This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2005. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
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This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2013. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2010. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2009. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2004. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2013. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2011. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2006. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2008. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2013. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2010. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2009. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2004. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2013. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2011. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2006. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
JNU MA Economics Entrance Test Paper (2013)CrackDSE
This is the entrance exam paper for JNU MA Economics Entrance Exam for the year 2013. Much more information on the JNU MA Economics Entrance Exam and JNU MA Economics Entrance preparation help available on http://crackdse.com
The pattern of question paper in the subject Mathematics has been changed in CBSE,India.I am uploading the paper with marking scheme so that students will be benefitted-Pratima Nayak,KVS
This is a 3 hour sample paper for cbse class 12 board exam. This covers all chapters of ncert 12th math book. For more such papers visit clay6.com/papers/.
This learner's module discusses or talks about the topic of Quadratic Functions. It also discusses what is Quadratic Functions. It also shows how to transform or rewrite the equation f(x)=ax2 + bx + c to f(x)= a(x-h)2 + k. It will also show the different characteristics of Quadratic Functions.
II PUC (MATHEMATICS) ANNUAL MODEL QUESTION PAPER FOR ALL SCIENCE STUDENTS WHO...Bagalkot
My dear Students,
Wishing you all happy SHIVRATRI. & ALL THE BEST IN YOUR ANNUAL EXAMS-2014
Here I have uploaded II- P.U.C MATHEMATICS MODEL QUESTION PAPER FOR the year 2014 Which i have designed according to New syllabus of CBSE. I hope this model paper will be helpful to all the students who are writing annual exams on 18-March-2014.
wish you all the best
Regards,
A. NAGARAJ
Director-Faculty
Shree Susheela Tutorials
BAGALKOT-587101
mob: 9845222682
JNU MA Economics Entrance Test Paper (2013)CrackDSE
This is the entrance exam paper for JNU MA Economics Entrance Exam for the year 2013. Much more information on the JNU MA Economics Entrance Exam and JNU MA Economics Entrance preparation help available on http://crackdse.com
The pattern of question paper in the subject Mathematics has been changed in CBSE,India.I am uploading the paper with marking scheme so that students will be benefitted-Pratima Nayak,KVS
This is a 3 hour sample paper for cbse class 12 board exam. This covers all chapters of ncert 12th math book. For more such papers visit clay6.com/papers/.
This learner's module discusses or talks about the topic of Quadratic Functions. It also discusses what is Quadratic Functions. It also shows how to transform or rewrite the equation f(x)=ax2 + bx + c to f(x)= a(x-h)2 + k. It will also show the different characteristics of Quadratic Functions.
II PUC (MATHEMATICS) ANNUAL MODEL QUESTION PAPER FOR ALL SCIENCE STUDENTS WHO...Bagalkot
My dear Students,
Wishing you all happy SHIVRATRI. & ALL THE BEST IN YOUR ANNUAL EXAMS-2014
Here I have uploaded II- P.U.C MATHEMATICS MODEL QUESTION PAPER FOR the year 2014 Which i have designed according to New syllabus of CBSE. I hope this model paper will be helpful to all the students who are writing annual exams on 18-March-2014.
wish you all the best
Regards,
A. NAGARAJ
Director-Faculty
Shree Susheela Tutorials
BAGALKOT-587101
mob: 9845222682
Question 1 Aggregate Demand and Aggregate Supply (This question i.docxIRESH3
Question 1: Aggregate Demand and Aggregate Supply (This question is worth 20 points if correctly answered.)
Assume the U.S. economy is in long-run equilibrium. Analyze each of the following events independently and include answers to the following in your analysis: (1) Explain whether AD or SAS changes and why the change occurred. (2) Explain what happens to the equilibrium price level and equilibrium output in the U.S. in the short run. (3) Describe the type of gap facing the economy. (4) Draw a graph to illustrate your answer.
a. The bubble in the housing market bursts, and prices of houses quickly begin to fall.
b. With plenty of slack in the labor market, firms lower wages.
c. Anticipating the possibility of war, the government increases its purchases of military equipment.
d. Productivity in the U.S. continues to increase.
Question 2: More Aggregate Demand/Aggregate Supply (This question is worth 10 points if correctly answered.)
a. Suppose the United States’ economy is in short run equilibrium producing RGDP equal to $150 billion. Potential GDP equals $250 billion. The marginal propensity to consume in the U.S. is 0.5. Draw a graph illustrating the U.S. economy. Is the economy characterized by a recessionary gap or an inflationary gap? What problems does the gap present for United States?
b. You are an economic advisor to the President. He asks you to design a fiscal policy to close the gap. What fiscal policy do you propose? Why did you choose this particular policy? Explain how your policy works. Draw a graph illustrating your answer.
c. Describe any costs the United States may bear in the long run due to the implementation of the policy you designed in part (b).
d. If your policy is not acceptable to Congress, describe the self-correction mechanism by which the economy could return to long-run equilibrium. Draw a graph illustrating the self-correction process. Describe any costs the United States may pay with self-correction.
Question 3: The Federal Reserve System (the Fed). (This question is worth 10 points if correctly answered.)
a. Describe the structure of the Federal Reserve System.
b. The government of Turtleville uses measures of monetary aggregates similar to the United States, and the central bank of Turtleville imposes a required reserve ratio of 10%. Given the following information, answer the questions below.
Bank deposits at the central bank = $200 million
Currency held by the public = $150 million
Checkable bank deposits = $500 million
Currency in bank vaults = $100 million
Traveler’s checks = $10 million
1. M1 = _____________
2. The Monetary Base = _____________
3. Excess Reserves = _______________
4. The amount by which commercial banks in Turtleville can increase checkable deposits: _____________
1
Solving Differential Equations:
1. Solve the following diffe ...
1 Assignment #2 MAC 1140 – Spring 2020 – Due Apr.docxkarisariddell
1
Assignment #2
MAC 1140 – Spring 2020 – Due: April 7, 2020
1. We are given the polynomial 𝑓(𝑥) = 𝑥7 − 𝑥6 − 11𝑥5 + 11𝑥4 + 19𝑥3 − 19𝑥2 − 9𝑥 + 9.
(a) What is the degree of this polynomial? How many zeros does it have? Do these zeros have
to be real and/or distinct?
(b) What is the behavior of the polynomial as 𝑥 → +∞ and 𝑥 → −∞? Explain your answer.
(c) Describe, in your own words, the rational zero theorem. Taking into account the form of the
polynomial, can we use the rational zero theorem to find if the polynomial has rational
zeros? If yes, what are the possible zeros?
(d) Describe in your own words Descartes’ rule of signs. Using this rule, what is the possible
number of positive zeros of the polynomial, and what is the possible number of negative
zeros?
(e) Calculate the following values:
𝑓(−3) = ________ 𝑓(−2) = ________ 𝑓(−1) = ________ 𝑓(0) = ________
𝑓(1) = ________ 𝑓(2) = ________ 𝑓(3) = ________
𝑓(−4) = ________ 𝑓(4) = ________
2
(f) Describe in your own words the Factor Theorem. Using this theorem show that 𝑓(𝑥) =
(𝑥 + 3)(𝑥 + 1)(𝑥 − 1)(𝑥 − 3) ⋅ 𝑔(𝑥).
(g) Using long division, find 𝑔(𝑥). Show all your work.
(h) Calculate the following values:
𝑔(−1) = ________ 𝑔(1) = ________
(i) Using the Factor Theorem and synthetic division, factor 𝑔(𝑥). Show all your work.
(j) Describe the multiplicity of all the zeros of 𝑓(𝑥), and describe the behavior of the graph of
𝑓(𝑥) at these zeros (i.e., is the graph crossing the 𝑥-axis at these zeros or touches and turns
around?).
3
(k) What is the maximum number of turning points of 𝑓(𝑥)?
(l) Graph 𝑓(𝑥).
4
2. We are given the polynomial 𝑓(𝑥) = 4𝑥5 + 4𝑥4 + 𝑥3 − 2𝑥2 − 2𝑥 + 1.
(a) What is the degree of this polynomial? How many zeros does it have? Do these zeros have
to be real and/or distinct?
(b) What is the behavior of the polynomial as 𝑥 → +∞ and 𝑥 → −∞? Explain your answer.
(c) Describe, in your own words, the rational zero theorem. Taking into account the form of the
polynomial, can we use the rational zero theorem to find if the polynomial has rational
zeros? If yes, what are the possible zeros?
(d) Describe in your own words Descartes’ rule of signs. Using this rule, what is the possible
number of positive zeros of the polynomial, and what is the possible number of negative
zeros?
(e) Calculate the following values:
𝑓(−2) = ________ 𝑓(−1) = ________ 𝑓(0) = ________
𝑓(1) = ________ 𝑓(2) = ________
(f) Describe in your own words the Intermediate Value Theorem. Based on the results in (e)
above, and the possible rational zeros described in (c), show that 𝑥 −
1
2
is a factor of 𝑓(𝑥).
Clearly describe your reasoning.
5
(g) Describe in your own words the Factor Theorem. Using this theorem show that 𝑓(𝑥) =
(𝑥 + 1)(2𝑥 − 1) ⋅ 𝑔(𝑥
Calculus Application Problem #3 Name _________________________.docxhumphrieskalyn
Calculus Application Problem #3 Name __________________________________________
The Deriving Dead! Due at the beginning of class ______________________
Introduction: Imagine that you are one of many people at a “party” and that, unknown to everyone else, one
person was bitten by a zombie on the way to the party! How quickly will the “zombiepocalypse” spread, and
what are the chances that you will leave the party as a zombie? The objective of this activity is to create a
mathematical model that describes the spread of a disease (such as a zombie virus) in a closed environment, and
then apply calculus concepts to this mathematical model.
Collecting the Data:
Let’s collect some data from an activity that will simulate the spread of a communicable disease over a period of
time, divided into “stages”.
The number of people in our “closed environment” is ________________
1
1
131211109876543210
Number
of Total
Infected
Number
of Newly
Infected
Stage
Number
Applying Calculus to the Data:
1. Using the data from the chart, make a scatterplot of the "Stage Number" (in L1) vs. the "Number of Total
Infected" (in L2). Sketch the scatterplot below. Connect the data points to create a continuous function for Y(t).
2. Using the data that was collected in the activity, answer the following questions about the derivative
function Y’(t), which represents the instantaneous rate of change of the number of infected at any stage.
Consider the domain to be [ 0 , 13 ].
a. When, if ever, is Y’(t) positive? ____________________________________
b. When, if ever, is Y’(t) negative? ___________________________________
c. When, if ever, is Y’(t) increasing? ____________________________________
d. When, if ever, is Y’(t) decreasing? ____________________________________
e. From your answers above, sketch a graph of Y’(t) below.
f. The t-value where Y’(t) changes from increasing to decreasing is the inflection point on Y(t).
According to the data in the chart, this occurs when t = _________, and the corresonding “y-value”
is ________.
(Note: We will check this later in the problem!)
Finding a Logistic Function that Models the Data
3. Since the data (should) appear to be a model for a logistic function, we need to find a function in the
form:
Y(t ) =
c
1 + a ⋅ e− b⋅t
,
where t represents the stage number and Y(t) represents the total number of infected people in stage t.
Therefore, we need to find values for the three constants a, b, and c. The value of c should be easy. For our
activity,
c = _________
To find a, use the initial point ( 0 , 1 ). Substitute this ordered pair, with the value of c into our logistic model and
solve for a. Show your work below.
a = _______________
To find b, the last constant in the model, we need another ordered pair. Let’s use an ordered pair near the middle
of the data, say during Stage #7.
Record this ordered pair: ( 7 , _________)
Substitut ...
MATH 107 FINAL EXAMINATIONMULTIPLE CHOICE1. Deter.docxTatianaMajor22
MATH 107 FINAL EXAMINATION
MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function.
A. Domain [–2, 2];
B. Domain [–1, 1];
C. Domain [–1, 3];
D. Domain [–3/2, –1/2];
2. Solve:
A. 3
B. 3,7
C. 9
D. No solution
3. Determine the interval(s) on which the function is increasing.
A. (−1.3, 1.3)
B. (1, 3)
C. (−∞,−1)and (3,∞)
D. (−2.5, 1)and (4.5,∞)
4. Determine whether the graph of y = 2|x| + 1 is symmetric with respect to the origin,
the x-axis, or the y-axis.
A. symmetric with respect to the origin only
B. symmetric with respect to the x-axis only
C. symmetric with respect to the y-axis only
D. not symmetric with respect to the origin, not symmetric with respect to the x-axis, and
not symmetric with respect to the y-axis
5. Solve, and express the answer in interval notation: | 9 – 7x | ≤ 12.
A. (–∞, –3/7]
B. (–∞, −3/7] ∪ [3, ∞) C. [–3, 3/7]
D. [–3/7, 3]
6. Which of the following represents the graph of 7x + 2y = 14 ?
A. B.
C. D.
7. Write a slope-intercept equation for a line parallel to the line x – 2y = 6 which passes through the point (10, – 4).
A.
B.
C.
D.
8. Which of the following best describes the graph?
A. It is the graph of a function and it is one-to-one.
B. It is the graph of a function and it is not one-to-one.
C. It is not the graph of a function and it is one-to-one.
D. It is not the graph of a function and it is not one-to-one.
9. Express as a single logarithm: log x + log 1 – 6 log (y + 4)
A.
B.
C.
D.
10. Which of the functions corresponds to the graph?
A.
B.
C.
D.
11. Suppose that a function f has exactly one x-intercept.
Which of the following statements MUST be true?
A. f is a linear function.
B. f (x) ≥ 0 for all x in the domain of f.
C. The equation f(x) = 0 has exactly one real-number solution.
D. f is an invertible function.
12. The graph of y = f(x) is shown at the left and the graph of y = g(x) is shown at the right. (No formulas are given.) What is the relationship between g(x) and f(x)?
y = f (x) y = g(x)
A. g(x) = f (x – 3) + 1
B. g(x) = f (x – 1) + 3
C. g(x) = f (x + 3) – 1
D. g(x) = f (x + 1) .
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Digital Logic.pptxghuuhhhhhhuu7ffghhhhhgAnujyotiDe
Jdjddjdjjfjrjrhhfbrhrjhjjfjrjfrifjhfjdirurfu8fi3hdudoickegdhejdofjrvdjozdkjieofiudjrhciyyfifjjvi9r7ugidof8cdukrkfj2keoekeRecombination in bacterial growth refers to the process by which bacteria exchange genetic material with each other, leading to the formation of new genetic combinations. This process can occur through several mechanisms, including transformation, conjugation, and transduction.
1. Transformation: In transformation, bacteria take up free DNA from their environment and incorporate it into their genome. This DNA may come from lysed bacterial cells or be released into the environment by other means. Once inside the cell, the foreign DNA can recombine with the bacterial chromosome, leading to genetic diversity.
2. Conjugation: Conjugation involves the direct transfer of genetic material from one bacterium to another through physical contact. This transfer typically occurs through a conjugative pilus, a structure that forms a bridge between the donor and recipient cells. During conjugation, a copy of the donor's DNA, often in the form of a plasmid, is transferred to the recipient cell, where it can integrate into the chromosome or exist as a separate genetic element.
3. Transduction: Transduction occurs when bacterial DNA is transferred from one bacterium to another by a bacteriophage (a virus that infects bacteria). During the lytic cycle of viral replication, some bacteriophages may accidentally package bacterial DNA instead of their own genome. When these phages infect other bacteria, they inject this bacterial DNA into the new host, where it can recombine with the recipient chromosome.
Recombination plays a crucial role in bacterial evolution and adaptation by facilitating the exchange of beneficial genetic traits, such as antibiotic resistance or metabolic capabilities. It contributes to the genetic diversity of bacterial populations and can influence their ability to survive and thrive in various environments.In enzymes, a domain refers to a distinct structural and functional unit that contributes to the overall activity of the enzyme. Domains are often modular components within the enzyme's overall structure, each with its own specific role or function. These functions may include substrate binding, catalysis, regulation, or interaction with other molecules. Domains can have specific shapes, surface properties, and active sites tailored to perform particular biochemical tasks within the enzyme's catalytic cycle. Additionally, enzymes can contain multiple domains, which may interact with each other to modulate enzyme activity or to confer versatility in substrate recognition and binding. The organization of domains within an enzyme contributes to its overall efficiency and specificity in catalyzing biochemical reactions.Superscalar architecture is a CPU design paradigm that enables the simultaneous execution of multiple instructions within a single clock cycle. This is achieved by having multiple execution units, allowing t
Fai alshammariChapter 2Section 2.1 Q1- Consider the gr.docxmydrynan
Fai alshammari
Chapter 2
Section 2.1
Q1:- Consider the graph to the right. Explain the idea of a critical value. Then determine which x-values are critical values, and state why.
Q2:-
Find the relative extreme points of the function, if they exist. Then sketch a graph of the function.
f(x)equals=x squared plus 6 x plus 15x2+6x+15
Q3:-
Find the relative extreme points of the function, if they exist. Then sketch a graph of the function.
G(x)equals=x cubed minus 9 x squared plus 1x3−9x2+1
· Identify all the relative minimum points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice
· Identify all the relative maximum points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
·
· Graph the function. Choose the correct graph below.
SECTION 2.2
Q1:-
Find all relative extrema and classify each as a maximum or minimum. Use the second-derivative test where possible.
f(x)equals=negative 27 x cubed plus 9 x plus 2−27x3+9x+2
_Identify all the relative minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
_Identify all the relative maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice
Q2:-
Sketch the graph of the following function. List the coordinates of where extrema or points of inflection occur. State where the function is increasing or decreasing as well as where it is concave up or concave down.
f left parenthesis x right parenthesisf(x)equals=x Superscript 4 Baseline minus 4 x cubed plus 3x4−4x3+3
_What are the coordinates of the relative extrema? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
_Identify all the relative maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
_On what interval(s) is f increasing or decreasing?
_On what interval(s) is f concave up or concave down?
_ SKETCH GRAPH
Q3:-
Sketch the graph that possesses the characteristics listed.
f is concave
up at
(negative 1−1,66),
concave
downdown
at
(77,negative 4−4),
and has an inflection point at left parenthesis 3 comma 1 right parenthesis .(3,1).
SECTION 2.3
Q1:-
Determine the vertical asymptote(s) of the following function. If none exist, state that fact.
f(x)equals=StartFraction x plus 3 Over x squared plus 9 x plus 18 EndFractionx+3x2+9x+18
Q2:-
Determine the horizontal asymptote of the function.
f(x)equals=StartFraction 8 x cubed minus 8 x plus 3 Over 10 x cubed plus 4 x minus 7 EndFraction8x3−8x+310x3+4x−7
Q3:-
Sketch the graph of the function. Indicate where each function is increasing or decreasing, where any relative extrema occur, where asymptotes occur, where the graph is concave up or concave down, where any points of inflection occur, and where any intercepts occur.
f(x)equ ...
JNU MA Economics Entrance Test Paper (2013)CrackDSE
This is the entrance exam paper for JNU MA Economics Entrance Exam for the year 2013. Much more information on the JNU MA Economics Entrance Exam and JNU MA Economics Entrance preparation help available on http://crackdse.com
JNU MA Economics Entrance Test Paper (2009)CrackDSE
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JNU MA Economics Entrance Test Paper (2010)CrackDSE
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JNU MA Economics Entrance Test Paper (2011)CrackDSE
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JNU MA Economics Entrance Test Paper (2012)CrackDSE
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Delhi School of Economics Entrance Exam (2004)CrackDSE
This is the entrance exam paper for the Delhi School of Economics for the year 2004. It contains both options A and B. Exam papers for other years are available as well here. Much more information on the DSE Entrance Exam and DSE Entrance preparation help available on www.crackdse.com
Delhi School of Economics Entrance Exam (2014)CrackDSE
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Delhi School of Economics Entrance Exam (2004)CrackDSE
This is the entrance exam paper for the Delhi School of Economics for the year 2004. It contains both options A and B. Exam papers for other years are available as well here. Much more information on the DSE Entrance Exam and DSE Entrance preparation help available on www.crackdse.com
Delhi University Master's Courses Admission Bulletin 2014CrackDSE
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This is Delhi University PG/ Master's Courses 2014 Admissions Bulletin. Other application related information available at the website above
Delhi School of Economics Entrance Exam (2008)CrackDSE
This is the entrance exam paper for the Delhi School of Economics for the year 2008. It contains both options A and B. Exam papers for other years are available as well here. Much more information on the DSE Entrance Exam and DSE Entrance preparation help available on www.crackdse.com
Delhi School of Economics Entrance Exam (2009)CrackDSE
This is the entrance exam paper for the Delhi School of Economics for the year 2009. It contains both options A and B. Exam papers for other years are available as well here. Much more information on the DSE Entrance Exam and DSE Entrance preparation help available on www.crackdse.com
Delhi School of Economics Entrance Exam (2010)CrackDSE
This is the entrance exam paper for the Delhi School of Economics for the year 2010. It contains both options A and B. Exam papers for other years are available as well here. Much more information on the DSE Entrance Exam and DSE Entrance preparation help available on www.crackdse.com
Delhi School of Economics Entrance Exam (2013)CrackDSE
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Delhi School of Economics Entrance Exam (2012)CrackDSE
This is the entrance exam paper for the Delhi School of Economics for the year 2012. It contains both options A and B. Exam papers for other years are available as well here. Much more information on the DSE Entrance Exam and DSE Entrance preparation help available on www.crackdse.com
Delhi School of Economics Entrance Exam Paper (2011)CrackDSE
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Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
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ISI MSQE Entrance Question Paper (2005)
1. Test code: ME I/ME II, 2005
Syllabus for ME I, 2005
Matrix Algebra: Matrices and Vectors, Matrix Operations.
1
Permutation and Combination.
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 a single variable, Theory of Sequence and
Series.
Linear Programming: Formulations, statements of Primal and Dual
problems. Graphical Solutions.
Theory of Polynomial Equations (up to third degree).
Elementary Statistics: Measures of central tendency; dispersion,
correlation, Elementary probability theory, Probability mass function,
Probability density function and Distribution function.
2. Sample Questions for ME I (Mathematics), 2005
For each of the following questions four alternative answers are provided.
Choose the answer that you consider to be the most appropriate for a
question and write it in your answer book.
1. X ~ B(n, p). The maximum value of Var (X) is
n ; (D)
A , then A100 + A5 is
2
(A)
n ; (B) n ; (C)
4
2
1 .
n
2. The function x x is
(A) discontinuous at x = 0;
(B) continuous but not differentiable at x = 0;
(C) differentiable at x = 0;
(D) continuous everywhere but not differentiable anywhere.
1 −
1
3. If =
2 −
2
0 0
0 0
(A)
1 1
−
2 2
; (B) −
1 1
−
2 2
−
; (C)
; (D) none of these.
4. The maximum and minimum values of the function
,4
2
3 2 ) ( 2 − + = x x x f + 1.5 x loge , over the interval
1 , are
(A) (21 + 3 loge 2 , – 1.5 loge 2 ); (B) (21 + loge 1.5 , 0);
(C) (21 + 3 loge 2 , 0); (D) (21 + loge 1.5 , -1.5 loge 2 ).
3. 5. Let α and β be the roots of the equation x2 − px + q = 0 .
Define the sequence xn = αn + βn . Then n+1 x is given by
(A) −1 − n n px qx ; (B) −1 + n n px qx ;
(C) −1 − n n qx px ; (D) 1 − + n n qx p x .
6. Let f : [−1,1]→ R be twice differentiable at x = 0 , f (0) = f ′(0)= 0 ,
Lt f x − f x +
f x
x
and f ′′(0) = 4 . Then the value of 0 2
x ; (B) greater than
3
2 ( ) 3 (2 ) (4 )
x
→
is
(A) 11 ; (B) 2 ; (C) 12 ; (D) none of these.
7. For e < x1 < x2 < ∞ ,
e 2
is
log x
1
log x
e
(A) less than
2
x
1
x , but less than
2
x
1
2
x
2
1
x ;
(C) greater than
3
x
2
1
x ; (D) greater than
2
x 2
, but less than
1
x
3
x
2
1
x .
8. The value of the expression
... 1
99 100
1
2 3
1
1 2
+
+ +
+
+
+
is
(A) a rational number lying in the interval (0,9) ;
(B) an irrational number i lying in the interval (0,9) ;
(C) a rational number lying in the interval (0,10) ;
(D) an irrational number lying in the interval (0,10).
4. 9. Consider a combination lock consisting of 3 buttons that can be
pressed in any combination (including multiple buttons at a time), but in
such a way that each number is pressed exactly once. Then the total
number of possible combination locks with 3 buttons is
( A ) 6 ; ( B ) 9 ; ( C ) 10 ; ( D ) 13 .
10. Suppose the correlation coefficient between x and y is denoted by R,
and that between x and (y + x), by R1.
Then, ( A ) R1 > R ; ( B ) R1 = R ;
(C ) R1 < R ( D ) none of these.
4
11. The value of (x x ) dx 1
∫ + −
1
is
(A) 0; (B) -1; (C) 1; (D) none of these.
12. The values of 0 1 x ≥ and 0 2 x ≥ that maximize 1 2 Π = 45x + 55x
subject to 6 4 120 1 2 x + x ≤ and
3 10 180 1 2 x + x ≤
are
(A) (10,12) ; (B) (8,5) ; (C) (12,11) ; (D) none of the above.
5. Syllabus for ME II (Economics), 2005
Microeconomics: Theory of consumer behaviour, Theory of producer
behaviour, Market forms (Perfect competition, Monopoly, Price
Discrimination, Duopoly – Cournot and Bertrand) and Welfare economics.
Macroeconomics: National income accounting, Simple model of income
determination and Multiplier, IS – LM model, Money, Banking and
Inflation.
Sample questions for ME II (Economics), 2005
1. (a) A divisible cake of size 1 is to be divided among n (>1) persons. It
is claimed that the only allocation which is Pareto optimal allocation is
(
1 ). Do you agree with this claim ? Briefly justify your
n
5
1 ,
n
1 , . . ,
n
answer.
(b) Which of the following transactions should be included in GDP?
Explain whether the corresponding expenditure is a consumption
expenditure or an investment expenditure.
(i) Mr. Ramgopal , a private investment banker, hires Mr. Gopi to
do cooking and cleaning at home.
(ii) Mr. Ramgopal buys a new Maruti Esteem.
(iii) Mr. Ramgopal flies to Kolkata from Delhi to see Durga Puja
celebration.
6. (iv) Mr. Ramgopal directly buys (through the internet) 100 stocks
6
of Satyam Ltd..
(v) Mr. Ramgopal builds a house.
2. Roses, once in full bloom, have to be picked up and sold on the same
day. On any day the market demand function for roses is given by
P = α - Q (Q is number of roses ; P is price of a rose).
It is also given that the cost of growing roses, having been incurred by any
owner of a rose garden long ago, is not a choice variable for him now.
( a ) Suppose, there is only one seller in the market and he finds 1000
roses in full bloom on a day. How many roses should he sell on that day
and at what price?
( b ) Suppose there are 10 sellers in the market, and each finds in his
garden 100 roses in full bloom ready for sale on a day. What will be the
equilibrium price and the number of roses sold on that day? (To answer
this part assume α ≥ 1100).
( c ) Now suppose, the market is served by a large number of price taking
sellers. However, the total availability on a day remains unchanged at
1000 roses. Find the competitive price and the total number of roses sold
on that day.
3. Laxmi is a poor agricultural worker. Her consumption basket comprises
three commodities: rice and two vegetables - cabbage and potato. But
7. there are occasionally very hard days when her income is so low that she
can afford to buy only rice and no vegetables. However, there never arises
a situation when she buys only vegetables and no rice. But when she can
afford to buy vegetables, she buys only one vegetable, namely the one that
has the lower price per kilogram on that day. Price of each vegetable
fluctuates day to day while the price of rice is constant.
Write down a suitable utility function that would represent Laxmi’s
preference pattern. Explain your answer.
4. Consider a simple Keynesian model for a closed economy without
Government. Suppose, saving is proportional to income (y), marginal
propensity to invest with respect to y is 0.3 and the system is initially in
equilibrium. Now, following a parallel downward shift of the saving
function the equilibrium level of saving is found to increase by 12 units.
Compute the change in the equilibrium income.
5. Consider an IS–LM model. In the commodity market let the
consumption function be given by C = a + b Y, a>0, 0< b <1. Investment
and government spending are exogenous and given by I0 and G0
respectively. In the money market, the real demand for money is given by
L = kY – gr, k> 0, g >0. The nominal money supply and price level are
exogenously given at M0 and P0 respectively. In these relations C, Y and r
denote consumption, real GDP and interest rate respectively.
(i) Set up the IS – LM equations.
(ii) Determine how an increase in the price level P1, where P1 >
P0, would affect real GDP and the interest rate.
7