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CAT Exam: Maxima & Minima Solved questions, Algebra Quant, LR & DI - Day 19

CAT Exam: Maxima & Minima Solved questions, Algebra Quant, LR & DI - Day 19

Edited By Team Careers360 | Updated on Sep 19, 2024 02:34 PM IST | #CAT

We're back with a strategy for the Day 19 of our preparation for the CAT 2024. In this article, we will be discussing strategies for the following topics: Maxima and Minima Questions for CAT, problem-solving questions in maths, Puzzle-solving questions, Logical Reasoning puzzles for CAT exam and questions from CAT previous year papers.

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

Algebra and Maxima and Minima Questions for the CAT Exam

Maxima Minima CAT Questions are used to find the maximum or minimum possible value of a function.

Because the shape of the graph depends on these values.

Example:

In a polynomial function, the maxima is the highest point and the minima is the lowest point and the graph looks like a parabola.

How to find maxima and minima?

Depending on the function, there are several ways to find the maximum and minimum value of a function.

Two main methods are:

  • Graphical method: In the graphical method, we have to plot the polynomial function on a coordinate plane and visually identify the highest and lowest points on the graph.

  • Algebraic method: In the algebraic method, we use calculus to find the critical points and then determine whether these points are maxima, minima, or neither.

In maxima minima aptitude questions, the function given can be:

  • Quadratic function

  • Linear function

  • Polynomial function etc.

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For such functions, we need to find the maximum or minimum values.

We need to study “local Maxima and Minima ”, “maxima and minima formula”, “absolute maxima and minima”, “Maxima and Minima calculator”, and “global maxima and minima” for more details.

CAT Exam: Tips And Approaches To Solve The Maxima and Minima Questions for CAT

Here are some tips and tricks to solve maxima minima aptitude questions:

  1. If the sum of positive numbers is constant then their product is maximum when all numbers are equal.
    Example:
    a + b + c = 36, find maximum value of a.b.c
    The answer is (36/3)3 = 1728

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  1. Arithmetic Mean ≥ Geometric Mean
    a + b + c = 11; find Maximum value of a3 × b4 × c5
    a + b + c = a/3 + a/3 + a/3 + b/4 + b/4 + b/4 + b/4 + c/5 + c/5 +c/5 + c/5 + c/5 = 11
    Now, AM ≥ GM
    So, (a/3 + a/3 + a/3 + b/4 + b/4 + b/4 + b/4 + c/5 + c/5 +c/5 + c/5 + c/5)/12 ≥ (a/3 .a/3 .a/3 .b/4 .b/4 .b/4 .b/4 .c/5 .c/5 .c/5 .c/5 .c/5)1/12
    ⇒ (11/12)12 ≥ (a/3)3 .(b/4)4 . (c/5)5
    ⇒ a3. b4. c5 ≤ 33 × 44 × 55 × (11/12)12

Trick: To solve Maxima and Minima Questions, we can use the following trick.
Divide 11 in the ratio 3 : 4 : 5
i.e., a = (11/12)3; b = (11/12)4; c = (11/12)5
So, a3. b4. c5 = 33 × 44 × 55 × (11/12)12 (After putting the values of a, b and c)

  1. For a quadratic equation:
    If the minimum value is to be found, convert the equation in the form of (a – b)2 + k.
    (Minimum value is k)

    Example: find the minimum value of a2 + 26 – 4a
    a2 + 26 – 4a = (a – 2)2 + 22;

Minimum value is 22

  1. To find the maximum value of a function f(x) can be calculated with the help of a method of derivative.
    Step 1: find f’(x) i.e., the first derivative.

    Step 2: Put f’(x) = 0, and find values of x for which function is either maximum or minimum.
    Let the values of x be x1 and x2.

    Step 3: Find f’’(x) i.e., the second derivative.
    If f’’(x) > 0 at x = x1 then the function gives minimum value at x = x1.
    If f’’(x) < 0 at x = x2 then the function gives the minimum value at x = x2.
    These are local maxima and local minima.

  1. Learn the above concepts well and apply them to solve questions.

  1. Learn basic rules of differentiation.

  2. Use the graphical method to visually identify the maxima and minima.

  3. If the problem involves a specific interval, evaluate the polynomial at the endpoints and compare it with critical points within the interval.

CAT Exam: Maxima Minima Questions for CAT exam From CAT Previous Year Papers

Q1. If three sides of a rectangular park have a total length of 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is:

[CAT Exam 2017]

Solution:

Let one side be a and the other side be b.

So, a + 2b = 400
⇒ 2b = 400-a
⇒ b = 400-a/2

Area = ab = a (400-a)/2 = (400a – a2)/2

To find maximum value of (400a – a2); differentiate with respect to a

dA/da = 400 – 2a = 0 (For maxima)
⇒ a = 200

So, b = 100

Therefore, the longer side will be 200 ft for maximum area.

Q2. An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg. What is the maximum possible number of people in the group?

[CAT exam 2017, TITA]

Solution:

Each person must weigh 53 Kg or more.

So, remaining weight = 630 – 53 – 57 = 520

Therefore, no of remaining persons n ≤ 520/53

So, n ≤ 10 (For maximum value n = 9)

Therefore, total persons in the elevator = 9 + 2 = 11

Q3. If a and b are non-negative real numbers such that a + 2b = 6, then the average of the maximum and minimum possible values of (a + b) is:

[CAT 2022 Slot 2]

  1. 3

  2. 4

  3. 3.5

  4. 4.5

Solution:

a + 2b = 6

From the above equation, we can say that the maximum value b can take is 3 and the minimum value b can take is 0.
a + b + b = 6
a + b = 6 - b
a + b is maximum when b is minimum, i.e. b = 0

Maximum value of a + b = 6 - 0 = 6

a + b is minimum when b is maximum, i.e., b = 3

Minimum value of a + b = 6 - 3 = 3

∴ Average = (6 + 3) / 2 = 4.5

Hence, the correct answer is 4.5.

Q4. The minimum possible value of (x2 – 6x + 10) / (3 – x), for x < 3 is:

  1. –½

  2. 2

  3. ½

  4. –2

Solution:

(x2 – 6x + 10) / (3 – x)
= (x2 – 6x + 9 +1) / (3 – x)
= (x2 – 6x + 9)/ (3 – x) + 1 / (3 – x)

= (x – 3)2 / (3 – x) + 1/ (3 – x)

As, (x – 3)2 = (3 – x)2,

We can write,

(3 – x)2 / (3 – x) + 1/ (3 – x)

= (3 – x) + 1/ (3 – x)

Since x < 3, (3 – x) is positive.

Let k = 3 – x

Since k is positive, the minimum value of k + 1/k = 2

Hence, the correct answer is 2.

CAT Exam: Prerequisite to Maxima Minima Questions Maths

Before practising Maxima and Minima Questions for CAT, students must be well-versed with

CAT Exam: References to Study (Theory)

  • NCERT Class 12 (Chapter: Functions, Derivative, Maxima and Minima)

  • Functions and Graph (Arihant Publication)

  • 2IIM CAT Preparation

CAT Exam: References to Practise Maxima and Minima Questions for CAT 2024

  • R D Sharma

  • https://bodheeprep.com/maxima-minima

  • Previous Year's Question Papers

Part-B: CAT Logical Reasoning And Data Interpretation

Circular arrangement questions for CAT

The topic covered for the day and Logical Reasoning puzzles for the CAT exam are given below:

Problem Solving Questions in Maths/ Puzzles Solving Questions (Circular Arrangement questions or CAT Part-1)

Placing objects or persons in a circular table following a specific rule is a Circular arrangement.

According to a given set of rules or instructions, persons are to be arranged circularly.

Aspirants can also download the following circular arrangement questions for CAT pdf. for further references.

Concepts Involved and Importance of Circular Arrangement

Puzzles Solving Questions of Circular Arrangements involves the concept of Ranking , Blood Relation , Direction Sense etc.

It carries a good weightage in the CAT exam/SNAP and other MBA entrance Exams as seen in previous years.

Problem-solving questions in maths are generally based on:

  1. Facing towards centre

  2. Facing outward the centre

  3. Facing in two different directions.

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Knowledge of solving problems enables you:

  1. To identify the unique position of a person in an arrangement.

  2. To identify respective positions of persons.

  3. Relations among the persons/ objects.

In the CAT exam, linear and circular arrangement questions for CAT are very common.

Students can also study “circular arrangement questions pdf” and “Logical Reasoning circular arrangement questions” to know further about this topic.

Circular Arrangement Questions from CAT Previous Year Papers

Based on the information given below, answer the questions: (SNAP)

Ten friends Matt, Sam, Pat, Tom, Sid, Alex, Kat, Jim, Jane and John are having dinner on a rectangular table. Eight face each other along the length of the table while two face each other along the smaller side of the table. Pat is sitting diagonally opposite to Kat, Alex is facing Jim, John is to the right of Jane, Tom is sitting between Sam and Jim, Pat is to the extreme left of Jane who is sitting on the extreme right along the length of the table. Sid is facing Tom and Matt is on the right of Sam.

Q1. Who do you think is sitting in front of each other along the small sides of the table? (CAT exam)

  1. Matt and John

  2. Matt and Sam

  3. Matt and Kat

  4. John and Sam

Answer: A

Q2. Sid is sitting between which of the following two? (CAT exam)

  1. Sam and Kat

  2. Pat and Alex

  3. Alex and Jane

  4. Kat and Jane

Answer: B

Q3. Who is sitting diagonally opposite to each other? (CAT exam)

  1. Sid and Tom

  2. Sam and Jane

  3. Alex and Jim

  4. Jane and Kat

Answer: B

Q4. Who is sitting to the immediate right of Jim (CAT exam)

  1. Sam

  2. Jane

  3. Alex

  4. Tom

Answer: D

Q5. Who is sitting in two places left to Jane? (CAT exam)

  1. Pat

  2. Alex

  3. Sid

  4. Sam

Answer: C

Solution:

Based on the information given above; the following arrangement be formed

1695875994414

For this read every piece of information very carefully and place the persons.

Prerequisite to Logical Reasoning Puzzles for CAT Exam

  1. Knowledge of Ranking , Direction Sense and Blood Relation .

  2. Knowledge of Linear Arrangement.

Tips and Tricks for Puzzle Solving Questions of Circular Arrangement

Following are some tips and tricks to solve the problems with circular arrangement:

  1. There is no specific formula to solve CAT Circular arrangement questions.

  2. First, find the number of persons in the arrangement. Draw a circle or rectangle (as per the given condition) and mark their positions.

  3. If the persons are facing away from the centre, the left of the persons/ objects will be in the anticlockwise direction and the right of the persons/ objects will be in the clockwise direction.

  4. If the persons are facing towards the centre, the right of the persons/ objects will be in the anticlockwise direction and the left of the persons/ objects will be in the clockwise direction.

  5. Questions on rectangular arrangements are to be solved in the same way.

  6. Remember the information by short notations.

CAT Exam: References to Study Theory (CAT circular arrangement questions)

  • Verbal and Non-Verbal Reasoning by R S Agrawal

  • Cetking (YouTube Channel)

  • MBAP CAT EBook (Concept Theory)

CAT Exam: References to Practise Problem-Solving Questions in Maths

  • LRDI for CAT and GMAT by Nishit K Sinha. (Advance)

  • https://cetking.com/circular/

  • Previous Year's Question Papers

Part-C: CAT Exam VARC

Sentence Improvement Based on Articles

Correct Use of Articles is one of the most significant skills one should be aware of. “The” article is commonly used with an uncountable or countable noun, indefinite or definite noun, and plural or singular noun.

Sentence improvement questions based on articles are important for both the CAT exam and real life.

It is effective in the following ways:

  • If you want to rack your skills up in the verbal ability domain, then practise for sentence improvement based on Articles that should be a ‘not to be missed’ topic in your life.

  • Correct use of articles gives precise specifications about the noun.

  • With the knowledge of articles, one can easily enhance the quality of a sentence.

  • Adding articles to your sentence can help you to speak fluently.

Students can also practice “sentence improvement questions and answers pdf”, “sentence improvement rules pdf”, and “sentence improvement mcq” to grasp more about this topic.

CAT Exam: Practice Questions on Articles

Direction: Write the correct form of the underlined phrase.

Q1. Union Carbide Corporation (UCC) was asked to build a plant for manufacture of Sevin, a pesticide commonly used throughout Asia.

  1. of manufacturing the Sevin,

  2. As to manufacture of the Sevin,

  3. for the manufacture of Sevin,

  4. None of these

Answer: C

‘the’ should be used before “manufacture”.

Q2. CAT exam candidates are not allowed to use calculators during their examinations, although they are permitted to do so if certain models meet the requirements.

  1. are not allowed using calculator

  2. do not allowed using the calculator

  3. are not allowed to use a calculator

  4. No correction required

Answer: C

‘a’ should be used before the “calculator”.

Q3. After Geeta fought with Seeta, she moved to a second apartment.

  1. had moved to second apartment

  2. moved to the second apartment

  3. had been moved to the second apartment

  4. No correction required

Answer: B

‘the’ should be used before ‘second’.

Q4. The prime necessity, as the Director of ICRIER said, is to neutralise the amount of imports and exports in the country in a non-discriminatory manner.

  1. neutralising amount of the imports and the exports

  2. neutralise the amount of the imports and exports

  3. neutralise the amount of imports and exports

  4. No correction required

Answer: B

‘the’ should be used before “imports and exports”.

CAT Exam: Prerequisite

  • Basic Knowledge of Sentence Structure.

  • Basic Knowledge of the Usage of Articles.

Tips to Prepare Sentence Improvement on Articles and Uses

  1. Make sure you pay close attention to words whose first letters are vowels, but when they are pronounced, they have the sound of a consonant or vice versa. This is the case with words like university, an honest person, etc. For more details, you can head over to the Day-6 strategy.

  2. Practice error-based questions daily.

  3. Read newspapers, and listen to Ted Talks so that you will get more clarity about the uses of articles.

CAT Exam: References to Study (Theory)

  • How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)

  • Mastering A, An, The - English Articles Solved by Douglas Porter.

  • A' and 'The' Explained: A learner's guide to definite and indefinite articles by Seonaid Beckwith.

CAT Exam: References to Study (Practice)

  • The Article Book: Practice Toward Mastering a, an, and the by Tom Cole.

  • Oxford Practice Grammar (sixth edition)

  • engvid.com (Web)

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Frequently Asked Questions (FAQs)

1. What are maxima and minima?

Minima and maxima refer to the lowest and highest points, respectively, of a function within a given domain.

2. What is an absolute (global) maximum or minimum?

Global maximum: Global maximum is also called absolute maximum. The highest value of a given polynomial f(x) in the interval [a, b] is called the Absolute maxima.

Global minimum: Global minimum is also called absolute minimum. The lowest value of a given polynomial f(x) in the interval [a, b] is called the Absolute minima.

3. What types of errors are commonly tested in sentence improvement questions?

Some of the common errors include:

  • Tense error

  • Subject-verb agreement error

  • Pronoun reference and agreement error

  • Idiomatic expressions

  • Punctuation errors

  • Mispelt words

  • Preposition errors

  • Redundancy and wordiness

4. How do you handle pronoun reference and agreement errors?

Check if the pronoun correctly referred to the antecedent noun and maintained the number and gender forms.

Example:

Each of the students must submit their homework. (Incorrect)

Each of the students must submit his or her homework. (Correct)

5. What are the key differences between linear and circular arrangements?


  1. In circular arrangements, sitting positions are relative and cyclic with no ending point or starting point.
    In linear arrangements, sitting positions have distinct starting and ending points.

  2. Circular arrangements can be rotated without changing the relative positions of elements, making some configurations equivalent.

In linear arrangements, positions cannot be rotated without changing the relative positions.

6. How do you handle problems with clockwise and counterclockwise directions?

Clockwise and anticlockwise directions are relative.

  • Always draw a diagram to visualize better.

  • Pay close attention to terms like "left," "right," "next to," and "opposite," as they change based on the direction you consider.

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Questions related to CAT

Have a question related to CAT ?

Any tattoo on wrist should not cause any problems for your CAT exam. Tattoos have nothing to do with your analytical abilities and qualifications through written examination. Nothing is specified by the exam conducted authorities regarding tattoos that might cause issues. So ,you can go with tattoo.

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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.

Hello,

A blurry signature on your CAT admit card may raise concerns, as it could be difficult for authorities to verify your identity. However, if the rest of the admit card details, such as your photograph and personal information, are clear and accurate, it might not cause an immediate issue. It's advisable to ensure that your signature is clear during future document submissions.

But if your signature is still recognizable, even if it's slightly blurry, it should generally not cause a major issue. As long as the exam authorities can identify your signature, they may accept it. However, it's always best to ensure that all details on your admit card are clear to avoid any potential problems during the exam.

To know more about CAT admit card, visit: https://bschool.careers360.com/articles/cat-admit-card

Hope it helps !

If you have a leg fracture and are scheduled to appear for the CAT entrance exam, it’s best to contact the CAT exam conducting authorities directly rather than the local exam center alone. CAT is managed centrally by the Indian Institutes of Management (IIMs), and they have established protocols for handling candidates with medical needs. Informing the CAT exam cell (via their official contact channels) will ensure that your request is processed appropriately and documented centrally.


You should explain your medical situation and, if needed, request specific arrangements, such as additional assistance to navigate the exam center or seating adjustments. While reaching out to the CAT exam cell, you may also inquire if additional documentation, such as a medical certificate, is required to facilitate the arrangements. Additionally, contacting the allotted test center as a secondary step could be beneficial, as the local administrators may also help with on-ground assistance.


For official contact information, refer to the CAT website’s helpdesk or contact page, which will have the latest guidelines for handling such requests. Taking these steps should ensure a smoother exam experience despite your injury.

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


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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:

Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'. 

They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared. 

They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders. 

On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries. 

On the backdrop of the above information answer the questions given :

Question: 

Assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the first customer's order be considered closed ?

 

Option: 1

6.15 pm

 

 


Option: 2

6.17 pm

 


Option: 3

6.18 pm

 


Option: 4

6.20 pm


Directions for question :

Six sticks of equal lengths were kept in the vertical position in an empty flower-vase, to be arranged at the six corners of a regular hexagon. The two ends of each of the sticks were of different colours. 

The top ends of the sticks were one of each of the following colours – Red, Cyan, Pink, Brown, Black and Green. The bottom ends were one of each of the following colours – Blue, Yellow, White, Orange, Purple and Grey. Both the sets of colours mentioned were in no particular order.

It was also known that :

a) The stick with the red colour was opposite to the stick with the blue colour

b) There were exactly two sticks whose both ends had colours whose names started with the same letter

c) The stick with the grey colour was adjacent to the stick with the white colour

d) The stick with the cyan colour was adjacent to both the sticks with the brown colour and the one with the blue colour

e) The stick with the purple colour was adjacent to both the sticks with the grey colour and the one with the green colour

f) The stick with the white colour was opposite to the stick with the green colour

Question :

What was the colour of the bottom end of the stick having brown colour at the top end ?

Option: 1

 White 

 


Option: 2

Yellow 


Option: 3

Black

 


Option: 4

Grey


Directions for question:

Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'. 

They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared. 

They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders. 

On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries. 

On the backdrop of the above information answer the questions given :

Question: 

Assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the third customer's order be considered closed ?

 

Option: 1

6.28 pm

 


Option: 2

6.35 pm

 


Option: 3

6.38 pm


Option: 4

6.45 pm


Directions for question:

Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'. 

They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared. 

They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders. 

On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries. 

On the backdrop of the above information answer the questions given :

Question: 

Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis, when would the second customer's order be considered closed ?

Option: 1

6.20 pm

 

 


Option: 2

6.18 pm


Option: 3

6.15 pm

 


Option: 4

6.12 pm


Directions for question:

Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'. 

They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared. 

They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders. 

On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries. 

On the backdrop of the above information answer the questions given :

Question: 

Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis, when would the third customer's order be considered closed ?

 

Option: 1

6.22 pm

 


Option: 2

6.25 pm


Option: 3

6.28 pm 


Option: 4

6.30 pm


Directions for question:

Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'. 

They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared. 

They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders. 

On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries. 

On the backdrop of the above information answer the questions given :

Question: 

A fourth customer comes in and orders two plates of French Toast at 6.24 pm. Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis. For exactly how many minutes would one of the friends be idle from 6.00 pm till serving the last customer, assuming that the four customers were the only ones to have come in within the period being discussed ?

Option: 1

9

 


Option: 2

13


Option: 3

18


Option: 4

21


Directions for question:

Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'. 

They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared. 

They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders. 

On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries. 

On the backdrop of the above information answer the questions given :

Question: 

Had Niloy been absent on that day, and assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the fourth customer's order (refer to the previous question) be considered closed ?

Option: 1

6:38 pm

 


Option: 2

6:42 pm

 


Option: 3

6:47 pm


Option: 4

6:49 pm


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

Directions for question:

The Jadavpur University’s Prince Anwar Shah Road hostel consists of two large separate buildings, one for the ladies and the other for the gents, while having a common kitchen and dining hall. It is the hostel of the CS and the EEC department of engineering students of the university.

In recognition of the growing dissatisfaction and hence complaints among the inmates of the hostel regarding the menu served for dinner, the Dean of the engineering department, Dr Aparesh Sanyal, personally decided to investigate the matter. He set about collecting information about the preference of dinner among the inmates, separately from the gents and the ladies wing of the hostel.

Dr Sanyal was able to gather the following partial information :  

 

Hostel inmates

Menu preference for dinner

Total

Egg Meal

Fish Meal

Chicken Meal

Gents

   

20

 

Ladies

     

64

Total

 

60

   

 

The Warden of the hostel was consulted, who after investigation declared that the following facts were clear :

1. Forty percent of the hostel inmates were ladies

2. One-third of the gentlemen inmates preferred an egg meal for dinner

3. Half the hostel inmates preferred either fish meal or chicken meal

Question:

What proportion of the lady hostel inmates preferred a fish meal for dinner ?

 

 

Option: 1

0.25

 

 


Option: 2

0.50

 


Option: 3

0.75

 


Option: 4

1.00 


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