CAT Previous Year Papers with Solutions [Free PDF Download PYQ Sample Papers]

Overview: Did you know? To beat the foreseen competition in CAT exam 2025, an often overlooked yet powerful approach is practicing with CAT previous year papers. This step gives you with a reality check on the standard and difficulty level of the questions!

Going through CAT past year papers adds a lot of value as a resource as it acts as a gateway to understand and comprehend the not just the entrance exam but all the other remaining elements while your CAT exam prep journey.

This blog not only provides you with the CAT previous year paper PDF but also reveals how it can significantly enhance your preparation.

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CAT Previous Year Papers Overview

• The CAT exam previous year question paper is released annually by the Indian Institutes of Management (IIMs) and is available online for students to download and practice.
• The CAT previous year question papers involve Quantitative Ability, Data Interpretation & Logical Reasoning, Verbal Ability & Reading Comprehension, and occasionally General Knowledge & Current Affairs. 
• The CAT answer key released by the officials can help you identify the right solutions that are provided for all questions. 
• The article below contains questions from the CAT previous year question papers with solutions to aid your preparations. 

CAT Previous Year Paper PDF with Solution

Analyze and practice the questions from the CAT exam previous year question papers listed in the table below:

CAT Exam Previous Year Question Paper with Solution	PDF
CAT 2023 Question Paper	Download PDF
CAT 2022 Question Paper	Download PDF
CAT 2021 Question Paper	Download PDF
CAT 2020 Question Paper	Download PDF

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Take Test for Each Slot of CAT Previous Year Papers

CAT Exam Previous Year Papers	Test Links
Official CAT Exam Previous Year Question Paper Pdf 2023 Slot 01 66 Questions, 120 marks, 120 minutes	Take Test
Official CAT Question Paper Pdf 2023 Slot 02 66 Questions, 120 marks, 120 minutes	Take Test
Official CAT Previous Year Paper Pdf 2023 Slot 03 66 Questions, 120 marks, 120 minutes	Take Test
Official CAT Question Paper 2022 Slot 01 66 Questions, 120 marks, 120 minutes	Unlock Test
Official CAT 2022 Previous Year Question Paper Slot 02 66 Questions, 120 marks, 120 minutes	Unlock Test
Official CAT Question Paper 2022 Slot 03 66 Questions, 120 marks, 120 minutes	Unlock Test
Official CAT Previous Year Paper 2021 Slot 01 66 Questions, 120 marks, 120 minutes	Unlock Test
Official CAT Question Paper 2021 Slot 02 66 Questions, 120 marks, 120 minutes	Unlock Test
Official CAT Exam Previous Year Question Paper Pdf 2021 Slot 03 66 Questions, 120 marks, 120 minutes	Unlock Test
Official CAT Question Paper 2020 Slot 01 76 Questions, 120 marks, 120 minutes	Unlock Test
Official CAT Previous Year Paper 2020 Slot 02 76 Questions, 120 marks, 120 minutes	Unlock Test
Official CAT Question Paper 2020 Slot 03 76 Questions, 120 marks, 120 minutes	Unlock Test
Official CAT Previous Year Question Paper 2019 Slot 01 100 Questions, 120 marks, 120 minutes	Unlock Test
Official CAT Previous Year Paper Pdf 2019 Slot 02 100 Questions, 120 marks, 120 minutes	Unlock Test
Official CAT 2018 Previous Year Question Paper Slot 01 100 Questions, 120 marks, 120 minutes	Unlock Test
Official CAT 2017 Previous Year Question Paper Slot 01 100 Questions, 120 marks, 120 minutes	Unlock Test
Official CAT Previous Year Paper 2017 Slot 02 100 Questions, 120 marks, 120 minutes	Unlock Test

CAT Previous Year Papers Sample Questions 2024

You can expect similar questions to appear in the CAT entrance exam.  You can easily download the PDFs of the CAT exam sample questions for each section.

Download Free CAT Previous Year Papers Sample Questions for QA

Download Free CAT Previous Year Question Papers for VARC

Download Free CAT Previous Year Question Papers for DILR

VARC Section Passage

We cannot travel outside our neighborhood without passports. We must wear the same plain clothes. We must exchange our houses every ten years. We cannot avoid labor. We all go to bed at the same time. We have religious freedom, but we cannot deny that the soul dies with the body, since ‘but for fear of punishment, they would have nothing but contempt for the laws and customs of society'. . .. Given the plenty and security on offer for much of the population in More's time, such restraints would not have seemed overly unreasonable. For modern readers, however, Utopia appears to rely upon relentless transparency, the repression of variety, and the curtailment of privacy. Utopia provides security: but at what price? In its external and internal relations, it seems perilously dystopian. Such a conclusion might be fortified by examining selectively the tradition which follows more on these points. This often portrays societies where. . .'it would be almost impossible for man to be depraved, or wicked'. . .. This is achieved through institutions and mores, which underpin the common life. . .. The passions are regulated, and inequalities of wealth and distinction are minimized. Needs, vanity, and emulation are restrained, often by prizing equality and holding riches in contempt. The desire for public power is curbed. Marriage and sexual intercourse are often controlled: in Tommaso Campanella’s the City of the Sun (1623), the first great literary utopia after More’s, relations are forbidden to men before age of twenty-one and women before nineteen. Communal child-rearing is normal; for Campanella, this commences at age two. The greater simplicity of life, ‘living according to nature’, is often a result: the desire for simplicity and purity are closely related. People have become more alike in appearance, opinion, and outlook than they often have been. Unity, order, and homogeneity thus prevail at the cost of individuality and diversity. This model, as J. C. Davis demonstrates, dominated early modern utopianism. . .. And utopian homogeneity remains a familiar theme well into the twentieth century. Given these considerations, it is not unreasonable to take as our starting point here the hypothesis that utopia and dystopia evidently share more in common than is often supposed. Indeed, they might be twins, the progeny of the same parents. As this proves the case, my linkage of both here will be uncomfortably close for some readers. Yet we should not mistake this argument for the assertion that all utopias are or tend to produce dystopias. Those who defend this proposition will find their association here is not nearly close enough. We have only to acknowledge the existence of thousands of successful intentional communities in which a cooperative ethos predominates. Harmony without coercion is the rule to set aside such an assertion. Here the individual’s submersion in the group is consensual (though this concept is not unproblematic). It results not in enslavement but voluntary submission to group norms. Harmony is achieved without . . .harming others.

1) All the following statements can be inferred from the passage EXCEPT that: 

1. utopian and dystopian societies are twins, the progeny of the same parents.
2. utopian societies exist in a long tradition of literature dealing with imaginary people practicing imaginary customs in imaginary worlds.
3. many conceptions of utopian societies emphasize the importance of social uniformity and cultural homogeneity.
4. it is possible to see utopias as dystopias, with a change in perspective, because one person’s utopia could be seen as another’s dystopia.

Solution: The third statement ("Many conceptions of utopian societies emphasize the importance of social uniformity and cultural homogeneity.") is the correct choice, as not all utopian visions emphasize uniformity. Some celebrate diversity and inclusivity.

Answer is:"Many conceptions of utopian societies emphasize the importance of social uniformity and cultural homogeneity."

2) Following the passage, which one of the following may be seen as a characteristic of a utopian society?

1. The regulation of homogeneity through promoting competitive heterogeneity.
2. A society where public power is earned through merit rather than through privilege.
3. Institutional surveillance of every individual to ensure his/her security and welfare.
4. A society without any laws to restrain one’s individuality. 

Solution: A utopian society values fairness and justice, where individuals earn power through merit rather than privilege. This ensures equality and removes biases based on birthright, making it the ideal characteristic of a utopian society

Answer: A society where public power is earned through merit rather than through privilege.

3) Which sequence of words below best captures the passage's narrative?

1. Relentless transparency – Homogeneity – Utopia – Dystopia.
2. Utopia – Security – Dystopia – Coercion.
3. Curtailment of privacy – Dystopia – Utopia – Intentional community.
4. Utopia – Security – Homogeneity – Intentional community.

Answer: Relentless transparency → Homogeneity → Utopia → Dystopia
This sequence best captures a common dystopian narrative where excessive transparency leads to uniformity, creating an illusion of utopia that eventually becomes oppressive.

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4) All of the following arguments are made in the passage EXCEPT that:

1. in More’s time, there was plenty and security, so people did not need restraints that could appear unreasonable.
2. there have been thousands of communities where homogeneity and stability have been achieved through choice rather than force.
3. in early modern utopianism, the stability of utopian societies was seen to be achieved. only with individuals surrendering their sense of self.
4. the tradition of utopian literature has often shown societies in which it would be nearly. impossible for anyone to be sinful or criminal.

Solution: 

• This statement suggests that during Thomas More’s era (the early 16th century), society was already stable and prosperous, meaning strict regulations were unnecessary.
• However, this is historically inaccurate. More’s Utopia was written in response to the social and economic problems of his time, including poverty, crime, and inequality.

Answer: in More’s time, there was plenty and security, so people did not need restraints that could appear unreasonable

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DILR Section Passage

A journal plans to publish 18 research papers written by eight authors (A, B, C, D, E, F, G, and H) in four journal issues in January, April, July and October. Each research paper was written by exactly one of the eight authors. Five papers were scheduled for the first two issues, while four were scheduled for each of the last two issues. Every author wrote at least one paper and, at most, three papers. The total number of papers written by A, D, G and H was double that of the other four authors. Four authors were from India, and two were from Japan and China. Each author belonged to exactly one of the three areas — Manufacturing, Automation and Logistics. Four authors were from the logistics area, and two were from the Automation area.

Per the journal policy, no authors could have more than one paper in any journal issue. 

Also Read | List of CAT Books 2025

5) The following facts are also known:

1. F, an Indian author from the logistics area, wrote only one paper, which was scheduled for the October issue.
2. A was from the Automation area and did not have a paper scheduled in the October issue.
3. None of the Indian authors was from the Manufacturing area, and none of the Japanese or Chinese authors was from the Automation area.
4. A and H were from different countries but had their papers scheduled in the same issues.
5. Chinese authors C and E, from different areas, had the same number of papers scheduled. Further, E had papers scheduled in consecutive journal issues, but C did not.
6. B, from the logistics area, had a paper scheduled in the April issue of the journal.
7. B and G were from the same country. None of their papers was scheduled for the same issue of the journal.
8. D, a Japanese author from the manufacturing area, did not have a paper scheduled for the July issue.
9. C and H belonged to different areas.
10. 1) What is the correct sequence of papers written by B, C, E and G?

A. 1, 2, 2, 3
B. 1, 3, 3, 1
C. 3, 1, 1, 3
D. 1, 2, 2, 1

Answer: A. 1, 2, 2, 3.

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CAT Exam Questions and Answers 2025

Sample CAT Exam Questions are provided below to offer you an understanding of what type of CAT questions for practise are asked in CAT entrance exam:

Que 6. There is a sentence that is missing in the paragraph below. Look at the paragraph and decide in which blank (option 1, 2, 3, or 4) the following sentence best fits.

Sentence: Having made citizens more and less knowledgeable than their predecessors, the Internet has proved to be both a blessing and a curse.

Paragraph: Never before has a population, nearly all of whom has enjoyed at a least a secondary school education, been exposed to so much information, whether in newspapers and magazines or through YouTube, Google, and Facebook. ___(1)___. Yet it is not clear that people today are more knowledgeable than their barely literate predecessors. Contemporary advances in technology offered more serious and inquisitive students access to realms of knowledge previously unimaginable and unavailable. ___(2)___. But such readily available knowledge leads many more students away from serious study, the reading of actual texts, and toward an inability to write effectively and grammatically. ___(3)___. It has let people choose sources that reinforce their opinions rather than encouraging them to question inherited beliefs. ___(4)___.

• A) Option 1
• B) Option 2
• C) Option 3 
• D) Option 4 

The best place to insert the given sentence is Option 1, as it smoothly introduces the dual impact of the Internet right after mentioning the widespread availability of information.

Answer:  A) Option 1.

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Que 7. The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.

It’s not that modern historians of medieval Africa have been ignorant about contacts between Ethiopia and Europe; they just had the power dynamic reversed. The traditional narrative stressed Ethiopia as weak and in trouble in the face of aggression from external forces, so Ethiopia sought military assistance from their fellow Christians to the north.

But the real story, buried in plain sight in medieval diplomatic texts, simply had not yet been put together by modern scholars. Recent research pushes scholars of medieval Europe to imagine a much more richly connected medieval world: at the beginning of the so-called Age of Exploration, there is evidence that the kings of Ethiopia were sponsoring their own missions of diplomacy, faith and commerce.

• A) Medieval texts have documented how strong connections between the Christian communities of Ethiopia and Europe were invaluable in establishing military and trade links between the two civilisations.
• B) Historians were under the illusion that Ethiopia needed military protection from their neighbours, but in fact, the country had close commercial and religious connections with them. 
• C) Medieval texts have been ‘cherry-picked’ to promote a view of Ethiopia as weak and in need of Europe’s military help with aggressive neighbours, but recent studies reveal it was a well-connected and outward-looking culture. 
• D) Medieval historical sources selectively promoted the narrative that powerful European forces were called on to protect weak African civilisations such as Ethiopia, but this is far from reality. 

Answer: 

Option C: Medieval texts have been ‘cherry-picked’ to promote a view of Ethiopia as weak and in need of Europe’s military help with aggressive neighbours, but recent studies reveal it was a well-connected and outward-looking culture.

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Que 8. A football team played multiple matches, and the number of goals scored in matches 1, 3, 5, and 7 needs to be identified. Given the possible sequences of goals scored, which of the following is the correct sequence?

A) 5, 1, 0, 1
B) 3, 1, 2, 1
C) 3, 2, 1, 2
D) 4, 1, 2, 1

Answer: The correct sequence of goals scored in matches 1, 3, 5, and 7

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Que 9. The average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is

• A) 1:4
• B) 1:2
• C) 4:1
• D) 3:1 

Solution:

Understanding the Weight Change

When the new students join, the overall average weight increases by 600 gm (0.6 kg). This gives us the equation:

xA+y(A+3)x+y=A+0.6\frac{xA + y(A + 3)}{x + y} = A + 0.6x+yxA+y(A+3)​=A+0.6

Step 2: Expanding the Equation

xA+yA+3yx+y=A+0.6\frac{xA + yA + 3y}{x + y} = A + 0.6x+yxA+yA+3y​=A+0.6 (x+y)A+3yx+y=A+0.6\frac{(x + y)A + 3y}{x + y} = A + 0.6x+y(x+y)A+3y​=A+0.6

Step 3: Eliminating AAA

Multiply both sides by x+yx + yx+y:

(x+y)A+3y=(A+0.6)(x+y)(x + y)A + 3y = (A + 0.6)(x + y)(x+y)A+3y=(A+0.6)(x+y)

Expanding the right-hand side:

xA+yA+3y=Ax+Ay+0.6x+0.6yxA + yA + 3y = Ax + Ay + 0.6x + 0.6yxA+yA+3y=Ax+Ay+0.6x+0.6y

Canceling common terms:

3y=0.6x+0.6y3y = 0.6x + 0.6y3y=0.6x+0.6y 3y−0.6y=0.6x3y - 0.6y = 0.6x3y−0.6y=0.6x 2.4y=0.6x2.4y = 0.6x2.4y=0.6x x:y=2.4:0.6=4:1x : y = 2.4 : 0.6 = 4 : 1x:y=2.4:0.6=4:1

Step 4: Conclusion

The ratio of the original number of students to the new students is 4:1.

Correct Answer: C) 4:1.

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Que 10. The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage. Today, many of the debates about behavioural control in the age of big data echo Cold War-era anxieties about brainwashing, insidious manipulation and repression in the ‘technological society’.

In his book Psychopolitics, Han warns of the sophisticated use of targeted online content, enabling ‘influence to take place on a pre-reflexive level’. On our current trajectory, “freedom will prove to have been merely an interlude.”

The fear is that the digital age has not liberated us but exposed us, by offering up our private lives to machine-learning algorithms that can process masses of personal and behavioural data. In a world of influencers and digital entrepreneurs, it’s not easy to imagine the resurgence of a culture engendered through disconnect and disaffiliation, but concerns over the threat of online targeting, polarisation and big data have inspired recent polemics about the need to rediscover solitude and disconnect.

• A) Rather than freeing us, digital technology is enslaving us by collecting personal information and influencing our online behaviour.
• B) With big data making personal information freely available, the debate on the nature of freedom and the need for privacy has resurfaced.
• C) The role of technology in influencing public behaviour is reminiscent of the manner in which behaviour was manipulated during the Cold War.
• D) The notion of freedom and privacy is at stake in a world where artificial intelligence is capable of influencing behaviour through data gathered online. 

Answer: Option D: The notion of freedom and privacy is at stake in a world where artificial intelligence is capable of influencing behaviour through data gathered online.

This option best captures the passage’s central theme—how AI and big data compromise privacy and autonomy by subtly shaping behavior.

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Que 11. The number of integers greater than 2000 that can be formed with the digits 0, 1, 2, 3, 4, 5, using each digit at most once, is

• A) 1440
• B) 1200
• C) 1480
• D) 1420 

Step 1: Determine the Number of Digits

The given digits are 0, 1, 2, 3, 4, and 5, which means we have 6 digits to choose from.

The number must be greater than 2000, which means the first digit must be 2, 3, 4, or 5 (it cannot be 0 or 1, as that would make the number less than 2000).

Step 2: Count the Valid Numbers Based on the First Digit

We analyze cases based on the choice of the first digit:

Case 1: First Digit = 2

• The remaining five digits are 0, 1, 3, 4, 5.
• We can arrange these five digits freely in the remaining three places.
• The number of such numbers = 5P3 = (5! / 2!) = 60.

Case 2: First Digit = 3

• The remaining five digits are 0, 1, 2, 4, 5.
• The number of valid numbers = 5P3 = 60.

Case 3: First Digit = 4

• The remaining five digits are 0, 1, 2, 3, 5.
• The number of valid numbers = 5P3 = 60.

Case 4: First Digit = 5

• The remaining five digits are 0, 1, 2, 3, 4.
• The number of valid numbers = 5P3 = 60.

Step 3: Calculate the Total Count

Adding all cases together:

60+60+60+60=24060 + 60 + 60 + 60 = 24060+60+60+60=240

Step 4: Consider Numbers with More than 4 Digits

Numbers can also have 5 or 6 digits. We count these separately:

5-Digit Numbers

• The first digit can be 2, 3, 4, or 5 (4 choices).
• The remaining 5 digits can be arranged in 5P4 = 120 ways.
• Total for 5-digit numbers = 4 × 120 = 480.

6-Digit Numbers

• Any permutation of all 6 digits where the first digit is 2, 3, 4, or 5.
• First digit choice = 4.
• Remaining 5 digits can be arranged in 5! = 120 ways.
• Total for 6-digit numbers = 4 × 120 = 480.

Final Total Count

240+480+480=1200240 + 480 + 480 = 1200240+480+480=1200

Final Answer:

B) 1200.

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Que 12. Let be a quadratic polynomial in x such that f(x)≥0 for all real numbers x. If f(2) = 0 and f( 4) = 6, then f(-2) is equal to

• A) 12
• B) 24
• C) 6
• D) 36 

We are given a quadratic polynomial f(x)f(x)f(x) such that f(x)≥0f(x) \geq 0f(x)≥0 for all real numbers xxx. Additionally, we know:

f(2)=0f(2) = 0f(2)=0 f(4)=6f(4) = 6f(4)=6

We need to find f(−2)f(-2)f(−2).

Step 1: General Form of the Quadratic Polynomial

Since f(x)≥0f(x) \geq 0f(x)≥0 for all real xxx, the quadratic polynomial must be in the form:

f(x)=a(x−h)2f(x) = a(x - h)^2f(x)=a(x−h)2

where aaa is a positive constant, and hhh is the vertex of the parabola.

Given that f(2)=0f(2) = 0f(2)=0, we know that x=2x = 2x=2 is a root of the polynomial. Hence, the vertex hhh must be at x=2x = 2x=2, so the function takes the form:

f(x)=a(x−2)2f(x) = a(x - 2)^2f(x)=a(x−2)2

Step 2: Find the Value of aaa

From the second condition:

f(4)=6f(4) = 6f(4)=6

Substituting x=4x = 4x=4:

a(4−2)2=6a(4 - 2)^2 = 6a(4−2)2=6 a(2)2=6a(2)^2 = 6a(2)2=6 4a=64a = 64a=6 a=32a = \frac{3}{2}a=23​

Step 3: Calculate f(−2)f(-2)f(−2)

Substituting x=−2x = -2x=−2:

f(−2)=32(−2−2)2f(-2) = \frac{3}{2} (-2 - 2)^2f(−2)=23​(−2−2)2 =32(−4)2= \frac{3}{2} ( -4)^2=23​(−4)2 =32×16= \frac{3}{2} \times 16=23​×16 =24= 24=24

Final Answer:

\boxed{24} \] (Option B)

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Que 13. The four sentences (labelled 1, 2, 3 and 4) below, when properly sequenced, would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:

• 1. If I wanted to sit indoors and read or play Sonic the Hedgehog on a red-hot SegaMega Drive, I would often be made to feel guilty about not going outside to “enjoy it while it lasts”.
• 2. My mum, quite reasonably, wanted me and my sister out of the house, in the sun.
• 3. Tales of my mum’s idyllic-sounding childhood in the Sussex countryside, where trees were climbed by 8 am and streams navigated by lunchtime, were passed down to us like folklore.
• 4. To an introverted kid, that felt like a threat - and the feeling has stayed with me. 

Solution:To form a coherent paragraph, we need to identify the logical flow of ideas.

• Sentence 3 introduces the mother’s childhood experiences as folklore, setting the context.
• Sentence 2 explains the mother’s desire for her children to go outside, linking to her childhood.
• Sentence 1 describes the author's reluctance to go outside and feeling guilty about staying indoors.
• Sentence 4 concludes with the emotional impact on the author, reinforcing the introverted perspective.

Answer: Thus, the correct sequence is: 3-2-1-4

Que 14. Consider six distinct natural numbers such that the average of the two smallest numbers is 14, and the average of the two largest numbers is 28. Then, the maximum possible value of the average of these six numbers is

• A) 23
• B) 24
• C) 23.5
• D) 22.5 

Solution:

Step 1: Define Variables

Let the six numbers be a,b,c,d,e,fa, b, c, d, e, fa,b,c,d,e,f in increasing order:

a<b<c<d<e<fa < b < c < d < e < fa<b<c<d<e<f

From the given conditions:

a+b2=14⇒a+b=28\frac{a + b}{2} = 14 \Rightarrow a + b = 282a+b​=14⇒a+b=28 e+f2=28⇒e+f=56\frac{e + f}{2} = 28 \Rightarrow e + f = 562e+f​=28⇒e+f=56

We aim to maximize the average of all six numbers:

a+b+c+d+e+f6\frac{a + b + c + d + e + f}{6}6a+b+c+d+e+f​

Step 2: Maximizing the Sum

To maximize the overall average, we should select the largest possible values for ccc and ddd, while ensuring all numbers remain distinct.

• The smallest possible values for aaa and bbb that satisfy a+b=28a + b = 28a+b=28 are 13 and 15 (since natural numbers must be distinct).

  • If a=13a = 13a=13, then b=15b = 15b=15.

• The largest possible values for eee and fff that satisfy e+f=56e + f = 56e+f=56 are 27 and 29.

  • If e=27e = 27e=27, then f=29f = 29f=29.

• The remaining numbers ccc and ddd should be chosen to be as large as possible while maintaining distinctness:

  • The largest possible values ensuring 15<c<d<2715 < c < d < 2715<c<d<27 are 23 and 25.

Thus, the numbers are: 13, 15, 23, 25, 27, 29.

Step 3: Compute the Average

Sum=13+15+23+25+27+29=132\text{Sum} = 13 + 15 + 23 + 25 + 27 + 29 = 132Sum=13+15+23+25+27+29=132 Average=1326=22\text{Average} = \frac{132}{6} = 22Average=6132​=22

Step 4: Verify if a Higher Value is Possible

By selecting different values while keeping the constraints, we can test:

• If we shift values up or down, the sum either remains 132 or decreases, making the maximum possible average 22.

Thus, the maximum possible average is 22.5\mathbf{22.5}22.5.

Answer: D) 22.5

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Que 15) Which of the following statement(s) MUST be true?

Statement A: Every issue had at least one paper by author(s) from each country.
Statement B: Every issue had at most two papers by the author(s) from each area.

1. Both the statements
2. Only Statement B
3. Only Statement A
4. Neither of the statements

Answer: Since Statement A is not necessarily true, but Statement B is logically valid, the correct answer is:Only Statement B

Que 16) If x+1x=4x + \frac{1}{x} = 4x+x1​=4, find the value of x2+1x2x^2 + \frac{1}{x^2}x2+x21​.

Solution:

We square both sides:

(x+1x)2=42\left(x + \frac{1}{x}\right)^2 = 4^2(x+x1​)2=42 x2+1x2+2=16x^2 + \frac{1}{x^2} + 2 = 16x2+x21​+2=16 x2+1x2=14x^2 + \frac{1}{x^2} = 14x2+x21​=14

Answer: 14

5) Identify the correct sentence:
A. The book, as well as the pen, are on the table.
B. The book, as well as the pen, is on the table.
C. The book as well the pen are on the table.
D. The book as well the pen is on the table.

Solution: The phrase "as well as" does not make the subject plural. The correct verb should match the singular subject "The book", making option B correct.

Answer: The book, as well as the pen, is on the table.

Que 17) A train travels at 60 km/hr for 2 hours, then at 80 km/hr for the next 3 hours. What is the average speed of the train for the entire journey?

Solution:

Total distance = (60 × 2) + (80 × 3) = 120 + 240 = 360 km
Total time = 2 + 3 = 5 hours
Average speed = Total Distance / Total Time

3605=72 km/hr\frac{360}{5} = 72 \text{ km/hr}5360​=72 km/hr

Answer: 72 km/hr

Why to Solve CAT Previous Year Papers?

• Solving the CAT Exam previous question paper is an important part of exam preparation. 
• It helps you build your knowledge and understanding of the key topics and develop an effective strategy for tackling the exam. 
• It also allows you to practice and familiarize yourself with the format and type of questions likely to appear in the actual CAT Exam. 
• Practicing CAT  question papers helps you to identify your strengths and weaknesses and also helps you to identify the areas that need more focused attention. 
• Finally, by solving previous years question papers of CAT, you will understand the time management required to complete the exam successfully. 

Read More | CAT Exam Preparation 2025

Conclusion

In conclusion, the CAT Previous Year Papers is an important tool for students to assess their knowledge and understanding of the topics covered in the CAT Exam syllabus. It allows students to practice their skills and prepare for the exam. It is also an effective way for students to evaluate their progress in their studies and analyze their strengths and weaknesses in each subject. Finally, it is important to remember that the CAT Exam Question Paper should be used as a guide to prepare for the actual CAT Exam.

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