Careers360 Logo
Conquering Functions & Graphs, Puzzle Questions for Linear Arrangement, and Conditionals- Day 18

Conquering Functions & Graphs, Puzzle Questions for Linear Arrangement, and Conditionals- Day 18

Edited By Irshad Anwar | Updated on Oct 04, 2023 04:15 PM IST | #CAT

Based on the CAT syllabus 2023, we have created a study schedule to ace the CAT Exam. We discussed a plan for every day from Day 1 through Day 17 in advance.

On the basis of the CAT syllabus 2023, we discussed strategies on how to prepare for inequalities (Algebra), puzzles/problem-solving based on linear arrangement, and vocabulary in the previous article - Day 17 of CAT preparation. We have brought you CAT problem-solving questions and answers for you to practice and learn the concepts for a better flow.

Conquering Functions & Graphs, Puzzle Questions for Linear Arrangement, and Conditionals- Day 18
Conquering Functions & Graphs, Puzzle Questions for Linear Arrangement, and Conditionals- Day 18

We're back with a strategy for the Day 18 of our preparation for the CAT 2023. In this article, we will be discussing strategies for the following topics and CAT problem-solving questions answers including function and graph CAT questions and CAT previous year questions on functions.

With the 60-day CAT exam preparation schedule we created for you, you can ace the CAT 2023 and get a flow, plan, and schedule for your preparation.

CAT Exam Part-A: Quantitative Aptitude for CAT 2023

Topic: Algebra (Functions and Graph) and CAT Problem-Solving Questions Answers

Definition: In a system, the output is a function of the input. Or, we can say function describes a relation between input and output.

For example: f(x) =x2, describes output (f(x)) varies as square of the input (x).

Functions can be well represented by graphs and with the help of graphs, solutions can be drawn effectively.

The graph shows the variation of output with the inputs.

1696411576416

Tips and tricks to Prepare Functions and Graph for CAT

  1. To solve the questions of function and graph for CAT, you have to learn some specific functions CAT questions and their graphs. A few of them are here with examples.

Even and Odd Function:

Odd Function:

If f (– x) = – f (x)

For example: f (x) = x3 + sin x; 0 ≤ x ≤ 2π

f(-x) = (-x)3 + sin (-x) = -x.3 – sin x = -f(x)

So, the given function is an odd function.

(Graph of odd functions are symmetrical about the origin).

Even function:

If f (– x) = f (x)

For example: f (x) = x2 + cos x; 0 ≤ x ≤ 2π

f(-x) = (-x)2 + cos (-x) = x2+ cos x = f(x)

So, the given function is an even function.

(Graphs of even functions are symmetrical about the y-axis).

Functions can neither be odd nor be even but can be expressed as sum of even and odd functions.

Composite Functions:

It is a function of some other function.

(g o f) (x) = g [f(x)]

(f o g) (x) = f [g(x)]

  1. Understand the concept of Domain and Range:

ICFAI Business School-IBSAT 2024

9 IBS Campuses | Scholarships Worth Rs 10 CR

Amity University Noida MBA Admissions 2024

Ranked as India’s #1 Not for profit pvt. University by India Today

Domain: Set of input values and represented on x-axis of the graph.

Range: Set of output values and represented on the y-axis of the graph.

  1. Learn the graphs of some functions as shown and that will be very helpful.

CAT 2024 Most Scoring Concepts- VARC, DILR & QUANT
Start your CAT journey today and download CAT 2024 most scoring concepts PDF, including study materials based on CAT previous year papers, CAT question papers, and CAT exam sample questions.
Download EBook

1696411577241

1696411577895

Functions Questions For CAT From CAT Previous Year Papers

Q1. If f(x)=x2−7x and g(x)=x+3, then the minimum value of f(g(x)) −3x is [CAT exam 2021, slot-3]

A. – 20 B. – 15 C. – 12 D. – 16

Ans: (D)

f (g(x))- 3x = (x+3)2 – 7(x+3) – 3x

= x2 + 9 + 6x -7x – 21 – 3x

= x2– 4x – 12

= x2 – 4x +4 – 4 – 12

= (x – 2)2 – 16

Minimum value of this function will be -16 for x =2.

Q2. If f(x+y) = f(x).f(y) and f(5) = 4, then f(10) - f(-10) is equal to [CAT exam 2020, slot-3]

A. 3 B. 0 C. 14.0625 D. 15.9375

Ans: (D)

It is given that f(x+y) = f(x) × f(y)

For y = 0, f(x) = f(x) × f(0) ⇒ f(0) = 1.

for, x = 5

f (5) = 4

f(10) = f(5+5) = f(5) × f(5) = 4 × 4 = 16

f(10) = 16

We can write;

f(0) = f(10 - 10) = f(10 + (-10)) = f(10) × f(-10) = 1

f(-10) = 1/16

f(10) - f(-10) = 16 – 1/16 = 15.9375.

CAT EXAM: Prerequisite to Problem Solving Questions For Entrance Exam based on functions and graphs for CAT

  • Linear Equation.
  • Quadratic Equation.
  • Polynomials.Equations of Geometrical figures.
Jindal Global Business School | MBA Admissions 2024

MBA (2 Years) & MBA in Business Analytics (1 Year) @ JGBS | NAAC Accredited | AACSB Member |92% Placement Track | Highest CTC 11 LPA

SKIPS PGDM Admissions 2024

AICTE Approved | Key Recruiters: MRF, Nestle, Federal Bank etc

CAT EXAM: References to Study (Theory):

  • Functions and Graph (Arihant Publication)
  • How to prepare Quantitative aptitude for CAT by Arun Sharma.
  • 2IIM CAT Preparation

CAT EXAM: References to Study (Practice):

  • The Pearson Guide to Verbal Ability and Reading Comprehension for CAT by Nishit Sinha (2020)
  • https://iim-cat-questions-answers.2iim.com
  • Previous Years Question Papers

Part-B: CAT Logical Reasoning and Data Interpretation:

The topic covered for the day is given below: Students can refer to Linear arrangement Part 1 for Day 16

Topic: Problem-Solving/ Puzzles (Linear Arrangement Part-2)

In this section, we will discuss the strategies to solve Puzzle questions for CAT exam based on the linear arrangement with the help of examples:

Type 1: Simple Linear Arrangement ( Puzzle questions for CAT exam)

Directions for Questions 1 to 4:

There are six friends (Andrew, Baithi, Charles, Duke, Elena, Flora) seated in a row with numbered chairs from 1 to 6. They follow the following sitting arrangement:

1. There are two places between Charles and Duke

2. There is one place between Andrew and Charles

3. There is one person between Flora and Elena

4. Elena is to be seated before Flora

5. Baithi is to be seated before Andrew, not necessarily immediately

6. The row does not start with Baithi

Question 1: The row would start with:

  1. Andrew
  2. Flora
  3. Duke
  4. Cannot be determined

Question 2: Elena will be seated on which seat number?

  1. 1
  2. 2
  3. 3
  4. Cannot be determined

Question 3: Who is seated at place number 6?

  1. Andrew
  2. Flora
  3. Duke
  4. Cannot be determined

Question 4: Baithi’s position is

  1. 6
  2. 5
  3. 3
  4. 2

The solution strategy for the above problem will be:

  1. While solving, use Initials for each Name, for example,

Write A for Andrew, B for Baithi etc.

  1. Mark the 6 places and fill them according to given instructions.

1

2

3

4

5

6







Given statements are

There are two places between Charles and Duke

C _____ _____ D or D ______ ______C

There is one place between Andrew and Charles

A _____ C or C _______ A

There is one person between Flora and Elena, Elena is to be seated before Flora

E _______ F

Baithi is to be seated before Andrew, not necessarily immediately

The row does not start with Baithi

  1. Eliminate the wrong possibilities

  • Find the person in the first place.
  • From above, In the first place either A, C, D and E will come.
  • We cannot start with A since B should come before B. and B cannot be in the first place.
  • If we start with C
  • C ___ A D __ ___ (we cannot place E and F in this arrangement since E and F must have one person in between them)
  • If we start with D
  • D ___ ____ C __ A (we cannot place E and F in this arrangement since E and F must have one person in between them)
    After placing E, F and B according to given condition
    D B E C F A
  • If we start with E
  • E ___ F ___ __ A (in this arrangement C must be just after F. So, we will not be able to place D. Therefore, this arrangement cannot be true)
  • Correct combination should be

1

2

3

4

5

6

D

B

E

C

F

A

Answer: 1 (c), 2 (c), 3 (a), 4 (d)

CAT Solved Questions

Type 2: When two arrangements are given.

Directions: Study the following information to answer the given questions:

Twelve people are sitting in two parallel rows containing six people each, in such a way that there is an equal distance between adjacent persons.

In row – 1, A, B, C, D, E and F are seated and all of them are facing south.

In row – 2, P, Q, R, S, T and V are seated and all of them are facing north.

Additional information is also given as

  • Each member seated in a row faces another member of the other row.
  • V sits third to the right of S.
  • S faces F and F does not sit at any of the extreme ends of the line.
  • D sits third to the right of C. R faces C.
  • The one facing E sits third to the right of P.
  • B and P do not sit at the extreme ends of the line.
  • T is not an immediate neighbour of V and A is not an immediate neighbour of F.
  • P sits to the left of S.

Question 1: If B and E interchange their places, who amongst the following faces B?

(a) T (b) P (c) Q (d) R (e) None of these

Ans: (c)

Question 2: Which of the following pairs must be at extreme ends but are not facing each other?

(a) R, F (b) T, A (c) D, R (d) C, Q (e) S, A

Ans: (b)

Question 3: If all the 12 persons are members of a family. Females are facing their husbands. All females are sitting at alternate places. If A is the husband of V. Then who is the husband of P?

(a) B (b) A (c) C (d) F (e) D

Ans: (a)

Solutions with Strategies:

  1. Take two rows of six places. Consider the upper side of paper as North and the down side as South.

1696411575934

  1. Place the six people above facing downward (South) and six people in other row facing towards the North.

V sits third to right of S.

S



V

S faces F and F does not sit at any of the extreme ends of the line.

F




S



V

D sits third to right of C. R faces C.

D



C




R


  • The one facing E sits third to right of P, P sits to the left of S. B and P do not sit at the extreme ends of the line, T is not an immediate neighbour of V and A is not an immediate neighbour of F.




E

P

S



Combining all the figure above

D

B

F

C

E

A

T

P

S

R

Q

V

CAT Exam: References to Study (Theory):

  • Verbal and Non-Verbal Reasoning by R S Agrawal
  • Cat preparation-iQuanta (YouTube Channel)
  • MBAP CAT EBook (Concept Theory)

CAT Exam: References to Study (Practice):

  • LRDI for CAT and GMAT by Nishit K Sinha. (Advance)
  • MBAP CAT EBook (Practice Questions).
  • Previous Years Question Papers

Part-C: CAT Exam VARC

Topic: Strategies to prepare Conditionals.

Conditionals and Rules, Tips to Prepare:

Conditionals are phrases used to explain the result of an event that might happen in present or future or that could have happened in the past but didn’t.

Conditionals are divided into four parts:

  • Zero Conditionals:

sentence formed two present simple verbs (one in the 'if clause' and one in the 'main clause'):

Rule: If + present simple, .... present simple.

Trick: Used when the result will always happen.

Examples:

If people eat too much, they get fat.

If you touch a fire, you get burned.

If babies are hungry, they cry

  • First Conditional:

Rule: If + Present Simple, (If Clause) ... will + infinitive (main clause)

Trick: used to talk about things which might happen in the future.

Examples:

If it rains, I won't go to the park.

If I study today, I'll go to the party tonight.

If I see her, I'll tell her.

  • The Second Conditional: Uses the past simple after if, then 'would' and the infinitive:

Rule: if + past simple, ...would + infinitive

Tricks:

We can use 'were' instead of 'was' with 'I' and 'he/she/it. This is mostly done in formal writing.

We can use it to talk about things in the future that are probably not going to be true. Maybe I'm imagining some dream for example.

We can use it to talk about something in the present which is impossible because it's not true.

Examples:

If I won the lottery, I would buy a big house.

If I met the Queen of England, I would say hello.

She would pass the exam if she ever studied. (She never studies, so this won't happen)

If I were you, I wouldn't go out with that man.

How is this different from the first conditional?

We can understand this with the following example:

For example (second conditional): If I had enough money, I would buy a house with twenty bedrooms and a swimming pool (I'm probably not going to have this much money, it's just a dream, not very real)

But (first conditional): If I have enough money, I'll buy some new shoes (It's much more likely that I'll have enough money to buy some shoes)

  • The Third Conditional: Use past perfect after 'if' and then 'would have' and the past participle in the second part of the sentence:

Rule: If + past perfect, ...would + have + past participle

Trick: It represents the incidents in Past. It's used to describe a situation that didn't happen, and to imagine the result of this situation.

Examples:

If she had studied, she would have passed the exam (but, really, we know she didn't study and so she didn't pass)

If I hadn't eaten so much, I wouldn't have felt sick (but I did eat a lot, and so I did feel sick).

If we had taken a taxi, we wouldn't have missed the plane

Some Additional Tips:

  • Differentiate between use of first (for particular situation) vs zero conditional (for general activities).
  • Differentiate between use of first (for situations likely to happen in future) vs second conditional (for general activities that I don't think will really happen).

Practice Questions for CAT pdf on Conditionals [Based on CAT previous year papers]

Q1. What would you do differently if you _____ to do this again?

  1. have

  2. had

  3. would have

  4. None of these

Ans: (1) According to the third conditional.

Q2. The work _____ delayed if payment from the ministry don't credit on time.

  1. is

  2. will be

  3. would be

  4. None of these

Ans: (2); According to the first conditional.

Q3. When I watch TV for too long, I _____ a headache.

  1. get

  2. got

  3. would get

  4. None of these

Ans: (1); According to Zero Conditional

Prerequisite

  • Parts of Speech
  • Tenses.

CAT Exam: References to Study (Theory)

  • Word Power Made Easy.
  • CAT Edurav (YouTube Channel)

CAT Exam: References to Study (Practice)

  • Wren and Martin
  • Practice Sample Question Papers.

Practice and remain focused; Day 19 will be posted tomorrow.

We appreciate you.

Best wishes.

Articles

Certifications By Top Providers

Explore Top Universities Across Globe

Questions related to CAT

Have a question related to CAT ?

Hello aspirant,
The CAT exam syllabus is not officially prescribed, but it generally includes topics from the following sections:

1. Verbal Ability and Reading Comprehension (VARC)
2. Data interpretation and logical reasoning
3. Quantitative ability

  • Arithmetic

  • Algebra

  • Geometry and Mensuration

  • Number System

  • Modern Math

It seems unlikely that you would be able to get admission in the BTech CS branch at BIT Sindri or Mesra with a CML rank of 2058 and category rank of 433.

Key points:

1. The search results indicate that a CML (Common Merit List) rank of 2058 is quite low for admission to premier engineering colleges like BIT Sindri or NIT Mesra.

2. The cutoff ranks for BTech CS branch at these institutes are usually much higher, often in the range of 1000-2000 for the general category.

3. With a category rank of 433, you may have a better chance of getting admission in the reserved category quota, but the competition is still quite high.

4. The search results do not provide specific cutoff details for BIT Sindri or NIT Mesra, but the general trend suggests your current ranks may not be sufficient for the CS branch in these institutes.

My advice would be to:

1. Check the latest cutoff ranks and admission criteria on the official websites of BIT Sindri and NIT Mesra.

2. Explore other options like state-level engineering colleges or NITs where your current ranks may have a better chance of securing admission.

3. Consider improving your performance in the next attempt of the entrance exam to increase your chances of getting into your desired BTech program.



For VARC, read daily from diverse sources (newspapers, novels, journals) to improve comprehension and vocabulary. Practice RC passages and verbal ability questions regularly. For DILR (Data Interpretation and Logical Reasoning) and QA (Quantitative Aptitude), solve previous years' papers and take mock tests to identify weak areas. Join a coaching institute or online courses for guidance and stay consistent with your study schedule. Review and analyze your performance in mocks to understand mistakes and improve. Maintain a positive mindset and stay disciplined in your preparation.

Hello aspirant,

Every year, IIMs conduct the Common Admission Test (CAT), a national MBA entrance exam, in rotation. For admission to over 1,200 institutions and premier B-schools in India, as well as PGDM, Executive MBA, PhD, and FPM programmes, the IIM CAT exam is regarded as one of the most difficult MBA entrance exams to pass. One of the best MBA schools in India, IIMs offers PGDM and MBA programmes for students who pass the CAT exam with scores in the 82nd to 99th percentiles.

For complete information you can visit our website by clicking on the link given below.

https://bschool-careers360-com.cdn.ampproject.org/v/s/bschool.careers360.com/exams/cat/amp?amp_gsa=1&amp_js_v=a9&usqp=mq331AQIUAKwASCAAgM%3D#amp_tf=From%20%251%24s&aoh=17204523672625&csi=1&referrer=https%3A%2F%2Fwww.google.com&ampshare=https%3A%2F%2Fbschool.careers360.com%2Fexams%2Fcat

Thank you

Hope this information helps you.

Hello!

The educational qualification required for CAT exam is bachelor's degree or its equivalent from a recognized university with minimum of 50% for the open category and 45% for the SC/ST/PwD category. Since you have secured more than the required percentage in your bachelor's degree, you are eligible for CAT exam.

For more information, please visit the website by clicking on the link given below:

https://bschool.careers360.com/articles/cat-eligibility-criteria

I hope you will find this information helpful. Best wishes ahead!

View All

1-radian measures 600. (True/False)

Option: 1

True


Option: 2

False


$111111^2$ = 

Option: 1

123456654321


Option: 2

123454321


Option: 3

123454321


Option: 4

12345654321


1111112 =___________ 

Option: 1

 123456654321


Option: 2

1234554321


Option: 3

123454321


Option: 4

12345654321


159702 is divisible by

Option: 1

7


Option: 2

9


Option: 3

11


Option: 4

6


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What best can be said about the number of satellites serving C? 

Option: 1

Must be between 450 and 725 

 


Option: 2

Cannot be more than 800 
 


Option: 3

Must be between 400 and 800 

 


Option: 4

Must be at least 100 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What is the minimum possible number of satellites serving B exclusively? 

Option: 1

100


Option: 2

200


Option: 3

500


Option: 4

250


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S? 

Option: 1

At most 475 

 


Option: 2

Exactly 475 
 


Option: 3

At least 475 

 


Option: 4

No conclusion is possible based on the given information 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

 If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE? 

Option: 1

The number of satellites serving C cannot be uniquely determined 

 


Option: 2

The number of satellites serving B is more than 1000 
 


Option: 3

All 1600 satellites serve B or C or S 

 


Option: 4

The number of satellites serving B exclusively is exactly 250 


2839155 is divisible by

Option: 1

2


Option: 2

7


Option: 3

55


Option: 4

None of the above


'a' for which x^{2}-ax+9= 0 can be written as square of a linear factor is

Option: 1

6


Option: 2

-6,6


Option: 3

\left ( 6,\infty \right )


Option: 4

\left ( -\infty,-6 \right )


Marketing Director

A career as Marketing Director is also known as a marketing expert who is responsible for the overall marketing aspect of the company. He or she oversees plans and develops the company's budget. The marketing Director collaborates with the business team to plan and develop the marketing and branding strategies for the company's products or services. 

4 Jobs Available
Business Development Executive

Business development executives strive to achieve maximum output with minimum input. If you are good at understanding and convincing people, the career as a business development executive can be enjoyable for you. Business development executives are candidates who have been transferred to the sales from other departments. In general, Business development executives are promoted to a management position. There are plenty of work openings throughout the profession because every company requires Business development executives.

3 Jobs Available
Content Marketing Specialist

Content Marketing Specialists are also known as Content Specialists. They are responsible for crafting content, editing and developing it to meet the requirements of digital marketing campaigns. To ensure that the material created is consistent with the overall aims of a digital marketing campaign, content marketing specialists work closely with SEO and digital marketing professionals.

3 Jobs Available
Sales Manager
2 Jobs Available
Business Analyst

Individuals who opt for a career as a business analyst look at how a company operates. He or she conducts research and analyses data to improve his or her knowledge about the company. This is required so that an individual can suggest the company strategies for improving their operations and processes. Students can visit the Great Lakes Institute of Management, Jamnalal Bajaj Institute of Management Studies to study Business Analytics courses. Business analyst jobs are usually done to help the company make more money, solve existing business problems and achieve its goals.

2 Jobs Available
Marketing Manager
2 Jobs Available
SEO Analyst

An SEO Analyst is a web professional who is proficient in the implementation of SEO strategies to target more keywords to improve the reach of the content on search engines. He or she provides support to acquire the goals and success of the client’s campaigns. 

2 Jobs Available
Digital Marketing Executive

Digital marketing is growing, diverse, and is covering a wide variety of career paths. Each job function aids in the development of effective digital marketing strategies and techniques. The aims and objectives of the individuals who opt for a career as a digital marketing executive are similar to those of a marketing professional: to build brand awareness, promote company services or products, and increase conversions. Individuals who opt for a career as Digital Marketing Executives, unlike traditional marketing companies, communicate effectively through suitable technology platforms.

2 Jobs Available
Back to top