CAT Quantitative Ability (Quant / Math)

Syllabus, Topics tested in IIM's Common Admissions Test

The Quant (Math) section in CAT usually accounts for a third of the questions in CAT. For instance, in CAT 2006 and CAT 2007 the quant section had 100 marks worth questions out of the total of 300 marks worth questions. More often than not students who take CAT find the quant section as the toughest one. Albeit, CAT 2006 was an exception

2IIM's CAT Math Refresher Books cover the following topics

Broadly categorized as Arithmetic, Algebra and Geometry CAT typically tests a student's quantitative ability from over 25 topics. These topics that appear in CAT are of high school level. Click on the links that follow each topic for details of what is covered in 2IIM's Quant Refresher books on these topic and for accesing an archive of sample questions from these topics.

1. Arithmetic
   
   1. Number Systems and Number Theory - Practice Questions
   2. Percentages - Details | Sample Test | Practice Questions
   3. Profit and Loss - Details | Sample Test | Practice Questions
   4. Simple & Compound Interest - Practice Questions
   5. Speed, Time and Distance - Practice Questions
   6. Pipes and Cisterns - Practice Questions
   7. Races - Practice Questions
   8. Averages - Practice Questions
   9. Ratio, Proportion - Practice Questions
   10. Mixtures and Alligations - Practice Questions


2. Algebra
   
   1. Linear and Quadratic Equation - Practice Questions
   2. Logarithm
   3. Progressions - AP, GP, HP
   4. Binomial Theorem
   5. Inequalities
   6. Permutation & Combination
   7. Probability
   8. Function
   9. Set Theory


3. Geometry
   
   1. Geometry
   2. Co ordinate Geometry
   3. Trigonometry
   4. Mensuration

CAT - The Course Material

You will be provided with comprehensive study material for CAT. The broad areas that are covered by the course material are listed below:

1. Quantitative Reasoning - Study Material>
   Refresher study material covering all relevant topics - starting from Number systems, Percentages to Permutation & Combination to Functions. The refresher contains introduction and explanation on concepts in each topic followed by adequate number of solved examples which cover most of the different types of questions that appear in each chapter. Solved examples are followed by adequate number of exercise problems which are provided with answers and solutions.
   
   A Speed Test in each of the above mentioned topics comprising 30 to 60 oft repeated questions will be conducted at the end of each topic. The Speed Tests have been designed to help you consolidate what you have learnt in the respective topics and to assit you in remembering various short cuts and techniques taught as part of covering concepts in each topic.
   
   Proficiency Tests, each of which will cover between 1 to 3 topics. Theses tests are designed to acquaint you to a variety of oft repeated questions and to help you master concepts in Math and skillfully employ smart techniques in answering these questions.
   
   
2. Verbal Ability - Study Material
   Word list - with around 2500 words. Also includes commonly used non-English foreign words.
   Alphabet wise tests on vocabulary
   Basic refresher in English Usage with emphasis on how to spot common errors in sentences
   Speed Tests on Sentence Correction
   Exercises and Tests on Sentence Re-arrangement.
   Syllogisms and critical reasoning - Refresher material.
   
   
3. Reading Comprehension - Course Material
   Tips and techniques on attempting RC questions
   Over 200 passages and 1000 questions from various topics - Speed Tests.
   
   
4. Data Interpretation - Course Material
   A Refresher with introduction to various types of questions that typically appear in Data Interpretation - viz. Tables, Pie Charts, Bar Charts, Line Graph ...
   A Refresher on Data Sufficiency with emphasis on common traps in these questions.
   7 Speed Tests on Data Interpretation
   
   
5. CAT Comprehensive Tests (Mock CAT Tests)
   20 full length comprehensive tests + 10 Mock CATs with explanatory answers.

ABOUT GATE EXAMINATION

Candidates will be required to appear in a single paper of three hours duration. The examination will be held from 09:30 hours to 12:30 hours on Sunday, February 08, 2009. The list of papers for GATE 2009 is given under Structure of GATE. The question papers will be in English only.

Before applying for GATE 2009, candidates must assure themselves that they have chosen the right paper, which qualifies them to become eligible to seek admission to the specific programme they are interested in. The criteria for postgraduate admission with Scholarship/ Assistantship are different in various Institutes/Universities. GATE Offices will not provide any information in this regard. For more details, the candidates are required to contact the Institutes/Universities to which they are interested in seeking admission.

The choice of the paper is the responsibility of the candidate.

Information about the pattern of the question papers is given under Question Paper Pattern.

ELIGIBILITY

Following categories of candidates are eligible to appear in GATE:

	Bachelor's degree holders in Engineering/ Technology/ Architecture/Pharmacy (4 years after 10+2) and those who are in the final or pre-final year of such programmes.
	Master's degree holders in any branch of Science/ Mathematics/ Statistics/ Computer Applications or equivalent and those who are in the final or pre-final year of such programmes.
	Candidates in the second or higher year of the Four-year Integrated Master's degree programme (Post-B.Sc.) in Engineering/Technology or in the third or higher year of Five-year Integrated Master's degree programme and Dual Degree programme in Engineering/Technology.
	Candidates with qualifications obtained through examinations conducted by professional societies recognized by UPSC/AICTE (e.g. AMIE by IE(I), AME by ICE(I)) as equivalent to B.E./B.Tech. Those who have completed section A or equivalent of such professional courses are also eligible.

Each paper contains 60 questions carrying 100 marks	TOP
	Question Paper Pattern of GATE papers bearing the codes AE, AG, AR, CE, CH, CS, CY, EC, EE, IN, MA, ME, MN, MT, PH, PI, PY and TF Question Paper Pattern of GATE paper bearing the code GG Question Paper Pattern of SECTION A in GATE paper bearing the code XE Question Paper Pattern of SECTIONS B to G in GATE paper bearing the code XE Question Paper Pattern of SECTION H in GATE paper bearing the code XL Question Paper Pattern of SECTIONS I to M in GATE paper bearing the code XL (Refer Exam Structure for GATE papers, codes & Syllabi) Types of multiple choice questions
Question Papers bearing the codes : AE, AG, AR, CE, CH, CS, CY, EC, EE, IN, MA, ME, MN, MT, PH, PI, PY and TF Paper Code Patterns of Question papers Negative Marks for wrong Answer AE, AG, AR, CE, CH, CS CY, EC, EE, IN, MA, ME, MN, MT, PH, PI , PY, TF Q.1 to Q.20 : Will carry one mark each (sub-total 20 marks). 1/3 mark will be deducted for each wrong answer. Q.21 to Q.50 : Will carry two marks each (sub-total 60 marks) 2/3 mark will be deducted for each wrong answer. Q.51 through Q.56 (3 pairs) will be common data questions. Each question will carry two marks 2/3 mark will be deducted for each wrong answer. Question pairs (Q.57, Q.58) and (Q.59, Q.60) will be linked answer questions. The answer to the second question of the last two pairs will depend on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is un-attempted, then the answer to the second question in the pair will not be evaluated. Each question will carry two marks There will be negative marks only for wrong answer to the first question of the linked answer question pair i.e. for Q.57 and Q.59, 2/3 mark will be deducted for each wrong answer. There is no negative marking for Q.58 and Q.60. Go to TOP GG Paper : (Geology & Geophysics) Paper PART A Part A common to both Geology & Geophysics candidates (Q.1 to Q.20) carrying one mark each (sub-total 20 marks). 1/3 mark will be deducted for each wrong answer. Sections 1 & 2 in PART B Part B will contain two sections : Section 1 (Geology) and Section 2 (Geophysics). In this section, Q.21 to Q.50 (30 questions) will carry two marks each (sub-total 60 marks). 2/3 mark will be deducted for each wrong answer. Q.51 to Q.56 (3 pairs) will be common data questions Each question will carry two marks. 2/3 mark will be deducted for each wrong answer. Question pairs (Q.57, Q.58) and (Q.59, Q.60) will be linked answer questions:. The answer to the second question in these two pairs will depend on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is un-attempted, then the answer to the second question in the pair will not be evaluated. There will be negative marks only for wrong answer to the first question of the linked answer question pair i.e. for Q.57 and Q.59, 2/3 mark will be deducted for each wrong answer. There is no negative marking for Q.58 and Q.60. Go to TOP XE Paper - Section A (Engineering Mathematics) Section A in XE paper There will be 12 questions carrying 20 marks in XE Section A (Engineering Mathematics) paper Q.1 to Q.4 (4 questions) will carry one mark each (sub-total 4 marks). 1/3 mark will be deducted for each wrong answer. Q.5 to Q.12 (8 questions) will carry two marks each (sub-total 16 marks) 2/3 mark will be deducted for each wrong answer. Go to TOP XE section papers (Sections B through G) will contain 24 questions carrying 40 marks Sections B, C, D, E, F & G in XE papers Q.1 to Q.8 (8 questions) will carry one mark each (sub-total 8 marks) 1/3 mark will be deducted for each wrong answer. Q.9 to Q.18 (10 questions) will carry two marks each (sub-total 20 marks). 2/3 mark will be deducted for each wrong answer. Q.19 through Q.22 (2 pairs) will be common data based questions. Each will carry two marks 2/3 mark will be deducted for each wrong answer. Q.23, Q.24 will be linked answer questions. The answer to the second question of the pair of linked question will depend on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is un-attempted, then the answer to the second question in the pair will not be evaluated. Each will carry two marks For Q.23, 2/3 mark will be deducted for wrong answer. There will be no negative mark for Q.24. Go to TOP XL Paper Section H (Chemistry) Section H in XL paper There will be 18 questions carrying 30 marks in XL Section H paper Q.1 to Q.6 (6 questions) will carry one mark each (sub-total 6 marks). 1/3 mark will be deducted for each wrong answer. Q.7 to Q.14 (8 questions) will carry two marks each (sub-total 16 marks) 2/3 mark will be deducted for each wrong answer. (Q.15, Q.16) will be common data questions . Each question will carry two marks each 2/3 mark will be deducted for each wrong answer. Question pair (Q.17, Q.18) will have linked answer question. Each question will carry two marks each. There will be negative marks only for wrong answer to the first question of the linked answer question pair. For Q.17, ⅔ mark will be deducted for wrong answer. There is no negative mark for Q.18. Go to TOP XL Paper Sections (Sections I through M) Sections I, J, K, L & M in XL paper XL section papers (Sections I through M) will contain 21 questions carrying 35 marks Q.1 to Q.7 (7 questions) will carry one mark each (sub-total 7 marks). 1/3 mark will be deducted for each wrong answer. Q.8 to Q.21 (14 questions) will carry two marks each (sub-total 28 marks). 2/3 mark will be deducted for each wrong answer. Types of multiple choice questions Multiple choice questions in all papers and sections will contain four answers, of which only one is correct. The types of questions in a paper may be based on following logic: (i) Recall: These are based on facts, principles, formulae or laws of the discipline. The candidate is expected to be able to obtain the answer either from his/her memory of the subject or at most from a one-line computation. Example Q. During machining maximum heat is produced (A) in flank face (B) in rake face (C) in shear zone (D) due to friction between chip and tool. (ii) Comprehension: These questions will test the candidate�s understanding of the basics of his/her field, by requiring him/her to draw simple conclusions from fundamental ideas. Example Q. A DC motor requires a starter in order (A) to develop a starting torque (B) to compensate for auxiliary field ampere turns (C) to limit armature current at starting (D) to provide regenerative braking (iii) Application: In these questions, the candidate is expected to apply his/her knowledge either through computation or by logical reasoning. Example Q. The sequent depth ratio of a hydraulic jump in a rectangular channel is 16.48. The Froude number at the beginning of the jump is: (A) 10.0 (B) 5.0 (C) 12.0 (D) 8.0 (iv) Analysis and Synthesis: These can be linked questions, where the answer to the first question of the pair is required in order to answer its successor. Or these can be common data questions, in which two questions share the same data but can be solved independently of one another. Go to TOP Common data questions: Multiple questions may be linked to a common data problem, passage and the like. Two or three questions can be formed from the given common data problem. Each question is independent and its solution obtainable from the above problem data/passage directly. (Answer of the previous question is not required to solve the next question). Each question under this group will carry two marks. Example Common Data, for instance, Questions 55 and 56 in main paper: Let X and Y be jointly distributed random variables such that the conditional distribution of Y, given X=x, is uniform on the interval (x-1,x+1). Suppose E(X)=1 and Var(X)=5/3. First question using common data: Q.55 The mean of the random variable Y is (A) 1/2 (B) 1 (C) 3/2 (D) 2 Second question using common data: Q.56 The variance of the random variable Y is (A) 1/2 (B) 2/3 (C) 1 (D) 2 Go to TOP Linked answer questions: These questions are of problem solving type. A problem statement is followed by two questions based on the problem statement. The two questions are designed such that the solution to the second question depends upon the answer to the first one. In other words, the first answer is an intermediate step in working out the second answer. Each question in such �linked answer questions� will carry two marks. Example Statement for Linked Answer Questions, for instance, for Questions 59 and 60 in Main Paper: Consider a machine with a byte addressable main memory of 216 bytes. Assume that a direct mapped data cache consisting of 32 lines of 64 bytes each is used in the system. A 50x50 two dimensional array of bytes is stored in the main memory starting from memory location 1100H. Assume that the data cache is initially empty. The complete array is accessed twice. Assume that the contents of the data cache do not change in between the two accesses. First question of the pair: Q.59 How many data cache misses will occur in total? (A) 48 (B) 50 (C) 56 (D) 59 Second question of the pair: Q.60 Which of the following lines of the data cache will be replaced by new blocks in accessing the array for the second time? (A) line 4 to line 11 (B) line 4 to line 12 (C) line 0 to line 7 (D) line 0 to line 8 The questions based on the above four logics may be a mix of single stand alone statement / phrase / data type questions, combination of option codes type questions or match items types questions.

Candidates can submit Application Form in two different modes : OFFLINE and ONLINE

OFFLINE			ONLINE
Application fee	General & OBC	Rs. 1000	Application fee	General & OBC	Rs. 900
	SC/ST/PD	Rs. 500		SC/ST/PD	Rs. 400
Application Submission Process			Application Submission Process
Step. 1 Procurement of Application Form Candidate can obtain a packet containing (i) OFFLINE Application Form (ii) Information Brochure (iii) Acknowledgment Card (iv) Envelope from: Designated Bank Branches corresponding to each zone on cash payment. Zonal GATE Office by sending a request letter and TWO self-addressed slips along with a Demand Draft for appropriate amount. Zonal GATE Office after handing over Demand Draft for appropriate amount.			Step. 1 Obtain a Demand Draft The candidates must obtain a Demand Draft, drawn on any nationalized bank in favor of Chairman of the corresponding zonal GATE Office, the website of which the candidate wishes to submit online Application.
			Step. 2 Online Application	New Registration Registered Candidates
Step 2. Fill in the Application Form			Step 3. Take print out of Application Form Save the PDF file, take a printout, Sign at appropriate places and paste photograph.
Step 3. Obtain SC/ST/PD/OBC (non creamy layer) Certificate SC/ST/OBC (non creamy layer) and Disability Certificate should be obtained from appropriate authority, if applicable. Authorities who can issue SC/ST/OBC (non creamy layer) Certificates.			Step 4. Obtain SC/ST/PD/OBC (non creamy layer) Certificate SC/ST/OBC (non creamy layer) and Disability Certificate should be obtained from appropriate authority, if applicable. Authorities who can issue SC/ST/OBC (non creamy layer) Certificates.
Step 4. Post/Submission Duly filled-in Application Form with appropriate enclosures must be sent by Registered or Speed post to the Chairman, GATE of the Zone, where the candidate prefers (corresponding to the 1st Choice of Examination City) to appear for the examination, on or before Wednesday, October 29, 2008. Or It can be handed over personally to respective Zonal GATE Office.			Step 5. Post/Submission Duly filled-in Application Form with appropriate enclosures must be sent by Registered or Speed post to the Chairman, GATE of the Zone, the website of which has been used for making ONLINE registration on or before Wednesday, October 29, 2008. OR It can be handed over personally to respective Zonal GATE Office.

GATE 2009 RESULTS

1. GATE 2009 results will be announced on March 15, 2009 at 10:00 hrs. at GATE offices and on the websites of IISc and seven IITs.
   
   
2. GATE 2009 score is valid for ONE YEAR ONLY from the date of announcement of the GATE 2009 results.
   
   
3. The GATE scores to both qualified and non-qualified candidates will be provided on the GATE websites.
   
   
4. The GATE results of the qualified candidates may be made available to interested organizations (educational institutions, R & D laboratories, industries, etc.) in India and abroad based on written request by the organization and on payment. Details can be obtained from GATE Chairmen of IITs/IISc.
   
   
5. The evaluation of the ORS is carried out by a computerized process using scanning machines, with utmost care.

GATE Scorecard

The GATE 2009 scorecard will consist of actual marks obtained by the candidate, the GATE Score, Percentile Score and All India Rank (AIR). Scorecard will be sent only to the qualified candidates. No information will be sent to candidates who are not qualified.

GATE scorecard is valid for ONE YEAR ONLY. Additional scorecards (up to a maximum of two) will be issued only once on request and on payment of Rs 300 per scorecard. Such requests should reach the Organizing Chairman, GATE 2009, Indian Institute of Technology Roorkee, Roorkee � 247 667 before August 31, 2009 together with a bank draft for the amount mentioned as above in favour of Chairman GATE, IIT Roorkee, payable at Roorkee. These scorecards will be labeled as Additional Scorecard -1 and Additional Scorecard - 2.

GATE Score

The GATE score, awarded in the range of 0 to 1000 reflects the candidate�s academic ability and will be based on his/her performance in GATE 2009 and the performances of all candidates who appeared in GATE in the last four years 2006-2009. Candidates with the same GATE score from different GATE papers and/or years can be considered to have the same performance level.

GATE Score
where,	m : marks obtained by the candidate. a: average of marks of all candidates who appeared in the paper mentioned on this scorecard in GATE 2009 s: standard deviation of marks of all candidates who appeared in the paper mentioned on this scorecard in GATE 2009 ag: average (global) of marks of all candidates who appeared across all papers and years 2006-2009 sg: standard deviation (global) of marks of all candidates who appeared across all papers and years 2006- 2009 The maximum score can be 1000.
GATE Percentile Score The percentile score of a candidate indicates the percentage of candidates who appeared in the same paper and scored less marks than him/her. It is calculated as follows: If N is the total number of candidates appearing in a paper, then the percentile score P is given as, P = (number of candidates who have scored less marks than the candidate / N) x 100

SYLLABUS

Aerospace Engineering -AE

ENGINEERING MATHEMATICS

Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors.

Calculus: Functions of single variable, limit, continuity and differentiability, mean value theorems, evaluation of definite and improper integrals, partial derivatives, total derivative, maxima and minima, gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals. Theorems of Stokes, Gauss and Green.

Differential Calculus: First order linear and nonlinear equations, higher order linear ODEs with constant coefficients, Cauchy and Euler equations, initial and boundary value problems, Laplace transforms. Partial differential equations and separation of variables methods.

Numerical methods: Numerical solution of linear and nonlinear algebraic equations, integration by trapezoidal and Simpson rule, single and multi-step methods for differential equations.

FLIGHT MECHANICS

Atmosphere: Properties, standard atmosphere. Classification of aircraft. Airplane (fixed wing aircraft) configuration and various parts.

Airplane performance: Pressure altitude; equivalent, calibrated, indicated air speeds; Primary flight instruments: Altimeter, ASI, VSI, Turn-bank indicator. Drag polar; take off and landing; steady climb & descent,-absolute and service ceiling; cruise, cruise climb, endurance or loiter; load factor, turning flight, V-n diagram; Winds: head, tail & cross winds.

Static stability: Angle of attack, sideslip; roll, pitch & yaw controls; longitudinal stick fixed & free stability, horizontal tail position and size; directional stability, vertical tail position and size; dihedral stability. Wing dihedral, sweep & position; hinge moments, stick forces.

Dynamic stability: Euler angles; Equations of motion; aerodynamic forces and moments, stability & control derivatives; decoupling of longitudinal and lat-directional dynamics; longitudinal modes; lateral-directional modes.

SPACE DYNAMICS

Central force motion, determination of trajectory and orbital period in simple cases. Orbit transfer, in-plane and out-of-plane. Elements of rocket motor performance.

AERODYNAMICS

Basic Fluid Mechanics: Incompressible irrotational flow, Helmholtz and Kelvin theorem, singularities and superposition, viscous flows, boundary layer on a flat plate.

Airfoils and wings: Classification of airfoils, aerodynamic characteristics, high lift devices, Kutta Joukowski theorem; lift generation; thin airfoil theory; wing theory; induced drag; qualitative treatment of low aspect ratio wings.

Viscous Flows: Flow separation, introduction to turbulence, transition, structure of a turbulent boundary layer.

Compressible Flows: Dynamics and Thermodynamics of I-D flow, isentropic flow, normal shock, oblique shock, Prandtl-Meyer flow, flow in nozzles and diffusers, inviscid flow in a c-d nozzle, flow in diffusers. subsonic and supersonic airfoils, compressibility effects on lift and drag, critical and drag divergence Mach number, wave drag.

Wind Tunnel Testing: Measurement and visualisation techniques.

STRUCTURES

Stress and Strain: Equations of equilibrium, constitutive law, strain-displacement relationship, compatibility equations, plane stress and strain, Airy's stress function.

Flight Vehicle Structures: Characteristics of aircraft structures and materials, torsion, bending and flexural shear. Flexural shear flow in thin-walled sections. Buckling. Failure theories. Loads on aircraft.

Structural Dynamics: Free and forced vibration of discrete systems. Damping and resonance. Dynamics of continuous systems.

PROPULSION

Thermodynamics of Aircraft Gas Turbine engines, thrust and thrust augmentation.

Turbomachinery: Axial compressors and turbines, centrifugal pumps and compressors.

Aerothermodynamics of non rotating propulsion components: Intakes, combustor and nozzle. Thermodynamics of ramjets and scramjets. Elements of rocket propulsion.