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CAT Aspirant's Triad: Mastering Quadratic Equations, Introduction to Cubes, and Tenses All in One - Day 14

CAT Aspirant's Triad: Mastering Quadratic Equations, Introduction to Cubes, and Tenses All in One - Day 14

Edited By Irshad Anwar | Updated on Sep 13, 2023 06:23 PM IST | #CAT

As the CAT 2023 exam date is approaching, you will get to know how to study for CAT in 2 months, what strategy to use, which sources are the best for theory and practice, or about the CAT exam preparation time required, Can I crack CAT in 2 months, how many months preparation is required for CAT, how to prepare for CAT in 2 months, or is there any CAT study plan for 2 months and many more. You might be looking for a CAT 2-month crash course. On day 14 we brought you different types of quadratic equation questions for CAT, students can practice and learn the concept through this article.

CAT Aspirant's Triad: Mastering Quadratic Equations, Introduction to Cubes, and Tenses All in One - Day 14
CAT Aspirant's Triad: Mastering Quadratic Equations, Introduction to Cubes, and Tenses All in One - Day 14

On the basis of the CAT syllabus 2023, we have created a preparation strategy to ace the CAT Exam. We have covered a strategy for every single day for up to 13 days to crack CAT 2023.

On the basis of the CAT syllabus 2023, we provided a Strategy to prepare Algebra (Linear Equation), direction (LR), and future tenses in the previous article - day 13 of CAT preparation. We're back with a strategy for the Day 14 of our preparation for the CAT 2023. In this article, we will be discussing strategies for the following topics, including quadratic equation questions for CAT.

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Part-1: Quantitative Aptitude for CAT 2023

Topic: Quadratic Equation (Algebra) And Quadratic Equation Questions For CAT

Quadratic Equations are the equations with degree 2. Quadratic Equations are an important part of Algebra as well as for the CAT exam. You can expect 1 or 2 algebra questions for CAT Exam (based on analysis of previous years question papers).

Quadratic Equations are of the form of ax2 + bx + c =0.

Here ‘x’ denotes variables (unknown) and a, b, c are constants and a≠ 0.

To prepare CAT Quadratic Equations questions, you should invest 4-5 hours.

Quadratic equation problems for CAT can be categorized into the following types:

  • Questions that involve calculations of some unknown variable.
  • Questions that involve calculations of the nature of roots.
  • Formation of the quadratic equation.
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How to solve quadratic Equations problems for CAT and quadratic equation questions for CAT.

There are three methods which are generally used to find the roots (zeros) of a quadratic equation.

Method of factorization

Example: 2x2 + 5x + 3 = 0

⇒ 2x2 + 2x + 3x + 3 = 0

⇒ 2x (x + 1) + 3 (x + 1) = 0

⇒ (x + 1) (2x + 3) = 0

⇒ x = -1 or x = -3/2.

This method is suitable only if factors of the quadratic polynomial are possible.


Quadratic Formula (Sridharacharya Formula)

For equation ax2 + bx + c =0.

x = [-b ± √D] /2a

where, D is discriminant which is equal to b2 - 4ac.

Example: 2x2 + 5x + 3 = 0

D = 52 - 4 x 2 x 3 = 1

x = [-5 ± √1] /4 = [-5 ± 1] /4

x = -1 or -3/2.


Method of completing the square:

Convert the given equation in the form of either (A+B)2 or (A-B)2

Example:

2x2+ 5x + 3 = 0

⇒ x2 + 5x/2 + 3/2 = 0

⇒ x2 + 2 x 5x/4 + 25/16 – 25/16 + 3/2 = 0

⇒ (x + 5/4)2 – 1/16 = 0

⇒ (x + 5/4)2 = 1/16

⇒ (x + 5/4) = ± ¼

⇒ x = ± ¼ - 5/4

⇒ x = -1 or -3/2

CAT quadratic equation questions with solutions:

The two Previously Asked Questions from Quadratic Equations in the CAT exam are given below, aspirants can also download CAT Previous Year Algebra Questions pdf for more practice and references.

Q1. Suppose one of the roots of the equation ax2 - bx + c = 0 is 2 + √3, where a, b, and c are rational numbers and a ≠ 0. If b = c3 then |a| equals [CAT question paper - 2021]

  1. 2

  2. 3

  3. 4

  4. 1

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Solution: (a)

For a quadratic equation, ax2 + b x + c = 0.

Since the roots, a, b, and c are all rational and if one of the roots is irrational, the other root of the equation will also be irrational and a conjugate of the first root.

So, the other root is 2 - √ 3.

Sum of roots = −(-b)/a = b/a = (2 + √ 3) + (2 - √ 3) = 4.

And Product of roots = c/a = (2 + √ 3) (2 - √ 3) = 4 - 3 = 1

But here the quadratic equation is ax2 - b x + c = 0.

Therefore,

b = 4a and c = a.

It is given that b = c3

4a = a3

So, a = 2 or -2.

So, |a| = 2.


Q2. Let m and n be positive integers, If x2 + mx + 2n = 0 and x2 + 2nx + m = 0 have real roots, then the smallest possible value of m + n is [CAT Question Paper 2020]

  1. 8

  2. 6

  3. 5

  4. 7

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Ans: B

CAT 2023 quadratic equations questions with answers

For real roots b2 ≥ 4ac

From first equation: m2 ≥ 4 (2n)

Or, m2 ≥ 8n

From second equation: (2n)2 ≥ 4m

Or, 4n2 ≥ 4m

Or, n2 ≥ m

If n = 1; m2≥ 8; m ≥ 3

If m ≥ 3 at n = 1, n2 ≥ m is not true.

If n = 2; m2 ≥ 16; m ≥ 4

If m ≥ 4 at n = 2, n2 ≥ m which is a valid result, if m = 4 and n = 2

So, the minimum sum of m and n is 4+2 = 6.

Prerequisite to Solve Quadratic Equation Questions For CAT

For this topic, students must have knowledge of

  • Linear equations

  • Factors

  • Degree of polynomial and zeros of a polynomial.

Tips to Prepare CAT previous year quadratic equations questions:

  • Learn all the methods of solving quadratic equations and use those methods according to the situation.

  • If the sum of zeros of a quadratic equation is ‘s’ and the product of zeros is ‘p’. Then the quadratic equation will be x2 - sx + p = 0

  • The nature of zeros is calculated by just finding the value of D.

If D = 0, zeros/ roots are real and equal.

If D > 0, zeros/ roots are real and unequal.

If D < 0, zeros/ roots are imaginary.

  • Sum of the roots = -b/a; Product of roots = c/a.

  • Always check for the feasibility of solutions.

References to Study (Theory):

  • How to Prepare Quantitative Aptitude by Arun Sharma (6th edition)

  • 2iim (You-Tube)

References to Study (Practice) Quadratic Equation Problems For CAT:


Part 2: CAT Logical Reasoning and Data Interpretation:

Topic: Cube Part-1 (LR) And CAT Questions On Cubes

A cube is a 3-D figure which consists of 6 faces, 12 edges, and 8 vertices.

1694606730536


CAT questions on Cube are based on the following concepts:

  • Painted surface
  • Opposite faces
  • Consecutive faces
  • Number of cuts to make smaller cubes of equal dimension

Approaches and tips to Solve Cube Questions Logical Reasoning:

  1. If all the faces of a cube (n x n x n) painted with the same color are cut into (n x n x n) equal parts.

  • Number of cubes with 3 faces painted = 8 cubes
  • Number of cubes with exactly 2 faces painted = (n-2) x 12
  • Number of cubes with exactly 1 face painted = (n – 2)2 x 6
  • Number of cubes with 0 faces painted = (n-2)3
  1. You can assume your room as a cube to analyze the situation.

  2. You can use the approach of the open cube to solve the question.


1694606733677


Six faces can be seen like this

(1,6), (2,4), and (3,5) form opposite pairs.

Adjacent faces to face 3 are 1,2,4 and 6. Similarly, we can find the others.

  1. Number of cuts to small cubes of equal size (n) from a larger cuboid of dimension (a x b x c) = (a/2 -1) + (b/2 -1) + (c/2 -1)

Questions that can help you to build the concept of Cubes (Based on CAT EXAM):

An Iron cube is coloured black on four adjoining surfaces while the opposite sides are coloured red. The cube is then cut two times vertically and four times horizontally at right angles. Based on the same answer to the next question.

Q1. How many cubes (cuboids) have exactly one face coloured black?

  1. 1

  2. 2

  3. 3

  4. 4

Ans: D


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One cube/cuboid at each black face has exactly one face black coloured.

Q2. How many cubes/cuboids have only one face painted that too in red?

  1. 2

  2. 3

  3. 4

  4. 5

Ans: A

The cube/cuboid with each red face has exactly one face red colored.

Q3. How many cubes/cuboids have more than 2 sides painted?

  1. 2

  2. 4

  3. 6

  4. 8

Ans: D

More than two faces painted means 3 faces painted i.e. a number of cubes formed at each corner.

Prerequisite to solve Cube And Cuboid Questions:

To Prepare the questions based on Cube, students must have the knowledge of

  • This topic requires basic calculations
  • Imagination
  • Analytical Approach

References to 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

Part-3: CAT Exam VARC

Topic: How to solve problems of sentence correction based on Tenses.

In previous articles, we have made strategies to prepare tenses. Today we are going to discuss how to solve problems of sentence correction based on Tenses.

Errors in sentences can be due to any of the following reasons:

  1. Confusion in present tenses

  2. Confusion in past tenses

  3. Confusion in future tenses

  4. Use of the wrong verb

You have to identify which type of error is there in the sentence and prepare them accordingly.

Practice Questions on Sentence correction that can boost your preparation: [Based on PYQs]

CAT Verbal Ability Questions

Here are some CAT verbal ability questions curated for aspirants to practice:

Find the correct phrase for underlining.

Q1. The glass of the car broke while the players were playing football.

  1. Broke

  2. Was broken

  3. No correction is required

  4. Was broke

Ans: a

The action was done in the past but the time is not known. So, Past indefinite tense is used.

Q2. I will be meeting you in the morning.

  1. Meet

  2. Meeting

  3. No correction is required

  4. Met

Ans: (a)

Future indefinite tense should be used.

Q3. Preeti attended dance class every Thursday.

  1. Attends

  2. No correction required

  3. Is attending

  4. Will attending

Ans: (a)

Action is in the present time at a regular interval of time. Present indefinite should be used.

Q4. Rani was playing when her father entered the room.

  1. Played

  2. No correction required

  3. Plays

  4. Is playing

Ans: (b)

Past continuous tense is to be used as the other sentence is in Past indefinite tense.

Q5. It had stopped raining when I was leaving the office.

  1. Leave

  2. Was leaving

  3. Left

  4. Leaves

Ans: (c)

Past perfect tense should be used as the first phrase in the past perfect tense.

Prerequisite:

  • Basic Knowledge of Nouns, Pronouns and Verbs.
  • Basic knowledge of Tenses.
  • Knowledge of the use of helping verbs.

Tips to Prepare Error Correction in Tenses:

  • Practice a lot to improve your grammar.
  • Write rules and revise them on a regular basis.
  • During the examination, check on every possibility of error.
  • Attempt Mock-Test papers and solutions after the test to check your mistakes.

References to Study (Theory):

  • Advanced English grammar by Wren and Martin
  • GMATPrepNow (Youtube Channel)

References to Study (Practice):

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

We will be back with Day 15 tomorrow. Do practice and be focused.

Thank You

All the best.

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Questions related to CAT

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Hello student

The eligibility criteria for the CAT exam are set by the Indian Institutes of Management (IIMs) that conduct the test. Here's a breakdown of the main requirements:

Educational Qualification: You must possess a Bachelor's degree with a minimum of 50% marks or equivalent CGPA (45% for SC, ST and PwD candidates) from a recognized university

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eligibility criteria for cat exam



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The eligibility criteria for the CAT exam are set by the Indian Institutes of Management (IIMs) that conduct the test. Here's a breakdown of the main requirements:


Educational Qualification: You must possess a Bachelor's degree with a minimum of 50% marks or equivalent CGPA (45% for SC, ST and PwD candidates) from a recognized university

Opens in a new window

www.fnu.edu

Bachelor's degree

A recognized university here refers to an institution established by an act of the central or state legislature in India or any educational institution established by an Act of Parliament or declared as a deemed university under Section 3 of the UGC Act, 1956.


Final Year Students: Final year students of a Bachelor's degree course can also appear for the CAT exam.


Professional Degrees: Candidates with professional degrees like CA, CS, and ICWAI with a minimum of 50% aggregate marks are also eligible.


There is no upper age limit for appearing in the CAT exam. However, there is an implicit age limit by virtue of the educational qualification requirement.

https://www.careers360.com/mht-cet-college-predictor?utm_source=qna&utm_medium=ini-cet_cp

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

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

  • Arithmetic

  • Algebra

  • Geometry and Mensuration

  • Number System

  • Modern Math

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

Key points:

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

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

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

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

My advice would be to:

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

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

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



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

Hello aspirant,

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

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View All

1-radian measures 600. (True/False)

Option: 1

True


Option: 2

False


$111111^2$ = 

Option: 1

123456654321


Option: 2

123454321


Option: 3

123454321


Option: 4

12345654321


1111112 =___________ 

Option: 1

 123456654321


Option: 2

1234554321


Option: 3

123454321


Option: 4

12345654321


159702 is divisible by

Option: 1

7


Option: 2

9


Option: 3

11


Option: 4

6


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

The following facts are known about the satellites: 

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

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

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

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

Question:

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

Option: 1

Must be between 450 and 725 

 


Option: 2

Cannot be more than 800 
 


Option: 3

Must be between 400 and 800 

 


Option: 4

Must be at least 100 


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

The following facts are known about the satellites: 

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

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

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

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

Question:

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

Option: 1

100


Option: 2

200


Option: 3

500


Option: 4

250


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

The following facts are known about the satellites: 

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

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

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

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

Question:

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

Option: 1

At most 475 

 


Option: 2

Exactly 475 
 


Option: 3

At least 475 

 


Option: 4

No conclusion is possible based on the given information 


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

The following facts are known about the satellites: 

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

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

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

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

Question:

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

Option: 1

The number of satellites serving C cannot be uniquely determined 

 


Option: 2

The number of satellites serving B is more than 1000 
 


Option: 3

All 1600 satellites serve B or C or S 

 


Option: 4

The number of satellites serving B exclusively is exactly 250 


2839155 is divisible by

Option: 1

2


Option: 2

7


Option: 3

55


Option: 4

None of the above


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

Option: 1

6


Option: 2

-6,6


Option: 3

\left ( 6,\infty \right )


Option: 4

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


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