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CAT 1998 Question Paper with Solutions

68 questions in 120 minutes, in three timed sections. Below: how the paper is built, the topics each section tested, and a solved sample from every section. Take the whole paper in the simulator to get your Score Waterfall, Topic ROI Map and Strategic IQ.

Paper structure and topics

VARC

Verbal Ability & Reading Comprehension

24 questions · 24 MCQ · 0 TITA

  • Reading Comprehension · 16
  • Verbal Ability · 8

DILR

Data Interpretation & Logical Reasoning

22 questions · 22 MCQ · 0 TITA

  • Data Interpretation · 12
  • Logical Reasoning · 10

QA

Quantitative Ability

22 questions · 22 MCQ · 0 TITA

  • Arithmetic · 9
  • Algebra · 5
  • Number System · 5
  • Geometry · 3

Sample questions with solutions

12 of the 68 questions: the first passage, the first DILR set and the first QA questions of the paper.

VARC · Verbal Ability & Reading Comprehension

Passage

The narrator of Midnight's Children describes it as a kind of collective fantasy. I suppose what he, or I, through him was trying to say, was that there never had been a political entity called India until 1947. The thing that became independent had never previously existed, except that there had been an area, a zone called India. So it struck me that what was coming into being, this idea of a nation-state, was an invention. It was an invention of the nationalist movement. And a very successful invention.

One could argue that nation-states are a kind of collective fantasies. Very similar things happened with the unification of Italy, and also with the unification of Germany. The history of India is a history of independent nation-states. It is a history of Oudh or Bengal or Maratha kingdoms. All those independent histories agreed to collectivise themselves into the idea of the nation of India. In the case of Pakistan, it was less successful. Pakistan was under-imagined. It did not survive as a nation-state.

If you ask people in general, they would have absolutely no problem with the idea of India at all. I think, in a way the strength of the nationalist idea is shown by its ability to survive the extraordinary stresses that it was placed under. I think the stresses of things — communalism, the high degree of public corruption, of regional rivalries, of the tension between the centre and the state, the external pressures of bad relations with Pakistan — these are colossal pressures which any state could be forgiven for being damaged by. I think the thing to say about the success of the idea is that it remains an idea though people might not find it very easy to give a simple definition of it. But that it does exist and that it is something to which people feel they belong, I think is now the case. That it survives these stresses is an indication of its strength.

I'm not interested in an idealised, romantic vision of India, I know it is the great pitfall of the exile. So you know for me, always, the issue of writing about India has been not to write as an outsider. On the other hand, evidently something has changed in the last 10 years, which is that as a result of various circumstances, I've not been able to return. All I can say is that I have felt it as the most profound loss and I still do. There have been many losses in the last decade but the loss of the easy return to India has been for me an absolute anguish, an inescapable anguish. I feel as if I've lost a limb. I am very anxious to bring that period to an end.

I do not think that one of the most interesting phenomena for India as a country is the phenomenon of the Indian Diaspora. I often think Indian — Indian Indians — find that very hard to understand. In England, when people call themselves British Indian, they mean both halves of that. And yet, what it means to be a British Indian is very alien to an Indian Indian. The same is true in the Caribbean, in Africa, in Canada, in the United States, and so on. The thing that has interested me is that there are now many, many ways of being something which you can legitimately call Indian. Being an Indian in India is just one of those ways.

The forces of disintegration are always there. I think in every society there is the tension between the forces that bring it together and the forces that pull it apart. I'm worried, above all, of the communal issue because half a century is no time at all in the eye of history, and half a century ago something of colossally horrible proportion took place. The fact that it hasn't happened for 50 years on quite the same scale means nothing. It could still happen tomorrow. One of the things that I remember very vividly, being there 10 years ago at about the time of the killings that took place in Assam, is discussing this with good friends and fellow writers. And I remember somebody said to me, until we understand that we are capable of these things, we can't begin to move beyond them. Because it's a very easy response to atrocities, to say: oh those terrible people did that, and we are not like that. I think the difficult response is to accept we are also capable of that, the thing that happened there could also, in certain circumstances, be something that we were able to perpetrate. The civilising influence is what prevents most of us from giving vent to those terrible urges. Those urges are part of humanity as well as the more civilized urges.

Of course, I fear in India the recurrence of communal or regionalist inter-community violence. I fear the long-term damage to a democracy that can be done by mass corruption. I think corruption is in a way a subversion of democracy and the commonplace view in India is that corruption is everywhere. In a sense, you could say that is not a democratic society. If money, favour and privilege is what makes the place work, then that's not a democracy. At least it runs the danger of being no longer able to call itself a democracy.

What was happening, I thought, was that people were trying to seize control of that rhetoric. That is to say, special interest groups. You could say Hindus are a very large special interest group. If any group inside such a complex and many faceted country tries to define the nation exclusively in its own terms, then it begins to create terrible stresses. I do think that the kind of attempt to define India in Hindu terms is worrying for that reason. It creates backlashes, it creates polarisation, and it creates the risk of more upheaval. Partly, I am saying this as a kind of objective observer, but nobody is an objective observer. I come from an Indian minority, I no doubt have a minority perspective. I can't ignore that and nor would I wish to. Partly, also I am speaking temperamentally. That is to say, the kind of religious language in politics is something I find temperamentally unpleasant. I don't like people who do that, whether they be sectarians in Northern Ireland or India. I believe in, if possible, separating one's personal spiritual needs and aspirations from the way in which a country is run. I think in those countries where that separation has not taken place, one can see all kinds of distortions of social and ordinary life which are unpleasant. Iran is an obvious example. The country in which that kind of separation has completely fragmented it.

Where Naipaul is right, although I don't share his conclusions about it, but I think where he is right, is in saying that this is a great historical moment. One reason why the 50th anniversary is interesting is that it does seem to represent the end of the first age and the beginning of second age. And to that extent that is true now, if someone was born today, they would be born into a very different set of cultural assumptions and hopes than somebody born 50 years ago. We were entirely sold on the Nehru-Gandhi kind of plan. We grew up and that was the portrait of the nation we had hung on our wall, and to the extent that you never entirely lose those formative ideas, that's still the picture of the country I've got on my wall. But it's clear that for somebody being born now, they are being born into a very different country.

I also think of taking the Naipaul point on what would happen if the BJP were to form a government. Well, what I would like to think is that in order for the BJP or anybody of that persuasion to form a government, they would have to change. There is even some kind of suggestion that it may even be happening a little bit because they are intelligent people. They understand their weaknesses as well as their strengths. Clearly, for a Hinduist party to form the government of the country is not at all unlikely. So I think one does have to engage with that in the same way as many people in the country who, like myself, were not remotely in tune with the Thatcherite revolution but have to engage with it because it was in fact happening, and kept winning elections, and the world was not going to go back. So, of course, both people inside the Hindu political enterprise and people outside it will have to shift. I am optimistic about India's ability to force those changes that are necessary because I do believe it is not fundamentally an intolerant country and will not fundamentally accept intolerant politics.

On the other hand, there has to be reckoning with the fact that these are ideas, which are gaining in popularity. I'll tell you where I would draw the line myself. I think there was a great historical mistake made in Europe about the Nazi Party. People attempted to see whether they could live with it and discovered very rapidly that was a mistake, that appeasement was a great historical mistake. So, it seems to me, the question is: What do we make of this political enterprise? Is it fundamentally democratic or fundamentally anti-democratic? If democratic, then we must all learn to make the best of it. If anti-democratic, then we must fight it very hard.

What happened in India happened before the book (Satanic Verses) had actually entered. It happened because of an article in India Today, which, I must say, I thought was an irresponsibly written article, because it was written by somebody, who, as a friend, asked me for an early copy of the book, and then presented that book in the most inflammatory sort of way. This was one of the things that disappointed me, that after a lifetime of having written from a certain sensibility, and a certain point of view, I would have expected people in India to know about it since it was all entirely about India. It was written from a deep sense of connection and affection for India. I would have expected that I had some money in the bank. That is to say, if Salman Rushdie wrote any book, then we know who he is. He is not some idiot who just arrived from nowhere shouting abuse. This is somebody whose work, whose opinions, whose lectures and whose stories we know. I would have hoped that my work would have been judged in the context of what people already knew about me. Instead, it seemed as if everything I had been in my life up to that point suddenly vanished out of the window and this other Rushdie was invented who was this complete bastard who had done this terrible thing. There did not seem to be any attempt to correct that or to combat that. I was surprised and disappointed it did not. It didn't happen here either. It didn't happen anywhere in the world. It was as if the force of history, the force of a historical event was so huge that it erases all that goes before it.

The negative response to the Satanic Verses, let us remember that there was also a positive response, was such that it erased my personality and put in its place some other guy who they didn't recognize at all. Anybody who knows anything about these countries, and I do know something about these countries, knows that every cheap politician can put a demonstration in the street in five minutes. That doesn't represent in any sense the people's will. It represents a certain kind of political structure, political organization. It doesn't represent truth.

But I always believed and I still believe that India would come back. I never believe that the loss of India is forever. Because India is not Iran, it’s not even Pakistan, and I thought good sense will prevail in India because that's my life experience of Indian people and of the place.

Question 1 · MCQ

The idea of India that inspired the writer's generation was the one dominated or formed by
  1. A.
    the Nehru-Gandhi politics.
  2. B.
    the Nehru-Gandhi ideology.
    ✓ Correct
  3. C.
    the Nehru-Gandhi idea regarding India's formative years.
  4. D.
    the Nehruvian idea of socialism.
Solution
The writer states: "We were entirely sold on the Nehru-Gandhi kind of plan. We grew up and that was the portrait of the nation we had hung on our wall." This refers to the ideology or vision of the Nehru-Gandhi era, not merely politics or a specific idea about formative years.

Question 2 · MCQ

The writer does not share
  1. A.
    Naipaul's stand that the 50th anniversary is a historical moment.
  2. B.
    Naipaul's stand that the 50th anniversary is not a historical moment.
  3. C.
    Naipaul's conclusion on the 50th anniversary being a historical moment.
    ✓ Correct
  4. D.
    Naipaul's conclusion on the 50th anniversary not being a historical moment.
Solution
The writer says: "Where Naipaul is right, although I don't share his conclusions about it, but I think where he is right, is in saying that this is a great historical moment." Thus he agrees that it is a historical moment, but disagrees with Naipaul's conclusions about that moment.

Question 3 · MCQ

The writer shows faith in India's basic
  1. A.
    stability.
  2. B.
    resilience.
    ✓ Correct
  3. C.
    fortitude.
  4. D.
    democracy.
Solution
The writer expresses optimism that India will withstand stresses and remain fundamentally tolerant: "I do believe it is not fundamentally an intolerant country and will not fundamentally accept intolerant politics." This reflects faith in India's resilience.

Question 4 · MCQ

According to the writer,
  1. A.
    politicians incite the general public to demonstrate against writers.
  2. B.
    a politician's demonstration does not reflect the people's will.
  3. C.
    Both (a) and (b)
    ✓ Correct
  4. D.
    Neither (a) nor (b)
Solution
The writer notes: "every cheap politician can put a demonstration in the street in five minutes. That doesn't represent in any sense the people's will." In the context of the negative response to his book, this implies politicians incite demonstrations against writers, and such demonstrations do not reflect genuine public will.

DILR · Data Interpretation & Logical Reasoning

Set

Answer the questions based on the following information.
A, B, C and D are to be seated in a row. But C and D cannot be together. Also B cannot be at the third place.

Question 1 · MCQ

Which of the following must be false?
  1. A.
    A is at the first place
    ✓ Correct
  2. B.
    A is at the second place
  3. C.
    A is at the third place
  4. D.
    A is at the fourth place
Solution
Enumerate all seating orders satisfying the constraints (C & D not adjacent; B ≠ 3).
Pos1Pos2Pos3Pos4
BCAD
BDAC
CBAD
CBDA
DBAC
DBCA
CADB
DACB
A appears in positions 2, 3, and 4, but never in position 1. Hence "A is at the first place" must be false.

Question 2 · MCQ

If A is not at the third place, then which of the following options does C have?
  1. A.
    The first place only
  2. B.
    The third place only
  3. C.
    The first and third place only
    ✓ Correct
  4. D.
    Any of the places
Solution
Given A ≠ 3, we only use the valid arrangements where A is not in position 3: C B D A, D B C A, C A D B, D A C B.

In these, C is at position 1 (C B D A, C A D B) or position 3 (D B C A, D A C B).
C never occupies position 2 or 4. Thus C can only be at the first or third place.

Question 3 · MCQ

If A and B are together, then which of the following must be necessarily true?
  1. A.
    C is not at the first place
  2. B.
    A is at the third place
    ✓ Correct
  3. C.
    D is at the first place
  4. D.
    C is at the first place
Solution
When A and B are together, only two arrangements satisfy all constraints: C B A D and D B A C.

In both, A is at position 3. Hence it must be true that A is at the third place.

QA · Quantitative Ability

Question 1 · MCQ

A company has a job to prepare certain number cans and there are three machines A, B and C for this job. A can complete the job in 3 days, B can complete the job in 4 days, and C can complete the job in 6 days. How many days will the company take to complete the job if all the machines are used simultaneously?
  1. A.
    4 days
  2. B.
    \(\frac{4}{3}\) days
    ✓ Correct
  3. C.
    3 days
  4. D.
    12 days
Solution
Work done by A in 1 day = \( \frac{1}{3} \)
Work done by B in 1 day = \( \frac{1}{4} \)
Work done by C in 1 day = \( \frac{1}{6} \)
Total work per day = \( \frac{1}{3} + \frac{1}{4} + \frac{1}{6} = \frac{4+3+2}{12} = \frac{9}{12} = \frac{3}{4} \)
Hence, time taken = \( \frac{1}{\frac{3}{4}} = \frac{4}{3} \) days.

Question 2 · MCQ

\(n^3\) is odd. Which of the following statement(s) is(are) true?
I. \(n\) is odd.
II. \(n^2\) is odd.
III. \(n^2\) is even.
  1. A.
    I only
  2. B.
    II only
  3. C.
    I and II
    ✓ Correct
  4. D.
    I and III
Solution
\( n^3 \) is odd ⇒ \( n \) must be odd (if \( n \) were even, \( n^3 \) would be even).
So I is true.
\( n \) odd ⇒ \( n^2 = n \times n \) is odd.
So II is true, III is false.
Hence, I and II are true.

Question 3 · MCQ

One bacterium splits into eight bacteria of the next generation. But due to environmental condition only 50% survives and remaining 50% dies after producing next generation. If the seventh generation number is 4,096 million, what is the number in first generation?
  1. A.
    1 million
    ✓ Correct
  2. B.
    2 million
  3. C.
    4 million
  4. D.
    8 million
Solution
Each bacterium produces 8 bacteria, but only 50% survive, so effective growth factor \(= 8 \times 0.5 = 4\).
Thus \(N_n = N_1 \times 4^{\,n-1}\).
Given \(N_7 = 4096\) million, and \(4^6 = 4096\), we have \(N_1 = 1\) million.

Question 4 · MCQ

Three circles, each of radius 20, have centres at P, Q and R. Further, AB = 5, CD = 10 and EF = 12. What is the perimeter of \(\Delta PQR\)?
Question 4, figure 1
  1. A.
    120
  2. B.
    66
  3. C.
    93
    ✓ Correct
  4. D.
    87
Solution
For two circles of radius 20 with centres distance \(d\) apart (\(d < 40\)), the segment of the centre line that lies inside both circles has length \(40 - d\).
Here, AB, CD, EF are these intersection segments on sides PR, QR, PQ respectively.
\(AB = 5 \Rightarrow PR = 40 - 5 = 35\)
\(CD = 10 \Rightarrow QR = 40 - 10 = 30\)
\(EF = 12 \Rightarrow PQ = 40 - 12 = 28\)
Perimeter \(= 35 + 30 + 28 = 93\).

Question 5 · MCQ

\(\frac{(2 \# 1)}{(1 \nabla 2)} =\)
  1. A.
    \(\frac{1}{8}\)
  2. B.
    1
  3. C.
    \(\frac{3}{8}\)
    ✓ Correct
  4. D.
    3
Solution
\(2 \# 1 = 2+1 = 3\) (both positive).
\(1 \nabla 2 = (1\times2)^{1+2} = 2^3 = 8\).
Thus \(\frac{2\#1}{1\nabla2} = \frac{3}{8}\).

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