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Conquering Functions & Graphs, Puzzle Questions for Linear Arrangement, and Conditionals- Day 18
Edited By Team Careers360 | Updated on Sep 19, 2024 02:39 PM IST | #CAT
Based on the CAT syllabus 2024, 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 2024, 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.
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We're back with a strategy for the Day 18 of our preparation for the CAT 2024. 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 2024 and get a flow, plan, and schedule for your preparation.
CAT Exam Part-A: Quantitative Aptitude for CAT 2024
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.
Tips and Tricks to Prepare Functions and Graphs for CAT
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.
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Download EBookOdd Function: If f (– x) = – f (x)
For example: f (x) = x3 + sin x; 0 ≤ x ≤ 2π
f(–x) = (–x)3 + sin (-x) = – x3 – 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 even but can be expressed as the 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)]
Understand the concept of Domain and Range:
Domain: Set of input values represented on the x-axis of the graph.
Range: Set of output values represented on the y-axis of the graph.Learn the graphs of some functions as shown and that will be very helpful.
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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
The 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 2024, 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
Now, 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
Q3. For all real values of x, the range of the function f(x) = (x2 + 2x + 4)/(2x2 + 4x + 9) is:
(a) [4/9, 8/9] (b) [3/7, 8/9) (c) (3/7, 1/3) (d) [3/7, 1/2)
Ans: (d)
f(x) = (x2 + 2x + 4)/(2x2 + 4x + 9)
⇒ f(x) = (x2 + 2x + 4)/[2(x2 + 2x + 4) + 1]
Let x2 + 2x + 4 = (x + 1)2 + 3 = k
The minimum value of k is 3.
Now, f(x) = k/(2k + 1)
So, the minimum value of f(x) = 3/(2×3 + 1) = 3/7
For the maximum value of f(x), as the value of k increases, the value in the denominator also increases, which decreases the value of f(x). Thus, the fraction approaches 1/2 but never equals 1/2.
Hence, the correct answer is [3/7,1/2).
Q4. If f(x) = – 4x + 9 and g(x) = 2x – 7, then f(g(x)) = ?
(a) 6x – 16 (b) – 8x + 37 (c) 2x – 16 (d) – 2x + 2
Ans: (b)
Here f(x) = – 4x + 9 and g(x) = 2x – 7
So, f(g(x)) = f(2x – 7) = – 4(2x – 7) + 9 = – 8x + 28 + 9 = – 8x + 37
Hence, the correct answer is (b) – 8x + 37.
CAT EXAM: Prerequisite to Problem-Solving Questions For Entrance Exam based on functions and graphs for CAT
Polynomials Equations of Geometrical figures.
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 Year's 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, and Flora) seated in a row with numbered chairs from 1 to 6. They follow the following Seating 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
Q.1. The row would start with:
Andrew
Flora
Duke
Cannot be determined
Q.2. Elena will be seated on which seat number?
1
2
3
Cannot be determined
Q.3. Who is seated at place number 6?
Andrew
Flora
Duke
Cannot be determined
Q.4. Baithi’s position is
6
5
3
2
The solution strategy for the above problem will be:
While solving, use Initials for each Name, for example,
Write A for Andrew, B for Baithi etc.
Mark the 6 places and fill them according to the 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
Eliminate the wrong possibilities
Find the person in the first place.
From above, In the first place either A, C, D or 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 the given condition
D B E C F AIf 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)
The 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)
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.
Q.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)
Q.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)
Q.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:
Take two rows of six places. Consider the upper side of the paper as North and the downside as South.
Place the six people above facing downward (South) and six people in other row facing towards the North.
V sits third to the 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 the right of C. R faces C.
D | C | ||
R |
The one facing E sits third to the right of P, and 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 figures 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 Year's 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 the 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 the use of first (for particular situations) vs zero conditional (for general activities).
Differentiate between the 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?
have
had
would have
None of these
Ans: (1) According to the third conditional.
Q2. The work _____ delayed if payment from the ministry don't credit on time.
is
will be
would be
None of these
Ans: (2); According to the first conditional.
Q3. When I watch TV for too long, I _____ a headache.
get
got
would get
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.
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Have a question related to CAT ?
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Universities generally expect students to begin the first year of a masters' program even though they had qualifications at the level of a bachelor's degree. The university's curriculum along with the courses are planned to give an in-depth knowledge of the subjects.
But you could opt for:
Postgraduate Studies:
Research Career: In case research interests you, then you can pursue a Ph.D. in your specific interest.
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After gaining an MBA from a renowned institution, it's possible to get entry into the corporate world where the diversity in the career field is assured.
In the end, it would depend on what you would like and what you are particularly interested in. It will be better if you take a suggestion from your academic advisor or career counselor.
Samprikta Mondal 13 November,2024
Hello Pratik,
If your family income exceeds 8 LPA, it will affect your eligibility for the NC-OBC category under the CAT reservation rules. The NC-OBC category requires that the family income should be below 8 LPA to qualify. If you anticipate that your income will exceed this threshold, you should update your status and notify the CAT authorities .
Here's what you can do:
-
Email the CAT authorities : Inform them about the potential change in your income status and request to be considered under the General category, if applicable. You should do this before the examination or any further processing, as your eligibility for the OBC category depends on the income criteria.
-
Documents and Proof : Make sure you have a valid OBC certificate and any relevant documentation regarding your family income, in case they require verification. Also, be aware that if your income exceeds 8 LPA, you might need to apply under the General category, as the OBC-NC reservation is no longer applicable.
-
General Category Consideration : If your application is accepted as General, you will be evaluated based on the General category criteria, including cutoffs and ranking.
To summarize, notifying the CAT authorities is the correct approach to avoid discrepancies later, and if your income is above the threshold, you will be treated as a General candidate for the admissions process.
For more details about CAT exam you can check out an article by Careers360 whose link is given below:
Link: https://bschool.careers360.com/exams/cat
I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.
Thank you and wishing you all the best for your bright future.
kumardurgesh1802 08 November,2024
Hi Shreya ,
Having a tattoo on your wrist should not create a problem during the CAT exam as long as it does not contain any content that violates exam rules , such as communication-related symbols , unauthorised messages or any text resembling formulas or answers .
For a safe side , it is recommended :
1. Inform the Invigilators : Let them know about your tattoo during the identification check , so there are no misunderstandings .
2. Follow the Guidelines : Ensure you follow all instructions regarding permissible items and dress code on the exam day .
Hope this helps you .
ALL THE BEST .
Mitali Sharma 09 November,2024
To know about this please prefer our college predictor
Sumit Mishra 07 November,2024
Hello,
Yes, you can also join IIMs two years after graduation, depending upon the justification in interviews and your performance in entrance exams. If you are not sure about CAT, try those other management exams less hard:
Common Management Admission Test: Easier than CAT; 4-5 months of continuous preparation will suffice.
MAT : Much easier and takes place thrice a year.
SNAP (Symbiosis National Aptitude Test): A bit easier than CAT, apt for Symbiosis Institutes.
Xavier Aptitude Test or XAT : Hence, easier than CAT but the unique decision-making section.
Use exams like CMAT and MAT as a challenge to be competitively prepared. This can be given about 4-5 months, along with a few rounds of mock tests and smart studying.
Deepti Singh 06 November,2024
Popular CAT Questions
Directions for question :
M/s Deloitte Touche Tohmatsu Limited, one of the top four audit and accounting firms in the world with headquarters at London, UK, and with an operational presence in 153 countries, hires Management Trainees (MT) from all the premier management institutes of India thrice every year, in the months of January, May and September.
Each new group of Management Trainees (MT) have to go through a four month rigorous training schedule, after which they have to pass through a test consisting of a written assessment and a case-analysis. The top hundred ranked Management Trainees (MT) based on the performance in the test are confirmed as Management Executives (ME). The rest are given the opportunity of undergoing the training for four months one more time along with the next batch of Management Trainees (MT) and then passing through the subsequent test consisting of the written assessment and case-analysis. The Management Trainee (MT) who fails to get confirmed as a Management Executive (ME) the second time is fired.
The scatter-graph below depicts the number of Management Trainees (MT) at Deloitte taking the tests from January 2020 till May 2022, and the vis-à-vis hired Management Trainees (MT) at Deloitte who were fired :
It is also known that for the month of September 2019 at Deloitte, 96 hired Management Trainees (MT) failed to be confirmed as a Management Executive (ME) the first time, and that 36 hired Management Trainees (MT) were fired.
Question :
In which test did the minimum number of Management Trainees (MT) get confirmed as a Management Executive (ME) in the second attempt ?
Option: 1
September 2020
Option: 2
May 2021
Option: 3
January 2021
Option: 4
January 2022
Directions for question:
The bar-graph given below shows the foreign exchange reserves of Nepal (in million Rupees) from 2014 to 2021. Answer the following questions based on the graph :
Question:
What was the percentage increase (rounded to the nearest integer, if deemed necessary) in the foreign exchange reserves in 2020 over 2016 ?
Option: 1 None
Option: 2 None
Option: 3 None
Option: 4 None
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