidification, solid- fluid operations such as drying, leaching, adsorption and Ion exchange, liquid-liquid operations such as liquid extraction.

1. Estimate the mass transfer coefficient, kc, in a wetted-wall column (wetted with benzene) for the transfer of benzene into carbon dioxide at 0o C. The carbon dioxide gas velocity through the column is 1.25 m/s. The diameter of the column is 0.16 m. Assume that the benzene concentration in the carbon dioxide gas is very low.

Mass density of CO2 = 1.966 kg/m3

Viscosity of CO2 = 1.35 x 10-5 kg/m∙s

Diffusivity of benzene in CO2 = 5.28 × 10-6 m2 /s

Molecular weight of CO2 = 44 g/g mol

Molecular weight of benzene = 78 g/g mol

Note that the friction factor, f, can be correlated with the Reynolds number, Re, as follows: f/2 = 0.023Re^(-0.2) for Re between 5,000-200,000for f Calculate kc based on (a) the Reynolds Analogy, (b) the Chilton-Colburn Analogy, (c) mass transfer correlation (use the table given in the class). Which mass transfer coefficient is more accurate and why?

2. The total weight of the basket and the semi-wet clothes before drying was 13.9 kgs. Dr. Blowers’ wife pulled in the laundry that afternoon and weighed it again in the basket and it came in at 20.5 lbs. Estimate the volume of entering air that would have been needed to dry the Blowers’ clothing if they had used their dryer in the utility room instead of sun drying it, and the air coming in to the dryer was at 67% rh and was left with a humidity of 1% at 183 oC

Heat transfer deals with the transfer of heat from higher temperature to a lower temperature by three modes of transfer conduction, convection and radiation.This subject includes conduction, heat transfer in fluids with phase change and without phase change, radiation and heat exchange equipment.

1. A triple effect evaporator is supplied with saturated steam at 2500F. The temperature at the last effect is 150oF. The overall heat transfer coefficients are 150, 200, and 250 BTU/hr-ft2- oF in the 1st, 2nd, and 3rd effects, respectively. If the total BPR in the three effects is 55oF, what is the area of the first effect if the steam used is 10,000 lb/hr.

2. A turkey at room temperature is placed in a convection oven at 350 F (176.7 C). The turkey can be assumed to be a sphere with radius of 22 cm and thermal conductivity of 0.7 W/(m*K). The heat transfer coefficient between the turkey and the air in the oven is 5 W/(m^2*K). Will a temperature difference reading taken at a radial position of 8 cm be a good approximation to the temperature in the center of the turkey? Provide a quantitative answer.

Fluid mechanics is the subject which deals with the behaviour of fluids. It is divided into fluid statics (at rest) and dynamics (motion).Fluid mechanics includes the concepts flow of fluids through different boundaries and calculation of respective velocity gradients, pressure, friction factors of the fluid throughout the length of the boundary taken with respect to their flow types of laminar or turbulent

1. A 50 g/l of a solution of a BSA protein with a constant specific filtration resistance of 4 x 1011 m/kg is being filtered in a cross flow set up at a constant rate of 5 x 10-5m/s. In constant rate filtration, the pressure is varied as a function of time. If the membrane resistance is negligible and the reaction rate kr is 0.0015 s-1determine the pressure after 1 hour. If the area of the filter is 0.1 m2, what is the production rate of the clear permeate in litres per hour

2.In a natural gas pipeline at section 1 the pipe diameter is 1.5 ft and the flow conditions are 900 psia, , and 50 ft/sec velocity. At section 2 the pipe diameter is 3.5 ft and the flow conditions are 600 psia, . What is the velocity at section 2 and what is the mass flow rate.

Chemical process calculations deal with the unit operations involved in manufacturing industries. This subject introduces the fundamental concepts of the system of units and dimensions, mass and energy balances, their application in chemical process industries, Recycle, purge, degrees of freedom, balances on non-reactive and reactive processes.

1. I need to calculate the enthalpy Hrxn from the combustion of methane gas. Starting with 500kg of methane and 120 percent excess air. The temperature of the reactants are state functions at 25 C and products temp is 450 C.

2. A mixture of gaseous fuels is burned in an experimental furnace by conventional techniques. The combustion gas is analyzed there is no reason to question the dependability of the results. What is the composition of the fuel for the case in which:

a) The fuel is a mixture of CH4 and NH3 and the analysis results are 6.2% CO2, 4.6% O2, and 89.2% N2?

b) The fuel is a mixture of CH4 and HCN and the analysis results are 10.8% CO2, 4.1% O2, and 85.1% N2?

Chemical reaction engineering subject plays a key role in chemical process industries. It explains complex reactions, and studies how a reaction takes place in a reactor through reaction kinetics, and design of a chemical reactor.This subject introduces analysis of chemical reactors, an ideal flow and non-ideal flow in a chemical reactor, reactor kinetics, chemical reactor design, compartment models, fluid-solid catalytic reactors and biochemical reactor systems.

Process dynamics and control is the subject which deals with the disturbances occur in an equipment used in the chemical process and the control mechanisms of that disturbances to avoid undesired products.Process dynamics and control include the concepts of Laplace transforms, different types of disturbances occur in the equipment, order of the different systems, types of controllers, stability of the system, frequency response and design of control system by using frequency response.

Transport phenomena is a subject which deals with the transport of different quantities such as momentum, energy and mass in a chemical process. It is the combination of fluid mechanics, heat transfer and mass transfer. It gives the idea about the similarities among the three transport quantities.Transport phenomena include the concepts of basics laws of momentum, heat and mass, shell balances of momentum, energy and mass, distributions of velocity in momentum, distributions of temperature in energy and distributions of concentration in mass.

This topic deals with the designing of chemical plants based on economic evolution (profits and losses) and development of production. Plant design involves design of individual process equipment for the entire production. It includes:Process design development, cost estimation, taxes and insurance, depreciation, material selection and equipment fabrication and statistical analysis in design.

Surveying is generally referred as an art or science which helps in determining the locations of several points with respect to the earth’s surface. This is precisely performed on the surface of the earth. This is done by finding the spatial location which comprises both relative and absolute location of points on or near the surface of the earth. It can be used to measure the horizontal distance, vertical elevation, horizontal and vertical angles between two points.

This branch of engineering is deals with analysis and design of bridge spans, foundations, frames, dams, buildings and other structures that are subjected to dead loads, live loads or a combination of both. Structural analysis makes use of the concepts such as applied mechanics along with structural analysis concepts to calculate the deformation of the structures, internal forces, support reactions, and structural stability.

This division of engineering which involves the natural resources that are close to the earth’s surface. In this discipline the concepts and principles of soil mechanics and rock mechanics are applied in for designing of earth structures, retaining structures and foundation of various structures. Every civil engineering project or construction typically begins with a geotechnical engineer testing the soil.

1) Refer to the following data: yd in in borrow pit, 87.9 pcf; W in borrow pit, 13.0%; Gs, 2.70; Modified Proctor W(opt), 14.0%; Modified Proctor ydmax, 116.0 pcf. Assume that 50000 yd3 of the soil from the borrow pit is to be delivered to an embankment at a construction site. By the time it reaches the site, the water content is 9%. It will be compacted to a minimum of 90% of modified Proctor maximum dry density. Determine the total volume of water (in ft3) that must be added to the soil to increase the moisture content to the optimum level.

2) The post is made of Douglas fir and has a diameter of 100 mm . (Figure 1) It is subjected to the load of 20 kN and the soil provides a frictional resistance distributed along its length and varies linearly from w=2.4 kN/m at y=0 m to w=16.4 kN/m at y=2 m . Neglect the weight of the post. 3) Weight of dry aggregate = 41 lb. Weight of SSD aggregate = 43.46 lb Total particle volume- 0.25 ft. Calculate

(a) Bulk dry unit weight

(b) Bulk SSD unit weight

(c) Bulk dry specific gravity

(d) Bulk SSD specific gravity

4) Given: Bank Dry Density: 108 lb/CuFt

Loose Dry Density: 85 lb/CuFt , Compacted Dry Density: 120 lb/CuFt

Find: Swell%, Shrinkage%, Quantity of trucks needed for transport, Cost.

Transportation engineering or transport engineering is the branch of Civil Engineering which apply technology and scientific principles to the planning, functional design, operation and administration of services for any mode of transportation to provide for the safe, proficient, rapid, comfortable, convenient, economical, and environmentally compatible movement of populace and commodities transport. However, it is intrinsically multidisciplinary overlaying diverse fields as economics, psychology, geography, public administration, political science, industrial & electrical engineering.

a) An existing rural freeway in rolling terrain is to be analyzed using the following information: 2 lanes in each direction, Peak hour volume is 3000 veh/h, 13% trucks, 5% recreational vehicles, PHF is 0.91,Lane width12 ft, Lateral clearance 10 ft, Average interchange spacing 1.6 mi. Commuter traffic only. Determine the LOS.

b) The posted speed limit on a four-lane freeway (two lanes in each direction) in rolling terrain is 60mph. The highway has the following characteristics:12ft lanes , 6ft shoulders, Peak hour Factor = 0.92, Peak hour Volume = 2400vph which includes 10% trucks and 6% RVs.If there are no interchanges on the section of highway being analyzed, determine the adjusted demand flow rate, density, and Level of Service.

c) A sag vertical curve has back tangent grade of -8.3% and a forward tangent grade of +1.7%. The design speed is 65 mph. What is the minimum vertical curve length based on headlight sight distance? What is the minimum vertical curve length based on comfort? What is the maximum vertical curve length based on drainage? What is the acceptable range of vertical curve lengths?

d) A segment of multilane highway has the following known characteristics: Total volume 7,200 vehicles/hr Directional split = 6040. Vis (peak direction) = 1,350 vehicles/hr . 4-lane, undivided roadway. BFFS = 55 mph. Level terrain · 7% trucks, 1 % RVs 11-ft lane widths e Right shoulder width 8 ft Left shoulder width = 4 ft. Length = 9 miles .45 access points. Driver population – primarily daily commuters Determine the expected LOS of this multilane highway segment during the peak hour for the peak direction.

Software Engineering is the study of software deployment cycles that define processes for design, development, testing, and maintenance of softwares.

Ohio State University wants to develop a new room scheduling system with the following main goals: R1: Maximize the number of hours a room is occupied. R2: Minimize the distance instructors have to walk among rooms accordingly to their schedule. R2: Minimize the distance that a students who follows the suggested schedule has to do.

1. Identify one risk (Rk1), its likelihood and the impact it can have on the satisfaction of R1, R2, and R3.

2. Estimate the criticality of rk1. Notice that R1, R2 and R3 have priority 0.9, 0.6, and 0.4, respectively.

With an outburst of sensitive data in the world today, and the relative ease of transferring data, and connecting over the internet, it has become crucial to implement techniques that ensure security of data during transmission.

Square the polynomial x^5+x^3+1 in GF(2^6) where the reduction polynomial is x^6+x^3+1. Write your output in bit vector form.

One of the earliest programming languages, whose extension is C++, C remains one of the most versatile and flexible languages and is useful in kernel level programming.

I want to model a simple dice game in c using a drand48 generator.

Game with two dice, a red one and a blue one. six dots on their sides.

You throw the two dice. It will cost you $1.00 for each throw of two dice. (initial value)

If the number of dots on the red dice is greater than the number of dots on the blue dice, you win $2.25.

So you have to pay $1.00 each time you play but you can win $2.25.If the number of dots on the red dice is greater than the number on the blue dice.Program/game needs to model the game to show if you will win money or lose money with the system. Using drand48() excute the results for 100 throws of the two dice.

Computer Organisation dives deep into computing fundamentals and studies the interaction between the design of hardware and software layers, in a computer system.

Write an assembly program Motorola 68000 program that calculates X (a 16bit number stored in memory) raised to the Y (a 8bit number stored in memory) power. The program should have a while repetition control structure.

Algorithms are the fundamental building blocks of computer science. They involve creating step by step procedures to solve complex problems, in a simplified and efficient manner, which is essentially what a computer does.

The 2 algorithms for comparison here can be bubble sort and selection sort. Code the selected algorithms Instrument your sort algorithms to calculate efficiency by gathering data on: Time for algorithm to run Number of swaps Number of comparisons Download the Peak Wind speed at 80meter data for your birthday in 2013 from the following website: https://www.nrel.gov/midc/apps/daily.pl?site=NWTC&start=20010824&yr=2014&mo=7&dy=24 Enter the date of your 2013 birthday as both the starting and ending date. Check the box for the “Pk Wind Speed (80m)” in the right-hand column. Select the output type “1-Min data (ASCII text)” in the left-hand column near the bottom Click on the Submit button. This will generate an ACSII list of the Peak Wind speed at 80meter in Colorado on your birthday in 2013. Copy and paste the data into a file. Working from this data file, load the last column (wind speeds) of the comma delimited file into a one-dimensional array. Run both of your instrumented algorithms again with the wind speed data you created. Save the sorted data in a new file to be used in Question 2. Display your results and discuss which algorithm performed better on your data set.

Question 2:Using the sorted data you created in Question 1, identify the maximum and minimum wind speed values. Create an array consisting of five “bins” that divide the extremes of the data range into five equally spaced partitions. Create code that will read in the unsorted data, counting the frequency of instances of the data falling into each bin/partition. Print out the frequencies in an informative format.

Analog circuits involve the use of analog signals, which vary continuously with time. The study of analog circuits involves the operation, analysis and applications of analog circuits, and their troubleshooting concepts. Analog circuits include diodes, transistors, operational amplifiers. The applications of analog circuits include Filters, Amplifiers, Oscillators and Timers, Voltage Regulators, communication and data conversion circuits.

Q1. Draw a basic full bridge rectifier schematic

Q2. For Si with ND 1016 cm-3, how hot does the Si need to be for the intrinsic level to be the same as the doping level? (ignore the temperature dependence of Nc, Nv) Draw a log (n) vs 1/T plot. Compare with GaAs and Ge, would the temperatures be higher or lower (why?)

Q3. Consider a receiver with the following specifications: Ap=80, NFtot= 3.4, B=100khz, 01P3-20 dBm, OP18-10 dBm.

The minimum required SNR is 15 dB for acceptable signal. Find the spurious-free dynamic range (SFDR) for the receiver, including the minimum SNR requirement, as defined in class.

MATLAB is an acronym for Matrix Laboratory. It is a fourth-generation programming language with huge command library of inbuilt functions. From algorithm development and analyzing data to designing models and real-time simulations, MATLAB can realize all the user’s ideas through its Graphical User Interface (GUI) and SIMULINK packages. MATLAB finds it application in control systems, Analysis and design of power systems, Image and signal processing, robotics, and in financial computations.

Q1. MATLAB exercise: Consider a periodic signal composed of three sinusoids of frequencies 700Hz, 1300Hz, and 2000Hz. Sample this signal at 3000Hz. After sampling, apply a low pass filter with a cut-off frequency of 1500Hz. What will be the components of the output signal? Use MATLAB to do the filtering. Show the original periodic signal and the recovered signal after filtering as plots in MATLAB

Q2. Write a MATLAB function that will take as inputs the values of the parameters of the equivalent circuit model of the synchronous machine as well as the information about the load on the machine and will produce voltage regulation and efficiency.

Power Electronics deals with the study of switching electronic circuits for the control and conversion of electrical energy. The switching circuits use power devices like diodes, power transistors and thyristors. The power-electronic circuits include rectifiers, inverters, choppers, cyclo-converters, voltage regulators and their applications in starting and control of electrical machines.

Q1. Power Electronics:
Using PLECS:
Assume 100 kHz switching frequency for all the following problem
There is a 2 kW single phase full bridge inverter with 400 V input dc and 240 V output ac rms voltage with 60 Hz fundamental frequency, assume there is an output LC filter of the inverter which is 100 uH and 10 uF. And the output load resistance is 24 Ohm. Simulate the inverter at the full power with the corresponding input and output voltage. Calculate the modulation index M , Provide schematics , two fundamental cycle of output voltage , two fundamental cycle of inductor current

An electrical machine is a device that converts mechanical energy to electrical energy and vice-versa or transfers electrical energy from one circuit to the other. This subject covers the principle of operation, construction, working, testing and applications of the electrical machines such as motors, generators and transformers. Electrical machines can be classified into DC and single-phase or three-phase AC machines.

Elementary ac machine 2-pole, 2-phase machine

(a) For a 2-pole, 2-phase doubly fed induction machine, show the physical layout of the machine and the winding arrangement. Give the stator inductance matrix. Give the stator and rotor inductances in terms of self and mutual inductances and the complete machine inductance matrix. Give the flux linkages in terms of inductances and winding currents.

(b) Repeat for a 2-pole, 3-phase salient-pole synchronous machine. Explain the differences with the induction machine.

Electromagnetics is basically the combined study of electric and magnetic fields. It deals with the learning of the electromagnetic fields which are generated by time varying charge distributions. It also deals with the principles of electromagnetism. It includes Maxwell’s equations and basic laws like Faraday’s law, Lorentz law, etc. and their applications. The theory also explains the concept of transmission lines, waveguides and antennas.

A Class C amplifier has a load impedance of 600 ohms.Suppose this is to be connected to a Collins Coupler so that it connects to an antenna of 75 ohms. Assume a Q of 12 Calculate Xc, Xc, and X.

Draw your final circuit.

Microprocessor is the heart of computer as it is an integrated circuit containing all the functions of central processor (CPU), whereas Microcontroller is a computer on an IC. A microcontroller is a combination of processor, memory, and Input/outputs units fabricated on a single chip. Microprocessor is general purpose which could be programmed for any application, whereas microcontrollers is designed for specific application.

1) Given DO, write instructions to do the following: a. Set bits 113, 21 in D0 b. Reset bits 2,8,30 in DO

2) What are the differences between macro and subroutines and when are macros superior?

3) Represent 3697 in IEEE format

4) Hand assemble the following code Note: learn how to write displacement to an instruction written before the branch instruction which requires using the second complements.

5) List the micro step instructions for: 123(a0.al), 60(a2) 6) Discuss the execution of the rte instruction

Microelectronics deals with the assembly of electronics components (active such as transistor (BJT, FET, CMOS), diodes, and passive such as resistors, capacitor and inductor) on a single very small size chip called as microchip. Integrated Circuit also called IC is designed to perform specific task such as oscillator, timer, microprocessor. Microelectronic and Integrated Circuits covers topics from fabrication of electronic component to their assembling on a small size silicon IC called microchip.

Draw a 4×4 cell array of NAND flash memory with selection transistors on both sides of the string of floating gate cells. Considering the operating principles of NAND flash memory, determine the bias voltages of selected and unselected wordlines, bit lines, and selection transistors. In programming step, you have to program 1~3 bits among 4 bits. Assume that the tunneling requires 12V across the tunneling oxide and CC/CT = 1.5. CC and CT are capacitance of floating gate toward control gate and substrate, respectively.

Thermodynamics is an applied science used by many subdivisions of engineering, including engineering. It is the study of energy and transformation and usage through a system. Generally, thermodynamics is Related with changing energy from one form to another.

1. A gas is initially contained inside an insulated container A, at initial conditions P1, V1, m, and T1. These quantities represent pressure, volume, mass, and temperature, respectively. A valve is then opened which allows the gas to expand freely into an insulated container B, which is initially empty. After the gas has settled, the final conditions of the gas are P2, V2, m, and T2. In thermodynamics, a process is said to be reversible if it produces no entropy. This means that the process can happen in the reverse direction. Explain why the process described is not reversible.

2. A vortex tube, also known as a Ranque-Hilsch vortex tube, is a mechanical device without moving parts that separates a compressed gas into hot and cold streams. According to a manufacturer’s specifications, pressurized air enters a vortex tube at a temperature of 20°C and a guage pressure of 700 kPa. Cold air exits the left side of the tube at a temperature of -18°C and at atmospheric pressure. Hot air exits the right side of the tube at a temperature of 105°C and at atmospheric pressure. The ratio of mass flow rate between the cold stream and the inlet stream is 0.70. Are these specifications possible?

3. Steam at a temperature of 350°C and a pressure of 1 MPa is flowing through a pipe. What is the enthalpy of the steam?

Fluid Mechanics is the study which deals with the behaviour of liquids with respect to mechanics in motion or at rest i.e. Different reaction of fluids with different forces.

1. Find the pressure inside a water droplet having diameter of 0.5 mm at 20 0 C if the outside pressure is 1.03N/cm 2and the surface tension of water at that temperature is 0.0736 N/m.

2. A balloon is filled with hot air of 60°C. Its diameter is 10 m. The environmental temperature is 0°C. Pressure outside and inside the balloon is 105 Pa. The weight of the balloon material is can be neglected. Determine the buoyant force!

3. Calculate the horizontal force acting on the conical part of the pipe! q 3.5 m / min 3 V = Friction losses are negligible.

Machine Design or a Technical drawing also known as drafting is an illustration creating steps for manufacturing parts. Drafting has historically been a two-dimensional process, but computer-aided design (CAD) programs now allow the designer to create in three dimensions.

1. A helical compression spring must give a minimum force of 500 N and a maximum force of 750 N over an adjustment range of 2 cm static deflection. The spring material is A227 cold drawn wire; the loading is static. Design the spring. (G=79.6 Gpa)

2. The steel pipe shown in the figure has an inner diameter of 2 cm and outer diameter of 2.15 cm. If it is subjected to the force F = 80j + 40 k (N), determine the principal stresses in the pipe at point A and B which are located on the surface of the pipe.

3. A single square-thread power screw has an input power of 3 kW at a speed of 1 rev/s. The screw has a major diameter of 36 mm and a pitch of 6 mm. The frictional coefficients are 0.14 for the threads and 0.09 for the collar, with a collar friction radius of 45 mm.

a) Find the axial resisting load F and the combined efficiency of the screw and collar.

b) Indicate whether the screw is self-locking or not.

c) Find the most critical section and determine safety factor assuming that the load is static. Nut and power screw are made of AISI 1040 HR steel. (Do not consider buckling)

MATLAB also know as Matrix Laboratory is programming language developed by Maths Work. Its key use is numerical computing and Matrix Manipulation. It includes Functions, Structures, variables and vectors.

1. How could we write a function strpoint that returns a string (x,y) containing the x- and y-coordinates? For example, it might be called separately to create strings for the two endpoints and then printed as shown here: >>

fprintf(‘The line segment consists of %s and %sn’, …

strpoint(lineseg.endpoint1), …

strpoint(lineseg.endpoint2))

The line segment consists of (2, 4) and (1, 6)

2. Create three cell array variables that store people’s names, verbs, and nouns. For example, names = {‘Harry’, ‘Xavier’, ‘Sue’}; verbs = {‘loves’, ‘eats’}; nouns = {‘baseballs’, ‘rocks’, ‘sushi’};

3. The velocity of sound in air is 49.02 T feet per second where T is the air temperature in degrees Rankine. Write a function to implement this. If just one argument is passed to the function, it is assumed to be the air temperature in degrees Rankine. If, however, two arguments are passed, the two arguments would be first an air temperature and then a character ‘f’ for Fahrenheit or ‘c’ for Celsius (so this would then have to be converted to Rankine). Note: degrees R = degrees F + 459.67. Degrees F = 9/5 degrees C + 32

Q1. Classical physics vs. Quantum mechanics.When does classical physics become quantum mechanics?and when can’t we use classical physics; when do we use quantum mechanics?

Q2. Did Einstein support quantum mechanics as being fundamental physics, or did he think quantum mechanics was incomplete?

Q3. Are there real applications for using delta function potentials in quantum mechanics (other than using it as an exactly solvable toy model in introductory undergraduate quantum mechanics textbooks) ?

Q4. One important application of Quantum Mechanics is laser technology. Construct an information pamphlet including

– Uses of laser technology

– How it applies quantum mechanics

– Advantage/disadvantages of laser technology

Q1. An insulating spherical shell of radius R carries a uniform electric surface charge density σ . It rotates with angular velocity Ω about its center

(a) Find the current density K(r,θ,ϕ) resulting from the rotation (in spherical coordinates).

(b) Find the magnetic dipole moment m of the sphere.

(c) Show that for r > R (outside the sphere) the vector potential A(r,θ,ϕ) is exactly that of a perfect dipole, so that a spinning sphere produces a perfect dipole field, with no higher multipole contributions.

Q2. Electrodynamics: How are the boundary conditions related to the potential different for capacitors vs. linear dielectrics?

Q3. What is Maxwell’s contribution to the 4 most important electrodynamic equations? Explain completely.

Q1. Polarization of the Normal Modes of a Monatomic Bravais Lattice

(a) Show that if k lies along a 3-, 4-, or 6-fold axis, then one normal mode is polarized along k, and the other two are degenerate and polarized perpendicular to k.

(b) Show that if k lies in a plane of mirror symmetry, then one normal mode has a polariza-tion perpendicular to k, and the other two have polarization vectors lying in the mirror plane.

(c) Show that if the point k lies in a Bragg plane that is perpendicular to a plane of mirror symmetry, then one normal mode is polarized perpendicular to the Bragg plane, while the other two have polarizations lying in the plane. (Note that in this case the modes cannot be strictly longitudinal and transverse unless k is perpendicular to the Bragg plane.) To answer these questions, one must note that any operation that leaves both k and the crystal invariant must transform one normal mode with wave vector k into another. In particular, the set of three (orthogonal) polarization vectors must be invariant under such operations: in applying this fact one must remember that if two normal modes are degenerate, then any vector in the plane spanned by their polarization vectors is also a possible polarization vector. Q2. Using the Debye approximations for one- dimensional monatomic lattice with atomic spacing a and sound v, show thatD = v /a and D = h D / KB

Q3. Derive the integral expression for the thermal energy and phonon heat capacity. show thatCv= 2 KB (T/ D) / 3a per unit length at low temperature =KB / a per unit length at high temperature.

Q4. A weak periodic potential in the form of V(x) = V0 cos(2 kF x) is created for a one-dimensional electron system (kF is the Fermi wavenumber). Calculate E(k) for the lowest energy band, and determine the total energy of the system at zero temperature as a function of V0.

Q1. What is the difference between atomic line spectra and molecular/emission spectra?

Q2. Explain at the atomic/molecular level why each of the following are generated:

- line spectra
- band spectra
- continuum spectra

Q3. Discuss types and nature of atomic spectra.

Q4. What is the atomic spectra experiments, and what information is obtained by these experiments?

Q5. What are the similarities between the Bohr model and the atomic spectra equations?

Q1. Why do statistical mechanics not apply to nonideal gases?

Q2. Using the statistical mechanics of photon gas, How is it possible to derive the spectral density of a black body?

Q3. Why should the equilibrium constant be dependent on the difference in Gibbs energy? How is this relationship described using statistical mechanics?

Q4. A generalized form of the equation of state for gases that can be derived from the methods of statistical mechanics is called the____________ equation of state.

Q1. In an undisturbed ore containing .1% by weight of Uranium-238 there will be some Radium-226. Calculate the weight of this isotope of radium to be found in one metric ton of ore. What is the rate of generation of helium gas in kg per year in this amount of ore?

Q2. What is the Physical basis of the independent-particle model of the nucleus?

Q3. Because pions had not been discovered in 1936 when yukawa proposed the meson theory of the nuclear force, it was suggested that the meson was yukawa’s particle. what would the range of the nuclear force be if this were true?

Q4. Discuss the advantages and disadvantages of nuclear physics.

Biochemistry is a sub-discipline of both biology and chemistry. It deals with the chemical processes within and relating to living organisms. Biochemistry deals with the functions, structures, and interaction of biological macromolecules and their association with life. The biochemistry is diversified into three fields: molecular genetics, protein science, and metabolism.

1.Net equation for glycolysis and the citric acid cycle?

2.An aminoacyl tRNA analog causes premature polypeptide chain termination is:

a)Puromycin

b)Tetracycline

c)Erythromycin

d)Streptomycin

3. How many ATPs are produced incomplete oxidation of palmitic acid

a)129

b)132

c)131

d)140

4. When ATP molecule is hydrolyzed into ADP, it releases———calories of energy?

a)730

b)7300

c)68600

d)73000

Cell- biology deals with the physiological, metabolic, signaling pathways and life cycles of the cell. The components of the cell are studied to understand the fundamental properties and their mechanism. Cell-biology plays a crucial role in the bio-medical fields such as cancer and other diseases. This branch is associated with genetics, biochemistry, molecular biology, immunology, and cytochemistry.

1.Which of these units is most suitable for measuring the length of a cell?
a) Kilometer
b) Meter
c) Centimeter
d) Micrometer
2. Give two differences between plant and animal cells?
3. In an osmosis experiment, after 45 minutes, a potato cylinder had lost 2.4 g in mass.Calculate the rate of water loss from the potato cylinder in grams per hour?
4. Describe the similarities and differences between the processes of diffusion and osmosis?

This subject helps the student to understand the relationships between different organisms and their relationship with surroundings and how these surroundings help the organisms to change their characteristics over generations. This subject deals with different levels of hierarchy like the organisms, group of organisms (populations), group of populations (communities). The process of evolution is very complex and difficult to understand as there are many connecting links available in nature, which are obtained from fossil studies.

1.How does evolution play a role in ecology? In your opinion, are evolution and ecology separate fields of study?

2. Describe the role of ecology in food production, disease spread, exotic species invasions, and pest management. Can you think of an example for each and describe the important ecological interactions? What are the consequences of disruptions to these interactions?

3.How has ecology influenced evolution? What is the relationship between an organism and its environment?

Genetics is a branch of biology deals with the study of genes, genetic variation and heredity of organisms. The molecular inheritance mechanism and trait study are the major principles in genetics. Genetics has several subfields including behavioral genetics, epigenetics, and population genetics.

1. The difference between the test cross and back cross?
2. Suppose A Father of Blood Type-B and A Mother of Blood Type-O have a Child of Type-O. What are the chances that their Next Child will be Blood Type-O? Type B? Type A? Type Ab?
3. Describe the New Theory of Introns?4. Does a codon specifies one of which of the following?
a) Protein
b) DNA
c) Carbohydrate
d) Amino acids

This subject helps the student to understand how to grow and culture the microorganisms and how to apply these studies in different areas like agriculture, food industries, health and medicine etc. While many microorganisms are beneficial, and many are harmful which may cause many diseases in humans and animals.

1. How would you isolate a thermophilic chemolithotroph that uses sulphur compounds as a source of energy and electrons? What changes in the incubation system would be needed to isolate bacteria using sulphur compounds in anaerobic respiration? How would you tell which process is taking place through an analysis of the sulphur molecules present in the spent medium?
2.What would be the phenotype of an E. coli strain in which the tandem trp codons in the leader region were mutated so that they coded for serine instead?
3.Suppose that you insered a plasmid vector carrying a human interferon gene into E. coli but none of the transformed bacteria produced interferon. Give as many plausible reasons as possible for this result.
4.What are some logical physiological or morphological targets to exploit in treating animals or plants suffering from fungal infections? Compare these with the targets you would use when treating infections caused by bacteria.

The science that studies the interaction of nutrients in the body through the consumption of food is known as Nutrition. It identifies the role of nutrients on the body and how it helps in promoting growth and good health. The subject of nutrition science is based on a major amount of research and studies carried out to understand the importance of a specific component and its interactions in the body. It includes the understanding of the chemistry of the biological components within the body. The dietary reference index provides the values of nutrient intakes based on age and health conditions.

1. Illustrate two ways in which good blood glucose control during the periconeptional period can benefit fetal growth and development

2. Distinguish the different types of hypertensive disorders that occur during pregnancy, and connect two components of nutrition care recommended for women with each type.

3. Connect the different, major types of disorders in carbohydrate metabolism that occur during pregnancy and the key components of the nutritional management of each type.

4. Describe the components of a healthy diet during middle childhood and preadolescence as recommended by health and professional organizations and agencies.

The science that studies the interaction of nutrients in the body through the consumption of food is known as Nutrition. It identifies the role of nutrients on the body and how it helps in promoting growth and good health. The subject of nutrition science is based on a major amount of research and studies carried out to understand the importance of a specific component and its interactions in the body. It includes the understanding of the chemistry of the biological components within the body. The dietary reference index provides the values of nutrient intakes based on age and health conditions.

1. Illustrate two ways in which good blood glucose control during the periconeptional period can benefit fetal growth and development

2. Distinguish the different types of hypertensive disorders that occur during pregnancy, and connect two components of nutrition care recommended for women with each type.

3. Connect the different, major types of disorders in carbohydrate metabolism that occur during pregnancy and the key components of the nutritional management of each type.

4. Describe the components of a healthy diet during middle childhood and preadolescence as recommended by health and professional organizations and agencies.

Organic chemistry is the branch of chemistry that deals with the study of structural properties, reactions and preparation of carbon containing compounds. IUPAC nomenclature is used to name organic compounds. Different spectroscopic techniques are used to understand the structural properties of compounds. Reaction mechanism and synthesis are used to study preparation of different types of organic compounds.

Analytical chemistry is a branch of chemistry that deals with analysis of samples and separation of mixtures. It covers both qualitative and quantitative analysis. Various analytical technics are used in the analysis of samples. GC, HPLC, spectrophotometer, flame-ionization photometer, ICP-MS, voltammetry, potentiometry, coulometry, and titrations are different techniques used in the analysis and separation. Basic knowledge in statistics is essentially required for making plots and analysis of compounds. Spread sheets are widely used in solving problems in analytical chemistry.

Q1. The strengths of the interactions in nature, from strongest to weakest, are in the order

a. strong, weak, electromagnetic, gravitational. b. strong, electromagnetic, weak, gravitational.

c. strong, gravitational, electromagnetic, weak.

d. strong, electromagnetic, gravitational, weak.

e. gravitational, electromagnetic, weak, strong.

Q2. Two objects attract each other gravitationally. If the mass of each object doubles, how does the gravitational force between them change?The gravitational force decreases by a factor of 4.

The gravitational force increases by a factor of 4.

The gravitational force remains unchanged.

The gravitational force decreases by a factor of 2.

The gravitational force increases by a factor of 2.

Q3. Is Gravitational Potential and Gravitational Potential Energy are same?

Q4. A pendulum swings in a vertical plane. At the bottom of the swing, the kinetic energy is 8 J and the gravitational potential energy is 4 J. At the highest position of its swing, the kinetic and gravitational potential energies are a) kinetic energy = 0 J and gravitational potential energy = 4 J.b) kinetic energy = 12 J and gravitational potential energy = 0 J. c) kinetic energy = 0 J and gravitational potential energy = 12 J. d) kinetic energy = 4 J and gravitational potential energy = 8 J.e) kinetic energy = 8 J and gravitational potential energy = 4 J.

Q1. Find a derivation of SHM from Newton’s second law.

Q2. Find a derivation for the energy relationships for SHM.

Q3. Symbolically, write out the full position function for each (as a function of period rather than angular frequency):

1. SHM spring system

2. SHM pendulum system

Q4. At a time of 2.00 x 102, s after starting its SHM from maximum displacement, a mass on a spring has a displacement that is +2.65 cm from the equilibrium position. If the frequency of the SHM Is +2.76 Hz, what Is the amplitude of the SHM? _______cm

Q1. What is the difference between fluid mechanics and fluid dynamics?

Q2. What is fluids mechanics?

Q3. Give examples of disturbances for the following:·

- Solid Mechanics
- Fluid Mechanics
- Heat Transfer

Q4. What is the velocity magnitude in a plenum?

Q1. Wave theory selection example

Water depth=1 m

Wave period=7s

Wave height=0.3m

Find the best wave theory

Q2. What are some differences between Airy wave theory (classical) and long wave theory? Provide at least 4 major differences.

Q3. Who is credited with the wave theory of light?

Q4. Which theory of light, the wave theory or the particle theory, did the findings of Young, Maxwell, and Hertz support?

Q1. What is the difference between geometric optics and physical optics?

Q2. When can we use ray optics to characterize our system as opposed to physical optics. In physical optics, we consider processes such as diffraction and interference. In ray optics, we do not.

Q3. What is the different between nonlinear and linear optics? And also give an example of nonlinear optics?

Q4. What is the advantage of using a microscope with dark-field optics compared to a microscope with bright-field optics?

Q1. Name the differences between an electrostatic field and an electrostatic force

Q2. How is a low voltage two stage electrostatic precipitator different from a high voltage single stage electrostatic precipitator? Explain the operation of a plate type electrostatic precipitator. Include a schematic view of the electrostatic precipitator and mention the size-efficiency relationship.

Q3. Ionic bonds dearly result from electrostatic attraction between ions. In what way do covalent bonds also involve electrostatic attraction?

Q4. Applications of Electrostatics What are the similarities and differences between the processes in a photocopier and an electrostatic precipitator?

Q1. What is special about the special theory of relativity?

Q2. Does theory of relativity hold for motions on earth??

Q3. List five major predictions of the special theory of relativity

Q4. What was one of the key early tests of Einstein’s General Theory of Relativity?

Q1. What is modern physics?

Q2. Classical physics is a good approximation to modern physics under certain circumstances. What are they?

Q3. What is one situation in classical modern physics, that an experiment was defined using quantum theory?

Q4. A further discussion on the role of modern physics in the invention of lasers.

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