CAT 2023 Question Paper, Slot 1, 2 and 3: Sectionwise Questions With Solutions
The CAT 2023 Question Paper is one of the most important CAT preparation resources for any CAT exam aspirant. Careers360 has created a CAT 2023 Solutions PDF written by subject matter experts in the respective fields to ensure that the candidates receive the proper CAT exam 2024 preparation. Additionally, this article also has links to the CAT Previous Year Papers with Solutions so that the candidates can enhance their CAT preparation even further. This article is solely written for the purpose of understanding the CAT 2023 question paper from all 3 slots that took place on the 26th of November 2023.
Overview of CAT 2023 Exam Pattern
The CAT exam 2023 exam pattern followed the same structure as the previous years. There were 66 questions in total divided into three sections, Verbal Ability and Reading Comprehension (VARC), Data Interpretation and Logical Reasoning (DILR) and Quantitative Aptitude (QA). The number of questions was respectively divided into 24, 20 and 22 in each section. Now let us dive deeper into the CAT 2023 Question Paper Analysis and observe the major changes that were observed in the CAT 2023 Question Paper.
Key changes in the CAT 2023 exam pattern
Unlike the previous years, the number of CAT quantitative aptitude questions under the algebraic section was more than that from the algebraic section.
Questions on odd one out was present in the slot 1 question paper of the CAT 2023 exam. It was absent in the CAT 2022 question paper.
Most of the arithmetic questions in the slot 1 CAT 2023 question paper were of TITA type.
The CAT quantitative Aptitude questions were more difficult and lengthy as compared to the previous years.
As far as the Verbal Ability and Reading Comprehension section were concerned, the verbal ability questions were doable and easy type while the reading comprehension passages were of moderate to difficult difficulty.
CAT 2023 Question Paper Breakdown
Now let us break down the CAT 2023 question paper and understand the important aspects related to it. This would give the candidates a good idea on the CAT 2023 question paper and what to expect in the future.
CAT 2023 Question Paper  
Exam Name  Common Admission Test 
Conducting Body  IIM Lucknow 
Number of Sections 

Question Distribution  VARC  24 DILR  20 QA  20 
Number of Slots  CAT slot 1 timing: 8:30 am  10:30 am (Morning Session) CAT slot 2 timing: 12:30 pm  2:30 pm (Afternoon Session) CAT slot 3 timing: 4:30 pm  6:30 pm (Evening Session). 
Sectional Time Limits  40 minutes for each section 
Marking Scheme  For every right answer, +3 will be awarded For every wrong answer in MCQs, 1 will be deducted No negative marks for NonMCQs 
CAT 2023 Good Attempts
After the CAT 2023 exam concludes, the experts indulge themselves in an elaborated CAT 2023 Question Paper Analysis and devise the number of good attempts per section based on it. The number of good attempts is an indicator of the number of minimum attempts with accuracy that a candidate must make to expect a high CAT percentile.
Percentile  Score VARC  Score DILR  Score QA  Overall Score 
99.9 %  48  36  48  106 
99.50%  44  32  32  89 
99%  40  28  28  80 
98%  36  25  24  71 
95%  30  19  19  57 
90%  25  16  15  49 
85%  21  13  12  40 
80%  19  11  10  36 
75 %  17  10  9  31 
70 %  15  9  8  29 
SectionWise Breakdown of CAT 2023 Question Paper
The CAT 2023 question paper had a lot of differences when compared with the previous year’s CAT question papers. The proper approach to understanding the CAT 2023 question paper is through proper CAT 2023 exam analysis through a sectionwise breakdown. Let us now discuss the CAT 2023 exam paper sectionwise breakdown.
VARC (Verbal Ability and Reading Comprehension):
Number of Questions: 24
Time Allotted: 40 minutes
Difficulty Level: Easy to Moderate and slightly easier than last year
The Verbal Ability and Reading Comprehension section of the CAT 2023 question paper had 24 questions with a balance of CAT questions testing both verbal skills and reading ability questions of the candidates. The presence of the odd oneout questions was one deviation observed in the CAT 2023 question paper when compared with the CAT previous year’s question papers. The various questions and their difficulty level in the VARC section of the CAT 2023 question paper are given below:
CAT SLOT 1  
Section  No of Qs.  Difficulty Level 
RC1: Return of wolves' predation in a French region  4  Easy 
RC2: Current Economies of North and South Korea  4  Easy 
RC3: Indian Ocean Literature  4  Medium 
RC4: Modern materialism versus ancient societies  4  Difficult 
CAT SLOT 2  
RC  1: Secondhand Shopping and Fast Fashion  4  Easy 
RC2: Translated Streaming in Europe  4  Easy 
RC  3: Why Liberalism Failed (Book Review)  4  Medium 
RC  4: What is a Historical Fact  4  Difficult 
CAT SLOT 3  
RC Passage  Questions  Difficulty 
RC  1: Colonialism and Global Warming (The Nutmeg’s Curse)  4  Easy 
RC  2: Understanding Romantic Aesthetics  4  Easy 
RC  3: Cultural Patrimony Laws  4  Medium 
RC  4: Rationality by Steven Pinker  4  Difficult 
CAT Question Paper 2023: VARC Questions
DIRECTIONS for the question: The passage below is accompanied by a set of questions. Choose the best answer to each question.
The Positivists, anxious to stake out their claim for history as a science, contributed the weight of their influence to the cult of facts. First, ascertain the facts, said the positivists, then draw your conclusions from them…..This is what may [be] called the commonsense view of history. History consists of a corpus of ascertained facts. The facts are available to the historian in documents, inscriptions, and so on…[Sir George Clark] contrasted the "hard core of facts" in history with the surrounding pulp of disputable interpretation forgetting perhaps that the pulpy part of the fruit is more rewarding than the hard core.…. It recalls the favourite dictum of the great liberal journalist C. P. Scott: "Facts are sacred, opinion is free.". . .
What is a historical fact?..... According to the commonsense view, there are certain basic facts which are the same for all historians and which form, so to speak, the backbone of history—the fact, for example, that the Battle of Hastings was fought in 1066. But this view calls for two observations. In the first place, it is not with facts like these that the historian is primarily concerned. It is no doubt important to know that the great battle was fought in 1066 and not in 1065 or 1067, and that it was fought at Hastings and not at Eastbourne or Brighton. The historian must not get these things wrong. But [to] praise a historian for his accuracy is like praising an architect for using wellseasoned timber or properly mixed concrete in his building. It is a necessary condition of his work, but not his essential function. It is precisely for matters of this kind that the historian is entitled to rely on what have been called the "auxiliary sciences" of history—archaeology, epigraphy, numismatics, chronology, and so forth….
The second observation is that the necessity to establish these basic facts rests not on any quality in the facts themselves, but on an apriori decision of the historian. In spite of C. P. Scott's motto, every journalist knows today that the most effective way to influence opinion is by the selection and arrangement of the appropriate facts. It used to be said that facts speak for themselves. This is, of course, untrue. The facts speak only when the historian calls on them: it is he who decides to which facts to give the floor, and in what order or context. The only reason why we are interested to know that the battle was fought at
Hastings in 1066 is that historians regard it as a major historical event… Professor Talcott Parsons once called [science] "a
selective system of cognitive orientations to reality." It might perhaps have been put more simply. But history is, among other things, that. The historian is necessarily selective. The belief in a hard core of historical facts existing objectively and independently of the interpretation of the historian is a preposterous fallacy, but one which it is very hard to eradicate.
Question No. : 1
According to this passage, which one of the following statements best describes the significance of archaeology for historians?
A) Archaeology helps historians to interpret historical facts.
B) Archaeology helps historians to ascertain factual accuracy.
C) Archaeology helps historians to carry out their primary duty.
D) Archaeology helps historians to locate the oldest civilisations in history.
Solution:
Answer 2: The author in the passage explains that while historians depend on auxiliary sciences like archaeology to establish fundamental facts (such as the date and location of historical events), this accuracy is a prerequisite rather than the essence of their work. Praising historians for accuracy is akin to praising an architect merely for using good materials, which is necessary but not the core of their role. Thus, option 2 best aligns with this view.
Question No. : 2
All of the following, if true, can weaken the passage’s claim that facts do not speak for themselves, EXCEPT:
A) the truth value of a fact is independent of the historian who expresses it.
B) facts, like truth, can be relative: what is fact for person X may not be so for person Y.
C) a fact, by its very nature, is objective and universal, irrespective of the context in which it is placed.
D) the order in which a series of facts is presented does not have any bearing on the production of meaning.
Solution:
Answer 2: Option 2 is correct because it aligns with the passage's argument that the interpretation of facts can be influenced by different perspectives, suggesting that facts, much like truth, can be seen as relative.
Question No. : 3
If the author of the passage were to write a book on the Battle of Hastings along the lines of his/her own reasoning, the focus of the historical account would be on:
A) providing a nuanced interpretation by relying on the auxiliary sciences.
B) producing a detailed timeline of the various events that led to the Battle.
C) exploring the sociopolitical and economic factors that led to the Battle.
D) deriving historical facts from the relevant documents and inscriptions.
Solution:
Answer 3: The passage asserts that historians should go beyond mere factfinding to understand the context and motivations behind historical events. This comprehensive and interpretive approach is reflected in Option 3, which emphasizes understanding the underlying causes and influences.
Question No. : 4
All of the following describe the “commonsense view” of history, EXCEPT:
A) history can be objective like the sciences if it is derived from historical facts.
B) real history can be found in ancient engravings and archival documents.
C) history is like science: a selective system of cognitive orientations to reality.
D) only the positivist methods can lead to credible historical knowledge.
Solution:
Answer 3: Option 3 is the best choice because it highlights the fallacious belief in the objectivity of historical facts, which contrasts with the passage's critique of the oversimplified view of historical methodology as purely positivist.
DIRECTIONS for the question: The four sentences (labelled 1, 2, 3, and 4) given in this question, when properly sequenced, form a coherent paragraph. Decide on the proper order for the sentence and key in this sequence of four numbers as your answer.
Sentences:
Like the ants that make up a colony, no single neuron holds complex information like selfawareness, hope, or pride.
Although the human brain is not yet understood enough to identify the mechanism by which emergence functions, most neurobiologists agree that complex interconnections among the parts give rise to qualities that belong only to the whole.
Nonetheless, the sum of all neurons in the nervous system generates complex human emotions like fear and joy, none of which can be attributed to a single neuron.
Human consciousness is often called an emergent property of the human brain.
Solution:
Answer 4132: Sequence 4132 logically progresses from introducing the concept of human consciousness as an emergent property, elaborating on neuron organisation, and discussing the collective contribution of neurons to complex mental processes.
DILR (Data Interpretation and Logical Reasoning):
Number of Questions: 20
Time Allotted: 40 minutes
Difficulty Level: Slightly more difficult than 2022
The Data Interpretation and Logical Reasoning (DILR) section of the CAT 2023 question paper followed the same format as the CAT 2022 question paper. The number of questions under this section was set to be 20. The difficultly level of the DILR section however was observed to be slightly more difficult than the CAT 2022 question paper. There were 4 sets of questions with each set containing 5 questions. The analytical skills of the candidates were put to the test in this section. The various CAT 2023 DILR questions are given below:
CAT 2023 SLOT 1  
Set No.  Area  Set Descriptions  No. of Qs  LOD  Q. Type 
1  LR  (Arrangements) Professors in depart ments  5  Easy to Medium  5 MCQs 
2  DI  (Reasoning based DI) Gig workers and Restaurants, Mathematical Reasoning Involved Measures of central tendency  5  Medium to Difficult  1MCQ+4 TITA 
3  LR  Houses on sale  5  Medium to Difficult  3MCQ+2 TITA 
4  DI  Visa Office Special Equation handling  5  Medium to Difficult  3MCQ+2 TITA 
CAT 2023 SLOT 2  
1  LR  5 firms  Funds raised in consecutive years  5  4 MCQ, 2 TITA  Easy to Medium 
2  DI  Draw competition  5  1 MCQ, 4 TITA  Medium to Difficult 
3  LR  3 friends visited a park. Many rides. Scheduling questions.  5  2 MCQ, 3 TITA  Medium to Difficult 
4  DI  Nine Boxes  sudokutype puzzle  5  3 MCQ, 2 TITA  Medium to Difficult 
CAT 2023 SLOT 3  
1  DI  Number of enrollments in offline and online courses  5  3MCQ, 2 TITA  Easy to Medium 
2  DI  Six Police Stations with map (route based)  5  3 MCQ, 2 TITA  Medium 
3  DI  Projects and scores of 3 boys and 3 girls  5  3MCQ, 2 TITA  Medium to Difficult 
4  LR  AC Company  4 Dealers  5  3MCQ, 2 TITA  Medium to Difficult 
CAT Question Paper 2023: DILR Questions
Q1 Q5: Faculty members in a management school can belong to one of four departments – Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively.
Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q.
Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below.
1. There cannot be more than two candidates from a single department.
2. A candidate cannot vote for himself/herself.
3. Faculty members cannot vote for a candidate from their own department.
After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.
Question 1. Which two candidates can belong to the same department?
Prof. Pakrasi and Prof. Samuel
Prof. Pakrasi and Prof. Qureshi
Prof. Qureshi and Prof. Ramaswamy
Prof. Ramaswamy and Prof. Samuel
Correct Answer: B
Solution:
Here Take the first letter of the name of professor to represent the professor.
Given,
Department  No of Faculty members  Candidate for Dean  No of noncandidate voters 
FA  9  1 or 2  8 or 7 
MS  7  1 or 2  6 or 5 
OQ  5  1  4 
BH  3  1 or 2  2 or 1 
We know that the noncandidates in a particular department voted for the same candidate, and we also know that the least number of noncandidate voters in a particular department can be 1.
R got total 6 votes, out of which 1 is from the dean candidate P and 5 from noncandidates.
from above table we can see that 5 can be formed by (5 + 0) or (4 +1).
If we take 2nd case: It is only possible when there is 1 candidate from OQ, and there are 2 candidates from BH, which implies that number of candidates in FA and MQ is 1. But P received 2 non candidate votes only which is possible only if BH has 2 non candidate faculty and 1 candidate. So, this case is not possible.
Now, considering 1st case (a), we get that 5+0 will happen only one when there are 5 noncandidates in a single department.
This can be possible only in MS (where out of 7, there will be 2 candidates and 5 noncandidates)
So, we get the following table:
Department  No of Faculty members  Candidate for Dean  No of noncandidate voters 
FA  9  0  9 
MS  7  2  5 
OQ  5  1  4 
BH  3  1  2 
We also can draw
Candidate  Total Votes  Candidate Votes  NonCandidate Vote 
P  3  1(S)  2 (BH) 
Q  14  1(R)  13 (FA and OQ) 
R  6  1(P)  5 (MS) 
S  1  1(Q)  0 
Let's consider Department MS, we know that there are 2 candidates from MS and R can’t be one of them as the people in that department voted for him….. (3 rd condition)
Now, the possible combinations of candidates in MS are (P,Q), (Q,S) and (P,S).
Now , we can get that P and Q are from MS.
Question 2. Which of the following can be the number of votes that Prof. Qureshi received from a single department?
8
7
9
6
Correct Answer: C
Solution:
Here Take the first letter of the name of professor to represent the professor.
Given,
Department  No of Faculty members  Candidate for Dean  No of noncandidate voters 
FA  9  1 or 2  8 or 7 
MS  7  1 or 2  6 or 5 
OQ  5  1  4 
BH  3  1 or 2  2 or 1 
We know that the noncandidates in a particular department voted for the same candidate, and we also know that the least number of noncandidate voters in a particular department can be 1.
R got total 6 votes, out of which 1 is from the dean candidate P and 5 from noncandidates.
from above table we can see that 5 can be formed by (5 + 0) or (4 +1).
If we take 2nd case: It is only possible when there is 1 candidate from OQ, and there are 2 candidates from BH, which implies that number of candidates in FA and MQ is 1. But P received 2 non candidate votes only which is possible only if BH has 2 non candidate faculty and 1 candidate. So, this case is not possible.
Now, considering 1st case (a), we get that 5+0 will happen only one when there are 5 noncandidates in a single department.
This can be possible only in MS (where out of 7, there will be 2 candidates and 5 noncandidates)
So, we get the following table:
Department  No of Faculty members  Candidate for Dean  No of noncandidate voters 
FA  9  0  9 
MS  7  2  5 
OQ  5  1  4 
BH  3  1  2 
Question 3. If Prof. Samuel belongs to B&H, which of the following statements is/are true?
Statement A: Prof. Pakrasi belongs to M&S.
Statement B: Prof. Ramaswamy belongs to O&Q.
Both statements A and B
Only statement B
Only statement A
Neither statement A nor statement B
Correct Answer: A
Solution:
Here Take the first letter of the name of professor to represent the professor.
Given,
Department  No of Faculty members  Candidate for Dean  No of noncandidate voters 
FA  9  1 or 2  8 or 7 
MS  7  1 or 2  6 or 5 
OQ  5  1  4 
BH  3  1 or 2  2 or 1 
We know that the noncandidates in a particular department voted for the same candidate, and we also know that the least number of noncandidate voters in a particular department can be 1.
R got total 6 votes, out of which 1 is from the dean candidate P and 5 from noncandidates.
from above table we can see that 5 can be formed by (5 + 0) or (4 +1).
If we take 2nd case: It is only possible when there is 1 candidate from OQ, and there are 2 candidates from BH, which implies that number of candidates in FA and MQ is 1. But P received 2 non candidate votes only which is possible only if BH has 2 non candidate faculty and 1 candidate. So, this case is not possible.
Now, considering 1st case (a), we get that 5+0 will happen only one when there are 5 noncandidates in a single department.
This can be possible only in MS (where out of 7, there will be 2 candidates and 5 noncandidates)
So, we get the following table:
Department  No of Faculty members  Candidate for Dean  No of noncandidate voters 
FA  9  0  9 
MS  7  2  5 
OQ  5  1  4 
BH  3  1  2 
We also can draw
Candidate  Total Votes  Candidate Votes  NonCandidate Vote 
P  3  1(S)  2 (BH) 
Q  14  1(R)  13 (FA and OQ) 
R  6  1(P)  5 (MS) 
S  1  1(Q)  0 
Let's consider Department MS, we know that there are 2 candidates from MS and R can’t be one of them as the people in that department voted for him….. (3 rd condition)
Now, the possible combinations of candidates in MS are (P,Q), (Q,S) and (P,S).
Now , we can get that P and Q are from MS.
Question 4. What best can be concluded about the candidate from O&Q?
It was either Prof. Pakrasi or Prof. Qureshi.
It was Prof. Samuel.
It was Prof. Ramaswamy.
It was either Prof. Ramaswamy or Prof. Samuel.
Correct Answer: D
Solution:
Here Take the first letter of the name of professor to represent the professor.
Given,
Department  No of Faculty members  Candidate for Dean  No of noncandidate voters 
FA  9  1 or 2  8 or 7 
MS  7  1 or 2  6 or 5 
OQ  5  1  4 
BH  3  1 or 2  2 or 1 
We know that the noncandidates in a particular department voted for the same candidate, and we also know that the least number of noncandidate voters in a particular department can be 1.
R got total 6 votes, out of which 1 is from the dean candidate P and 5 from noncandidates.
from above table we can see that 5 can be formed by (5 + 0) or (4 +1).
If we take 2nd case: It is only possible when there is 1 candidate from OQ, and there are 2 candidates from BH, which implies that number of candidates in FA and MQ is 1. But P received 2 non candidate votes only which is possible only if BH has 2 non candidate faculty and 1 candidate. So, this case is not possible.
Now, considering 1st case (a), we get that 5+0 will happen only one when there are 5 noncandidates in a single department.
This can be possible only in MS (where out of 7, there will be 2 candidates and 5 noncandidates)
So, we get the following table:
Department  No of Faculty members  Candidate for Dean  No of noncandidate voters 
FA  9  0  9 
MS  7  2  5 
OQ  5  1  4 
BH  3  1  2 
We also can draw
Candidate  Total Votes  Candidate Votes  NonCandidate Vote 
P  3  1(S)  2 (BH) 
Q  14  1(R)  13 (FA and OQ) 
R  6  1(P)  5 (MS) 
S  1  1(Q)  0 
Let's consider Department MS, we know that there are 2 candidates from MS and R can’t be one of them as the people in that department voted for him….. (3 rd condition)
Now, the possible combinations of candidates in MS are (P,Q), (Q,S) and (P,S).
Now , we can get that P and Q are from MS.
Question 5. Which of the following statements is/are true?
Statement A: Noncandidates from M&S voted for Prof. Qureshi.
Statement B: Noncandidates from F&A voted for Prof. Qureshi.
Only statement B
Only statement A
Both statements A and B
Neither statement A nor statement B
Correct Answer: A
Solution:
Here Take the first letter of the name of professor to represent the professor.
Given,
Department  No of Faculty members  Candidate for Dean  No of noncandidate voters 
FA  9  1 or 2  8 or 7 
MS  7  1 or 2  6 or 5 
OQ  5  1  4 
BH  3  1 or 2  2 or 1 
We know that the noncandidates in a particular department voted for the same candidate, and we also know that the least number of noncandidate voters in a particular department can be 1.
R got total 6 votes, out of which 1 is from the dean candidate P and 5 from noncandidates.
from above table we can see that 5 can be formed by (5 + 0) or (4 +1).
If we take 2nd case: It is only possible when there is 1 candidate from OQ, and there are 2 candidates from BH, which implies that number of candidates in FA and MQ is 1. But P received 2 non candidate votes only which is possible only if BH has 2 non candidate faculty and 1 candidate. So, this case is not possible.
Now, considering 1st case (a), we get that 5+0 will happen only one when there are 5 noncandidates in a single department.
This can be possible only in MS (where out of 7, there will be 2 candidates and 5 noncandidates)
So, we get the following table:
Department  No of Faculty members  Candidate for Dean  No of noncandidate voters 
FA  9  0  9 
MS  7  2  5 
OQ  5  1  4 
BH  3  1  2 
We also can draw
Candidate  Total Votes  Candidate Votes  NonCandidate Vote 
P  3  1(S)  2 (BH) 
Q  14  1(R)  13 (FA and OQ) 
R  6  1(P)  5 (MS) 
S  1  1(Q)  0 
Let's consider Department MS, we know that there are 2 candidates from MS and R can’t be one of them as the people in that department voted for him….. (3 rd condition)
Now, the possible combinations of candidates in MS are (P,Q), (Q,S) and (P,S).
Now , we can get that P and Q are from MS.
CAT Question Paper 2023: QA (Quantitative Aptitude)
Number of Questions: 22
Time Allotted: 40 minutes
Difficulty Level: Lengthier than the 2022 paper, Medium to Difficult
Out of all the sections in the CAT 2023 question paper, the quantitative aptitude section posed the most difficulty for the candidates. The paper was lengthy and more difficult compared to the previous year's CAT question papers. The questions covered a wide range of mathematical concepts, requiring candidates to display their quantitative aptitude. Another interesting observation is that the algebraic questions outweighed the arithmetic questions in the CAT 2023 question paper on quantitative aptitude. The division of questions in the CAT 2023 question papers across all the slots is given below. Having a idea of the important CAT quantitative aptitude formulas can be really beneficial for the candidates while preparing for this section.
Area  Slot 1 (Total: 22)  Slot 2 (Total: 22)  Slot 3 (Total: 14) 
Arithmetic  7  7  8 
Algebra  8  8  4 
Geometry  4  3  3 
Modern Maths  2  2  4 
Numbers  1  2  3 
MCQs  15  14  14 
TITA  7  8  8 
CAT Question Paper 2023: Quantitative Aptitude Questions
Q. 1) If x is a positive real number such that x8 + (1/x)8 = 47, then the value of x9 + (1/x)9 isA. 34√5 B. 40√5 C. 36√5 D. 30√5
Ans: A
Solution:
Given:
xâ¸ + (1/x)â¸ = 47
⇒ (xâ´ + 1/xâ´)²  2 = 47
⇒ (xâ´ + 1/xâ´)² = 49
⇒ xâ´ + 1/xâ´ = 7
Next,
(x² + 1/x²)²  2 = 7
⇒ (x² + 1/x²)² = 9
⇒ x² + 1/x² = 3
Now,
(x + 1/x)²  2 = 3
⇒ x + 1/x = √5
Cubing both sides:
(x + 1/x)³ = 5√5
⇒ x³ + 1/x³ + 3 × √5 = 5√5
⇒ x³ + 1/x³ = 2√5
Cubing again:
xâ¹ + 1/xâ¹ + 3 × 2√5 = 40√5
⇒ xâ¹ + 1/xâ¹ = 34√5
Q. 2) Let n and m be two positive integers such that there are exactly 41 integers greater than 8m and less than 8n, which can be expressed as powers of 2. Then, the smallest possible value of n + m is
A. 44 B. 16 C. 42 D. 14
Ans: B
Solution:
Smallest value of 8m is 8 i.e. 23 (for m = 1)
Next integer in the form of 2x will be 24.
And we have 41 integers in the form of 2x greater than 8m and less than 8n.
So, last integer in the form of 2x and less than 8n is 244.
So, 8n = 245 which implies that 3n = 45 and n = 15.
So, smallest possible value of n + m = 15 + 1 = 16.
Q. 3) For some real numbers a and b, the system of equations x +y = 4 and (a+5)x + (b2 15)y = 8b has infinitely many solutions for x and y. Then, the maximum possible value of ab is
A. 15 B. 55 C. 33 D. 25
Ans: C
Solution:
For the given equations:
x + y = 4 and (a + 5)x + (b²  15)y = 8b
Condition for infinite many solutions:
1/(a + 5) = 1/(b²  15) = 4/(8b)
Solving 1/(b²  15) = 4/(8b),
we get 8b = 4(b²  15)
On solving this quadratic equation, we get b = 3, 5.
Next, solving 1/(a + 5) = 4/(8b),
we get 8b = 4(a + 5).
For b = 3, a = 11, and hence ab = (3) × (11) = 33.
For b = 5, a = 5, and hence ab = 5 × 5 = 25.
So, the maximum value of ab is 33.
CAT Exam Paper with Solutions 2023
The Common Admission Test is one of the most important management entrance exams in the country. Due to its fiercely competitive nature and varying difficulty levels, taking the CAT exam has become more tedious now. Practising with the previous year’s CAT question papers is a very effective way to enhance the candidate’s CAT preparation and ensure a high CAT 2024 percentile. Careers360 has designed an ebook that contains expertly crafted answers for the CAT 2023 question paper. This CAT 2023 answer sheet is written by experienced Subject Matter Experts in their respective fields. The candidates are requested to download and study the ebook from the link given below:
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CAT 2023 Official Question Paper with Solutions (Slot 1, 2 and 3)  Download Link 
If a candidate wishes to practice more CAT previous year’s papers, they may do so by referring to this article
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Benefits of Solving the CAT 2023 Question Papers
Solving the CAT 2023 question papers comes with a lot of advantages for the candidates. Some of the major reasons why the candidates must download and study CAT Question Paper PDFs are given below:
Familiarity with Exam Pattern: When a candidate solves the previous year’s CAT exam question papers, they get accustomed to the CAT exam pattern and through this, they will be able to understand the various exam question types and difficulty level. This makes them wellprepared for the CAT exam day.
Understanding the Difficulty Level: The CAT exam varies in difficulty each year. By working through the 2023 paper, candidates can understand the overall difficulty and adjust their CAT preparation strategy accordingly, focusing more on areas where they might struggle.
Identification of Key Topics: Practicing for the CAT exam using the CAT important topics is an essential skill that all candidates must possess. This means that having a good idea of the CAT's important topics would enable the candidates to make the most out of their CAT exam preparation and help them score the maximum marks in a limited time.
Improved Time Management: Time management is an essential skill that a candidate must have when it comes to preparing for the CAT exam and with constant previous year CAT papers practice and CAT sample papers, the candidates can ensure that they are able to meet the sectional time management constraint of the CAT exam and prepare well for the exam.
Error Analysis and Improvement: Reviewing mistakes made while solving the paper helps candidates understand their weak points. This analysis provides insights into areas that require more focus, enabling candidates to improve their CAT preparation.
Boosting Confidence: Regular practice with actual question papers helps build confidence. As candidates become more comfortable with the format and types of questions, they feel less anxious during the exam.
CAT Preparation Materials
Given below are some of the important ebooks and CAT materials designed by Careers360 for enhancing the CAT preparation of the candidates and helping them to secure a very high CAT percentile score. The candidates are also strongly advised to refer to the various important CAT books to improve their CAT 2023 performance.
eBook Title  Download Links 
3000+ Most Important Words  Vocabulary Builder  Download Here 
500+ Most Important Idioms and Phrases  Download Here 
300+ Most Important Phrasal Verbs  Download Here 
Permutation & Combination  Video Lectures and Practice Questions  Download Here 
Mastering DILR Questions with Expert Solutions  Download Here 
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