MBA Programme-2012-2014

1. Vinod Gupta School of Management (VGSOM) uses CAT for short-listing candidates for its MBA programme. IIMs have no role either in the selection process or in the conduct of the programme.

2. The CAT advertisement came out on August 7th 2011.

3. VGSOM advertisement on Admissions to 2012-2014 MBA Programme would be released on August 17th 2011 in the leading newspapers.

4. VGSOM e-Brochure on 2012-2014 MBA Admissions.

5. The following are the guidelines pertaining to 2012-2014 MBA Admissions-

A candidate who has either secured or is likely to secure a first class Bachelor’s degree in Engineering/Technology or a first class Master’s degree in Science (with Mathematics or Statistics at Bachelor’s level) or a first class Master’s degree in Economics or Commerce (with Mathematics or Statistics at Bachelor’s level) is eligible for admission. Selection will be based on application rating, performance in CAT for domestic students and GMAT for international students, and candidate’s performance in group discussion and personal interview. Post-qualification work experience in industrial organizations will be given due consideration. The School follows Government of India norms regarding eligibility and reservation of seats for qualified Scheduled Caste/Tribe candidates, Other Backward Classes and Persons with Disability.

6. Domestic candidates seeking admission to the MBA Programme of VGSOM must complete the following procedures:

TEST STRUCTURE AND SAMPLE QUESTIONS

MAT is an objective type test designed and developed to ascertain the aptitude of the candidates to undergo Post Graduate Programme in Management. Aptitude is the potential of an individual to perform subsequent to proper training. Therefore MAT is designed to identify the potential. It is tested and perfected over a decade.

The MAT has five sections, each section having forty questions. The total 200 questions are to be attempted over 150 minutes.

The test structure is given below:

A few sample questions are given below for the guidance of the candidates in the preparation. These samples do not necessarily indicate either the types or the difficulty levels of questions that can be in the actual test. In general the preparation standard expected is that of a graduate from an Indian University having completed 10 + 2 + 3 pattern of education. However, the knowledge level required for attempting the section on Mathematical Skills is that of 10th standard under Central Board of Secondary Education.

Q1. If both x and y are prime numbers, which of the following CANNOT be the difference of x and y?
(A) 1
(B) 3
(C) 9
(D) 15
(E) 23
Answer: Choice E is correct. This problem is solved fastest by process of elimination. Both 2 and 3 are prime and their difference is one (Eliminate Choice A). Both 5 and 2 are prime and their difference is 3 (Eliminate Choice B). Both 11 and 2 are prime and their difference is 9 (Eliminate C). Both 17 and 2 are prime and their difference is 15 (Eliminate D).

Q2. Car X and Car Y are five miles apart and are on a collision course. Car X is driving directly north and Car Y is driving directly east. If the point of impact is one mile closer to the current position of Car X than to the current position of Car Y, how many miles away from the point of impact is Car Y at this time?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Answer: Choice D is correct. This problem can be solved by using the Pythagorean theorem as Cars X and Y are 5 miles apart, which is the hypotenuse of a right triangle. Let d be the distance Car Y is from the point of collision. Then the distance Car X is from the collision is d-1. Solving for D: dd + (d-1)(d-1) = 25, d=4, -3. Since d denotes distance, we reject -3 as a valid answer.

Q3. In the diagram above, AD = BE = 6 and CD = 3(BC). If AE = 8, then BC = ?
(A) 6
(B) 4
(C) 3
(D) 2
(E) 1
Answer: Choice E is correct. Since AE is a line segment and all the lengths are additive, AE = AD + DE. We know that AD = 6 and AE = 8. So DE = AE - AD = 8 - 6 = 2. We also know that BE = 6. So BD = BE - DE = 6 - 2 = 4. We know BD is 4, but need to find BC.

Since CD = 3(BC), we can solve for BC: x + 3x = 4. x = 1.

Q4. If the length of rectangle A is one-half the length of rectangle B, and the width of rectangle A is one-half the width of rectangle B, what is the ratio of the area of rectangle A to the area of rectangle B?
(A) 1/4
(B) 1/2
(C) 1/1
(D) 2/1
(E) 4/1
Answer: Choice A is correct. This problem includes a common mistake: the ratio of areas is NOT the same as the ratio of lengths. Instead, the ratio of areas for similar polygons is equal to the square of the lengths of the lengths. If we use 4 and 2 as the length and width for rectangle A, its area is 8. Rectangle B would have an area of (8)(4) = 32, four times that of A.

Q5. If the length of rectangle A is one-half the length of rectangle B, and the width of rectangle A is one-half the width of rectangle B, what is the ratio of the area of rectangle A to the area of rectangle B?
(A) 1/4
(B) 1/2
(C) 1/1
(D) 2/1
(E) 4/1
Answer: Choice A is correct. This problem includes a common mistake: the ratio of areas is NOT the same as the ratio of lengths. Instead, the ratio of areas for similar polygons is equal to the square of the lengths of the lengths. If we use 4 and 2 as the length and width for rectangle A, its area is 8. Rectangle B would have an area of (8)(4) = 32, four times that of A.

Q6. A cube and a rectangular solid are equal in volume. If the length of the edges of the rectangular solid are 4, 8, and 16, what is the length of an edge of the cube?
(A) 4
(B) 8
(C) 12
(D) 16
(E) 64
Answer: Choice B is correct. We have all of the dimensions to calculate the volume of the rectangular solid, which is 16 x 8 x 4. This is also the volume of the cube. So, the length of an edge of the cube is the cubic root of (16 x 8 x 4), or 8.

1. A poultry farm has only chickens and pigs. When the manager of the poultry counted the heads of the stock in the farm, the number totaled up to 200. However, when the number of legs was counted, the number totaled up to 540. How many chickens were there in the farm?

1. 70
2. 120
3. 60
4. 130
5. 80

The correct choice is (4) and the correct answer is 130.

Explanatory Answer:
Let there by 'x' chickens and 'y' pigs.
Therefore, x + y = 200 --- (1)
Each chicken has 2 legs and each pig has 4 legs
Therefore, 2x + 4y = 540 --- (2)
Solving equations (1) and (2), we get x = 130 and y = 70.
There were 130 chickens and 70 pigs in the farm.
 

2. Three years back, a father was 24 years older than his son. At present the father is 5 times as old as the son. How old will the son be three years from now?

1. 12 years
2. 6 years
3. 3 years
4. 9 years
5. 27 years

The correct choice is (4) and the correct answer is 9 years.

Explanatory Answer:
Let the age of the son 3 years back be x years
Therefore, the age of the father 3 years back was x + 24
At present the age of the son is x + 3 and the father is 5 times as old as the son.
i.e., x + 24 + 3 = 5(x + 3)
i.e., x + 27 = 5x + 15
or 4x = 12 or x = 3.

Therefore, the son was 3 years old 3 years back and he will be 9 years old three years from now.

3. For what values of 'k' will the pair of equations 3x + 4y = 12 and kx + 12y = 30 not have a unique solution?

1. 12
2. 9
3. 3
4. 7.5
5. 2.5

The correct choice is (2) and the correct answer is 9.

Explanatory Answer:
A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point.

That is, if they are not parallel lines. i.e., the two lines should have different slopes.
ax + by + c = 0 and dx + ey + g = 0 will not represent two parallel lines if their slopes are different.
i.e., when
In the question given above, a = 3, b = 4, d = k and e = 12.
Therefore, or 'k' should not be equal 9 for the pair of equations to have a unique solution.

In other words, when k = 9, the system of equation will not have any solution as the two lines represented by the equations will be parallel lines.

4. The basic one-way air fare for a child aged between 3 and 10 years costs half the regular fare for an adult plus a reservation charge that is the same on the child's ticket as on the adult's ticket. One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs $327. What is the basic fare for the journey for an adult?

1. $111
2. $52.5
3. $210
4. $58.5
5. $6

The correct choice is (3) and the correct answer is $210.

1. If A can do a piece of work in n days, then A’s 1 day work = 1/n

2. If A’s 1 day’s work = 1/n, then A can finish the work in n days.
Example: If A can do a piece of work in 4 days,then A’s 1 day’s work = 1/4. If A’s 1 day’s work = 1/5, then A can finish the work in 5 days

3. If A is thrice as good workman as B,then: Ratio of work done by A and B = 3:1. Ratio of time taken by A and B to finish a work = 1:3

4. Definition of Variation: The change in two different variables follow some definite rule. It said that the two variables vary directly or inversely. Its notation is X/Y = k, where k is called constant. This variation is called direct variation. XY = k. This variation is called inverse variation.

5. Some Pairs of Variables:
1. Number of workers and their wages. If the number of workers increases, their total wages increase. If the number of days reduced, there will be less work. If the number of days is increased, there will be more work. Therefore, here we have direct proportion or direct variation.

2. Number workers and days required to do a certain work is an example of inverse variation. If more men are employed, they will require fewer days and if there are less number of workers, more days are required.

3. There is an inverse proportion between the daily hours of a work and the days required. If the number of hours is increased, less number of days are required and if the number of hours is reduced, more days are required.

6. Some Important Tips:
More Men - Less Days and Conversely More Day - Less Men.
More Men - More Work and Conversely More Work - More Men.
More Days - More Work and Conversely More Work - More Days.
Number of days required to complete the given work = Total work/One day’s work.

Since the total work is assumed to be one(unit), the number of days required to complete the given work would be the reciprocal of one day’s work. Sometimes, the problems on time and work can be solved using the proportional rule ((man*days*hours)/work) in another situation.

7. If men is fixed,work is proportional to time. If work is fixed, then time is inversely proportional to men therefore, (M1*T1/W1) = (M2*T2/W2)

Problems on Time and Work

1) If 9 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days?

Solution: From the above formula i.e (m1*t1/w1) = (m2*t2/w2)
so (9*6*88/1) = (6*8*d/1)
on solving, d = 99 days.

2) If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in 6 days working 9 hours a day?

Solution: From the above formula i.e (m1*t1/w1) = (m2*t2/w2)
so, (34*8*9/(2/5)) = (x*6*9/(3/5))
so x = 136 men
number of men to be added to finish the work = 136-34 = 102 men

3) If 5 women or 8 girls can do a work in 84 days. In how many days can 10 women and 5 girls can do the same work?

Solution: Given that 5 women is equal to 8 girls to complete a work
so, 10 women = 16 girls.
Therefore 10women +5girls = 16girls+5girls = 21 girls.
8 girls can do a work in 84 days

1. If psin X = q and X is acute, then ?(p2—q2) tanX is equal to
(a) p
(b) q
(c) pq
(d)p+q

Ans.b

2- If tan?=3/4 and 0 is less than 6 is less than 90°, then sin ? . cos ? is equal to
(a) 12/25
(b) 3/5
(c) 18/25
(d) 4/5

Ans.a

3 If cos? = 5/13 0 is less than ? is less than 90º then the value of (cos? + 5cot?) / (cosec? – cos? )
(a) 169/109
(b) 155/109
(c) 185/109
(d) 395/109

Ans.c

4. The value of sin 0° + cos 30° — tan 45° + cosec 60° + cot 90° is equal to
(a) (7?3 – 6 )/ 66
(b) (6 + 7?3)/ 6
(c) 0
(d) 2

Ans.a

5. If sin ? = -1/2 then the possible values of ? between 0 and 2 ? are
(a) 2l0° and 300°
(b) 240° and 230°
(c) 240° and 300°
(4) 210º and 330º

Ans.d

6- The value of sin?/6+cos?/3-tan²45° is equal to `
(a) 1
(b) 0
(c) -1
(d) 2

Ans.b

7. The value of sin l5° is equal to
(a) (?3 + 1)/ ?2
(b) (?3 – 1)/ ?2
(c) (?3 + 1)/ 2?2
(d) (?3 – 1)/2?2

Ans.d

8. If sinx = 0.5040, then x is equal to
(a) 180° 5’
(b) 60°15’
(c) 30°16’
(d) 90°10’

Ans.c

9. If A. B and C are angles of a triangle, then sin 2A + sin 2B + sin 2C is equal to
(a) 8sinAsinBsinC
(b) 2 sinA sin B sin C
(c) sinA sinB sinC
(d) 4 sin A sinB sinC

Ans.d

10. The value of sin²? — sin² ? is
(a) sin (? + ?) sin (? – ?)
(b) cos (? + ?) cos (? – ?)
(c) cos (? + ?) sin (? – ?)
(d) sin (? + ?) cos (? – ?)

Ans.a

11. If the angle of elevation of sun is ? and the length of the shadow of a pole f length p is s. then
(a) p = scos?
(b) p = ssin?
(c) p=s/cot?
(d) p= ccot?

Ans.c

12. The foot of 2. ladder leaning against a wall of length 5 meters nests on a level ground 5?3 metres from the base of the wall, The angle of inclination of die ladder with the ground is
(a) 60°
(b) 50°
(c) 40º
(d) 30º

Ans.d

13. From the top of a 60 metre high tower, I the angle of depression of the top and bottom of a building are observed to be 30° and 60° respectively. The height of the building is
(a) 60?3 metres
(b) 40?3 metres
(c) 40 metres
(d) 20 metres

Syllabus for TANCET Part I Exam | Engineering Maths

SYLLABI FOR THE TANCET PART – I
ENGINEERING MATHEMATICS (Common to all Candidates)

i) Determinants and Matrices : Solving system of equations – Rank of the Matrix – Eigenvalues and eigenvectors – Reduction of quadratic form to canonical form.

ii) Calculus and Differential Equations : Partial derivatives – Jacobians – Taylor’s expansion – Maxima and Minima. Linear ordinary differential equations with constant coefficients – Simultaneous first order linear equations with constant coefficients. Formation of partial differential equation (PDE) – Solution of first order PDE – Solution of linear higher order PDE with constant coefficients.

iii) Vector Calculus : Double and triple integrations and their applications – Gradient, Divergence, Curl and Laplacian – Green’s, Gauss divergence and Stroke’s theorem.

iv) Functions of Complex Variables and Complex Integration : Analytic functions – Conformal Mapping – Bilinear transformation – Cauchy’s integral theorem and integral formula – Taylor and Laurent Series – Singularities – Residues – Residue theorem and its applications.

ICET Model Question Paper | Analytical/Mathematical/Communication Ability

SECTION A

Analytical Ability

(i) Date Sufficiency
In each of the questions numbered 1 and 2, the question is followed by data in the form of two statements labelled as i and ii. You must decide whether the data given in the statements are sufficient to answer the questions. Using the data, make an appropriate choice form (1) to (4) as per the following guidelines.

1. If the statement i alone is sufficient to answer the question;
2. If the statement ii alone is sufficient to answer the question;
3. If both the statements i and ii are sufficient to answer the question but neither statement along is sufficient.
4. If both the statements i and ii together and not sufficient to answer the question and additional data is required.

1. What is the value of the non-negative integer x?

1. 2x is odd
2. 3x is odd

2. What is the length of the train?

1. It crosses a pole in 8 seconds.
2. It crosses a bridge of length 100 m in 12 seconds.

(i) Problem solving

a) Sequence and Series

Note: In each of the questions numbered 3 and 4, a sequence of numbers or letters that follow a definite pattern is given. Each question has a blank space. This has to be filled with the correct answer chosen from the given four options to complete the sequence without breaking the pattern.

3. AZBY, CXDW …………………. GTHS

1. EXUV
2. EVFU
3. EVRU
4. EVSU

Management Aptitude Test or MAT is the test conducted by All India Management Testing Service for entering into MBA or equivalent post graduate programmes.

There are five papers in MAT:

• Paper 1 : Language Comprehension
• Paper 2 : Mathematical Skills
• Paper 3 : Data Analysis
• Paper 4 : Intelligence & Critical Re
  

Tutorials on Quantitive Aptitude (Maths/Problem Solving) | Number System - Remainder Theorem

Description : The content of the video is espacially designed for MBA Aspirants who will be taking CAT and similar entrance examinations

Number System : Remainder Theorem

Part II

Tutorials on Quantitive Aptitude (Maths/Problem Solving) | Number System - Remainder Theorem

Description : The content of the video is espacially designed for MBA Aspirants who will be taking CAT and similar entrance examinations

Number System : Remainder Theorem

Part I

Tutorials on Quantitive Aptitude (Maths/Problem Solving) | Number System - Factor Theory

Description : The content of the video is espacially designed for MBA Aspirants who will be taking CAT and similar entrance examinations

Number System : Factor Theory

Tutorials on Quantitive Aptitude (Maths/Problem Solving) | Number System - Divisibility Test

Description : The content of the video is espacially designed for MBA Aspirants who will be taking CAT and similar entrance examinations

Number System : Divisibility Test

Part II

Tutorials on Quantitive Aptitude (Maths/Problem Solving) | Number System - Divisibility Test

Description : The content of the video is espacially designed for MBA Aspirants who will be taking CAT and similar entrance examinations

Number System : Divisibility Test

Part I

Tutorials on Quantitive Aptitude (Maths/Problem Solving) | Number System - Base System

Description : The content of the video is espacially designed for MBA Aspirants who will be taking CAT and similar entrance examinations

Number System : Base System

Part II

Tutorials on Quantitive Aptitude (Maths/Problem Solving) | Number System - Base System

Description : The content of the video is espacially designed for MBA Aspirants who will be taking CAT and similar entrance examinations

Number System : Base System

Part I

Set Theory for GMAT

Description :

SETS

• "Set" is synonymous with the words: "collection";, "aggregate", "class" and is comprised of elements/objects/members.
• The following are some examples of sets:
• The collection of vowels in English Alphabets.
• The collection of all past Presidents of the Indian Union.
• The weights of all the students of a class.

DEFINING A SET :A set is a collection of well defined entities, objects or elements. OR A set is a group of one or more elements with common characteristics. OR A set is a collection of distinct, unordered objects. Sets are typically collection of numbers. So, a set may contain any type of data (including other sets).

DESCRIBING A SET: A set is described by listing elements, separated by commas, within brackets. For example: A set of vowels of English Alphabet may be described as: {a, e, i, o, u} A set of even natural numbers can be described as: {2, 4, 6, 8,…} Note: The order in which the elements are written makes no difference. Also, repetition of an element has no effect. For example {1, 2, 3, 2} is the same set as {1, 2, 3}. DESCRIBING A SET

Model Practice Paper For CAT Exam: Based on Previous Year Papers (Solved)

1. This test is based on pattern of previous years’ CAT papers.

2. There are four sections

• Section I – English (40 Questions)
• Section II – Reading Comprehension (40 Questions)
• Section III – Quantitative Ability (40 Questions)
• Section IV – Data Interpretation & Data Sufficiency (40 Questions)

GRE Subject Test Notes For Mathematics

• The test consists of approximately 66 multiple-choice questions drawn from courses commonly offered at the undergraduate level.

• Although the Mathematics Test was rescaled in October 2001, the content of the test did not change.