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    CAT Exam- CAT Algebra question from Polynomials, LR & DI |Day 15

    CAT Exam- CAT Algebra question from Polynomials, LR & DI |Day 15

    #CAT
    Team Careers360Updated on 19 Sep 2024, 03:18 PM IST

    Based on the CAT 2024 syllabus, we previously covered strategies for Algebra (Quadratic Equations), Cube (Logical Reasoning), and Sentence Corrections with CAT algebra questions on Day 14 of our preparation series.

    This Story also Contains

    1. Quantitative Aptitude for CAT 2024
    2. CAT Logical Reasoning and Data Interpretation
    3. CAT Exam VARC
    4. CAT 2024 study material pdf
    CAT Exam- CAT Algebra question from Polynomials, LR & DI |Day 15
    CAT Algebra question from Polynomials

    Now, for Day 15, we’ll focus on strategies for tackling polynomial questions in the CAT exam.

    To excel in CAT 2024, follow our 60-day preparation schedule to ensure you stay organized and on track with your study plan.

    Quantitative Aptitude for CAT 2024

    Polynomial (Algebra), Polynomial Questions For CAT Exam & CAT algebra questions

    What is polynomials?

    Polynomials are mathematical expressions that consist of variables or determinants, coefficients, exponents, and constant terms combined with mathematical expressions like addition, subtraction, or multiplication.

    It is generally denoted by f(x).

    The general form of a polynomial equation is:

    an xn + an-1 xn-1 + an-2 xn-2 + ........ + a1 x + a0

    Example:

    4x2 + 2x + 3 is a polynomial where x is the variable.

    An example of a polynomial equation with two variables is:

    3x2 + 2xy + y2 + 4x + 5y + 7, where x and y are two variables.

    Degree of polynomials

    The degree of a polynomial is the highest exponent of a variable in the polynomial expression with a non-zero coefficient.

    Example:

    7x4 + 3x3 + 9x + 1; Degree of the polynomial = 4

    x3 + 3x2y4 + 3y4 + 5; Degree of the polynomial = 6

    It is also to be remembered:

    • A polynomial with degree 0 is called a Constant or zero polynomial.

    In other words, the degree of zero polynomial is zero.
    Example: f(x) = 2

    • A Polynomial with degree 1 is a Linear polynomial.
      Example: f(x) = 2x + 1

    • A polynomial with degree 2 is a Quadratic polynomial.
      Example: f(x) = 2x2 + x + 1

    • A polynomial with degree 3 is a Cubic polynomial.
      Example: f(x) = 2x3 + 3x2 + x + 1

    • A polynomial with degree 4 is a Biquadratic polynomial.
      Example: f(x) = 2x4 + 2y + 4z + 1

    Zeros of a polynomial

    A zero of a Polynomials is a value of the variable (often denoted as "x") that makes the entire polynomial equal to zero. In other words, if you substitute that value for "x" in the polynomial expression, the result will be zero. Another term for the zero of a polynomial is "root" or "solution."

    In general, the number of zeroes of a polynomial is equal to its degree, and some of the zeroes may be repeated. For example, a polynomial of degree 3 will have three zeroes (counting multiplicities), and so on. Understanding the zeroes of a Polynomials is crucial in solving various mathematical problems.

    There are a few ways to find the zeros of a polynomial.

    • The factorization method is the most commonly used.

    • Quadratic formula

    • Synthetic division

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    We also have to study “polynomial regression”, “Types of Polynomials ”, and “polynomial function” to learn more about this chapter.

    CAT Previous Year Algebra Questions/ Polynomials CAT questions/Polynomial Questions For CAT exam

    Here are some CAT previous year algebra questions shuffled up from different PYQs of the CAT exam before:

    Q1. If a, b, c, and d are integers such that a + b + c + d = 30, then the minimum possible value of (a – b)2 + (a – c)2 + (a – d)2 is:

    (TITA, CAT exam 2017)

    1. 5

    2. 6

    3. 2

    4. 8

    Solution:

    Given that a + b + c + d = 30.

    For the minimum possible value of (a – b)2 + (a – c )2+ (a – d)2,

    (a – b) = (a – c) = (a – d) = 0

    But this is not possible because 30 is not a multiple of 4.

    We should find a as close to b, c, and d as possible.

    We should take values of a, b, c and d close to 30/4 = 7.5

    So, a, b, c, and d should take the values of 7 or 8.

    For the minimum possible value of (a – b)2 + (a – c)2 + (a – d)2, the difference of a taken with b, c or d should not be greater than 1.

    So, Possible sets of a, b, c and d will be

    a

    b

    c

    d

    (a – b)2 + (a – c)2 + (a – d)2

    7

    7

    8

    8

    2

    8

    8

    7

    7

    2

    7

    8

    7

    8

    2

    7

    8

    8

    7

    2

    8

    7

    8

    7

    2

    8

    7

    7

    8

    2

    So, the minimum possible value of (a – b)2 + (a – c)2 + (a – d)2 is 2.

    Hence, the correct answer is 2.

    Q2. For real x, the maximum possible value of x/√(1+x4) is:

    [CAT exam 2020]

    A. 1

    B. ½

    C. 1/√2

    D. 1/√3

    Solution:

    Dividing both numerator and denominator by x, we get,

    1/√[(1/x2) + x2]

    The value of (1/x2) + x2 should be the minimum to get the original fraction maximum.

    For real values of x, (1/x2) + x2 has a minimum value equal to 2.

    So, the maximum value of x/√(1+x4) is 1/√2.

    Hence, the correct answer is 1/√2.

    Tips and Tricks to Prepare Polynomials Questions for CAT

    1. The standard form of a Linear polynomial is ax + b.

    2. The standard form of a Quadratic polynomial is ax2 + bx + c.

    3. The standard form of a Cubic polynomial is ax3 + bx2 + cx + d.

    4. The standard form of a biquadratic polynomial is ax4 + bx3 + cx2 + dx + e.

    5. The degree of a constant polynomial is 0.

    6. For the quadratic equation ax2 + bx + c = 0 if the roots are α and β, then
      Sum of the roots, α + β = –b/a
      Product of the roots, α β = c/a

    7. For the cubic equation ax3 + bx2 + cx + d = 0, if the roots are α, β, and γ, then
      Sum of the roots, α + β + γ = –b/a
      Product of the roots, α β γ = –d/a
      Sum of the product of roots taken two at a time, α β + β γ + α γ = c/a

    8. You have to solve different kinds of problems based on polynomials. Practice more and more problems on polynomials for CAT.

    9. Also, learn

    • (x + y)2 = x2 + y2 + 2xy

    • (x – y)2 = x2 + y2 – 2xy

    • (x + y)3 = x3 + y3 + 3xy2 + 3x2y

    • (x – y)3 = x3 – y3 – 3x2y + 3xy2

    • (x – y – z)3 = x3 – y3 – z3 – 3x2y + 3xy2 – 3y2z – 3yz2 + 3xz2 – 3x2z + 6xyz

    References to Study (Theory)

    • NCERT Class 9-10

    • How to Prepare Quantitative Aptitude by Arun Sharma (7th edition)

    • 2IIM CAT Preparation (You-Tube)

    References to Study (Practice) CAT Algebra Questions

    • Pearson (How to prepare quantitative aptitude for CAT)

    • https://iim-cat-questions-answers.2iim.com

    • Previous Year's Question Papers to practice polynomial questions for the CAT exam

    CAT Logical Reasoning and Data Interpretation

    Cube Part-2 (LR) And CAT Questions On Cubes

    The different kinds of questions asked in the CAT Exam on Cubes are:

    Type 1 Cubes questions in CAT:

    Question. A cube painted on all faces is cut into 1331 cubes of the same size.

    1. How many cubes are not painted on any face?

    1. 1000

    2. 729

    3. 81

    4. 270

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    Answer: (B)

    Trick: Only the inner cubes

    i.e., (k - 2)3, where k = dimension of larger cube/dimension of smaller cube

    Here, k = 11

    So, the number of cubes not painted on any face is (11 - 2)3 = 93 = 729

    2. How many cubes are painted on three faces?

    1. 8

    2. 16

    3. 36

    4. 54

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    Answer: (A)

    Trick: Corner cubes only.

    A cube has 8 corners.

    Hence, the correct answer is always 8.

    Type 2 Cubes questions for CAT:

    Question. A cube of 4 cm is painted yellow on the pair of one opposite surface, red on the pair of another opposite surface and blue on the remaining pair of opposite surfaces. The cube is now divided into smaller cubes of equal size of 1 cm each.

    3. Find the number of smaller cubes with three surfaces painted.

    1. 6

    2. 8

    3. 16

    4. 27

    Answer: (B)

    Trick: Corner cubes only.

    A cube has 8 corners.

    Hence, the correct answer is always 8.

    4. Find the number of smaller cubes with two surfaces painted.

    1. 24

    2. 8

    3. 16

    4. 30

    Answer: (A)

    Trick: Surface cubes except for the corner cubes.

    k = dimension of larger cube/ dimension of smaller cube

    Cubes with two face painted = 6 × (k – 2)2 = 6 × 22 = 24

    5. Find the number of cubes with two surfaces painted with yellow and red colour.

    1. 10

    2. 8

    3. 9

    4. 16

    Answer: (B)

    Trick: Cubes at the common edges of yellow and red surfaces, except corner cubes.

    Common edges of yellow and red will be 4 and 2 cubes (except at corners) at each edge.

    So, the number of cubes with two surfaces painted with yellow and red colour is 4 × 2 = 8

    Type 3 Cubes questions for CAT:

    Question. Here is the information given below. Based on this information, answer the questions.

    A cube has six sides, each of which has a different colour: black, blue, yellow, red, pink, and white.

    The red side is opposite the black.

    The yellow side is between the red and the black.

    The blue side is adjacent to the white.

    The black side is adjacent to the white.

    The red side is the bottom face.

    1. What are the four colours that are adjacent to the yellow?

    1. Black, blue, pink, red

    2. Black, blue, red, white

    3. Black, blue, pink, white

    4. Black, red, pink, white

    Answer: A

    Trick: Except for the colour opposite to the yellow face.

    1695908643980

    So, except for white, others are adjacent to yellow.

    2. Which of the information can be deduced from the information given in statements I, II, and VI?

    1. White is on the top.

    2. Blue is on the top.

    3. Black is on the top.

    4. White is opposite to black.

    Answer: C

    Trick: Draw an open cube diagram.

    1695908643761

    Black must be at the top according to statements I, II, and VI.

    References for Study (Theory):

    • Verbal and Non-Verbal Reasoning by R S Aggarwal. (Basic)

    • Cat preparation-iQuanta (YouTube Channel)

    References to Study (Practice):

    • Verbal and Non-Verbal Reasoning by R S Aggarwal. (Basic)

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

    • Previous Year's Question Papers

    CAT Exam VARC

    Subject-Verb Agreement

    A sentence is a group of words connected to make meaning. A sentence must use appropriate verbs, helping verbs, punctuation etc.

    The Subject and Verb must agree in number and Person (Noun/ Pronoun, Singular/ Plural). Mastering subject-verb agreement rules is crucial for effective communication and writing in the English language.

    Subject-verb agreement rules with examples

    Person Rule:

    Person

    Singular

    Verb

    Plural

    Verb

    First Person

    I

    Am/was/shall

    We

    Are/ were/ shall

    Second Person

    You

    Are/ were/ will

    You

    Are/ were/ will

    Third Person

    He/She/it

    It/was/will

    They

    Are/ were/ will

    Number Rule: The number rule is not as simple as the person's rule. There are a few exceptions too.
    There are many rules such as:

    1. Subject and Verb should be either singular or plural.

    2. Countable nouns can take a plural, can combine with counting quantifiers (e.g., one, hundred, every, many), and can take an indefinite article such as a or an. Examples of counting nouns are table, glass, and occasion.

    3. Uncountable nouns: they cannot take plurals or combine with number words.

    4. Proximity Rule: Where two or more subjects are connected by: or, either…or, neither…nor. The subject that is closest to the verb decides the number of the verb.

    Students can also practice on “subject-verb agreement worksheets with answers pdf”, “40 rules of subject-verb agreement pdf”, and “subject-verb agreement exercises with answers doc” to learn more about this chapter.

    VARC Questions For CAT On Subject-Verb Agreement: [Based on PYQs]

    The following subject-verb agreement exercises are VARC questions for CAT, based on topic subject-verb agreement based on the previous year's question papers of the CAT exam.

    Correct the sentences:

    Q1. The Seven Strangers, Manav included, was supposed to meet for dinner later that night after a conference.

    1. was supposed to meet

    2. was supposed to have met

    3. were suppose to be meeting

    4. were supposed to meet

    5. they were supposed to be meeting

    Answer: (D)

    Here the subject is “The seven strangers”, which is plural.

    So, the plural verb “were” will be used here.

    The correct sentence will be:

    “The Seven Strangers, Manav included, were supposed to meet for dinner later that night after a conference.”

    Q2. Without proper guidance and better support, there is no chances that our candidate will win the election.

    1. there is no chances that

    2. there can be no chance for

    3. there is no chance that

    4. there are no chances for

    5. there will be no chances for

    Answer: (C)

    Here the singular verb ‘is’ does not agree with the plural subject ‘chances’.

    So, replace chances with a chance.

    The correct sentence will be:

    “Without proper guidance and better support, there is no chance that our candidate will win the election.”

    Q3. After he attended the seminar, many more resources were at Philip’s disposal, including new contacts, excellent books and pamphlets to help him improve his resume.

    1. many more resources were at Philip’s disposal

    2. at Philip’s disposal were many more resources

    3. there were many more resources at Philip’s disposal

    4. Philip, at his disposal, had many more resources

    5. Philip had many more resources at his disposal

    Answer: (E)

    On Comparison, we found that ‘E’ is most suitable.

    The correct sentence will be:

    “After he attended the seminar, Philip had many more resources at his disposal, including new contacts, excellent books, and pamphlets to help him improve his resume.”

    Tips to Prepare Subject-Verb Agreement

    1. To identify the subject, one must spot the verb and ask a question that the verb along with the predicate is supposed to answer.

    2. A collective noun is considered as a whole and takes a singular verb.

    3. When the plural noun denotes some specific quantity considered as a unit, the verb used is generally singular.

    4. Words such as glasses, pliers, and scissors are regarded as plural and require plural verbs unless they’re preceded by the phrase ‘pair of ‘and this word becomes the subject.

    5. Write rules and revise them regularly.

    6. Attempt Mock-Test papers.

    Prerequisite:

    • Complete Knowledge of Nouns

    • Complete Knowledge of Pronouns

    • Knowledge of Articles

    • Knowledge of Verbs

    • Basic knowledge of Tenses.

    References to Study (Theory):

    • Advanced English grammar by Wren and Martin

    • CAT Edurav (Youtube Channel)

    References to Study (Practice):

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

    • https://www.800score.com/gmat-prep/prep-guide/sample-questions/

    • Practice Sample Question Papers.

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    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 


    Read Complete Answer

    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


    Read Complete Answer

    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


    Read Complete Answer

    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


    Read Complete Answer

    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


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    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


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    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


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    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


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    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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    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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