CAT 2013 QA Slot 1 Question Paper(Available):Download Solution with Answer Key

If \( n = 10 \), find the value of \( g(g(a_2, a_8), g(a_1, a_7)) \).

• (A) \( a_9 \)
• (B) \( a_7 \)
• (C) \( a_2 \)
• (D) \( a_0 \)

If \( h(a_k, a_m) = a_m \) for all \( m \), where \( 1 \leq m < n \) and \( 0 \leq k < n \), and \( m \) is a natural number, find \( k \).

• (A) \( 0 \)
• (B) \( 1 \)
• (C) \( n - 1 \)
• (D) \( n - 2 \)

In a bag there are a total of 150 coins in three denominations – Re.1, Rs.2 and Rs.5 – with at least one coin of each denomination. The total value of Re.1 coins is at least 50% of the total value of the coins. There are 23 Rs.5 coins and the total value of Rs.2 coins is at least 3% of the total value of coins. Find the number of Rs.2 coins in the bag.

• (A) 2
• (B) 3
• (C) 4
• (D) 1

Let P, Q, S, R, T, U and V represent the seven distinct digits from 0 to 6, not necessarily in that order. If PQ and RS are both two-digit numbers adding up to the three-digit number TUV, find the value of V.

• (A) 3
• (B) 6
• (C) 5
• (D) Cannot be determined

There are five cards in a row with numbers from 1 to 100. Each adjacent pair must not differ by a multiple of 4. The remainder when each number is divided by 4 is written on a sixth card, in that order. How many different sequences can be written on the sixth card?

• (A) \( 2^3 \cdot 3 \)
• (B) \( 4 \cdot 3^4 \)
• (C) \( 4^2 \cdot 3^3 \)
• (D) \( 4 \cdot 3^3 \)

If each X-Ray occupies 30MB and a new technology reduces space by 60%, what is the total magnetic media memory required to store all the X-Rays in the year 2000? (1MB = \(10^6\) Bytes)

• (A) 10,170 TB
• (B) 6,780 TB
• (C) 1,703,170 TB
• (D) None of these

What percentage of the total information stored on paper media is taken up by Newspapers, Books, and Periodicals? Assume equal space per unit of information.

• (A) 37.5%
• (B) 45%
• (C) 57%
• (D) 54%

When compared to the total memory space occupied by the information stored in any single category of storage media, what is the highest percentage share of memory space occupied by the information stored in any single media within that category (approximately)?

• (A) 68.75%
• (B) 62.5%
• (C) 96%
• (D) 98.3%

If information increases 20% per year, and memory space increases 10% per year from 2000 onwards (where 80% of total memory is already used), and usage grows at 45% more than current rate, when will there be shortage of memory?

• (A) 2002
• (B) 2003
• (C) 2004
• (D) 2005

If the equations below hold true for triangles ABC and DEF: \[ a(a + b + c) = d^2,\quad b(a + b + c) = e^2,\quad c(a + b + c) = f^2 \]
Then which of the following is always true of triangle DEF?

• (A) It is an acute-angled triangle.
• (B) It is a right-angled triangle.
• (C) It is an obtuse-angled triangle.
• (D) None of the above.

Sujith says:
- Multiplying first two digits by 3 gives all ones.

- Multiplying next two digits by 6 gives all twos.

- Multiplying last two digits by 9 gives all threes.

What is the sum of digits in the number?

• (A) 30
• (B) 33
• (C) 60
• (D) 45

Two cars P and Q start from points A and B simultaneously. They meet 40 km from B. After meeting, they exchange speeds and return. They meet again 20 km from A. Find distance AB.

• (A) 130 km
• (B) 100 km
• (C) 120 km
• (D) 110 km

Consider the curves: \[ y = 2x^3 + 3x^2 + 4,\quad y = 3x^2 - 2x + 8 \]
How many times do they intersect for \( -3 \leq x \leq 2 \)?

• (A) The two curves intersect thrice.
• (B) The two curves intersect twice.
• (C) The two curves intersect once.
• (D) The two curves do not intersect.

An aquarium of size 100 cm × 80 cm × 60 cm is tilted along the 80 cm edge. Water spills until the water line reaches 1/3 of the base width. Find the height of water reduced when box is restored.

• (A) 50 cm
• (B) 40 cm
• (C) 20 cm
• (D) 10 cm

Some persons are standing in a circle, all facing the center. Each pair not adjacent sings a 3-minute song, one after another. Total time = 1 hour. How many persons are there?

• (A) 5
• (B) 7
• (C) 9
• (D) 8

In triangle PQR, \( PQ = 12 \) cm, \( PR = 9 \) cm, and \( \angle Q + \angle R = 120^\circ \). Find the length of QR.

• (A) \( \dfrac{15}{\sqrt{2}} \) cm
• (B) \( 3\sqrt{13} \) cm
• (C) \( 5\sqrt{5} \) cm
• (D) \( 5\sqrt{17} \) cm

If the angle bisector of \( \angle P \) meets \( QR \) at point \( M \), find the length of \( PM \).

• (A) \( \dfrac{28\sqrt{5}}{9} \) cm
• (B) \( \dfrac{42\sqrt{5}}{11} \) cm
• (C) \( \dfrac{36\sqrt{3}}{7} \) cm
• (D) \( 4\sqrt{3} \) cm

Which of the following matches was a draw?

• (A) India vs South Korea
• (B) Spain vs Netherlands
• (C) Netherlands vs South Korea
• (D) Spain vs South Korea

The total number of points won by India is:

• (A) 5
• (B) 6
• (C) 7
• (D) Cannot be determined

Total number of goals scored in Netherlands vs Pakistan match is:

• (A) 0
• (B) 1
• (C) 2
• (D) Cannot be determined

The number of goals scored by Australia against India is at most:

• (A) 5
• (B) 4
• (C) 3
• (D) 2

Three words “Madhu”, “Sweet”, and “House” blink as follows:
- Each word flashes at regular interval and stays ON for 1 second.

- "Madhu" every 3.5 s, "Sweet" every 5.25 s, "House" every 6.75 s.

All three flash together at 8:00 a.m. Find time until next flash where last two words ("Sweet" and "House") flash together.

• (A) 45 seconds
• (B) 22.5 seconds
• (C) 112 seconds
• (D) 6.75 seconds

If \( g(x) = p(x) = qx^n \), and \( p \) and \( q \) are constants, then at \( x = 0 \), \( g(x) \) will be:

• (A) Maximum when \( p > 0, q > 0 \)
• (B) Minimum when \( p > 0, q < 0 \)
• (C) Minimum when \( p > 0, q > 0 \)
• (D) Maximum when \( p > 0, q < 0 \)

TV company makes 2 models A and B.
- A takes 4 hrs to make, B takes 2 hrs

- Max 1000 hrs available

- Profit per unit: A → ₹1200, B → ₹800

- Want to maximize profit under constraints

• (A) 200 model As and 400 model Bs
• (B) 100 model As and 600 model Bs
• (C) 800 model Bs
• (D) None of the above

In a college election, 5 candidates contested and 100 students voted. If each student voted for 2 candidates, and each pair of candidates received the same number of votes, how many votes did each candidate get?

• (A) 40
• (B) 50
• (C) 60
• (D) 80

If \( x + \frac{1}{x} = 2 \), find the value of \( x^{10} + \frac{1}{x^{10}} \).

• (A) 1024
• (B) 2
• (C) 1
• (D) 0

What is the number of positive integers less than or equal to 1000 that are divisible by neither 2 nor 5?

• (A) 400
• (B) 300
• (C) 500
• (D) 600

A number when divided by 4, 5 and 6 leaves remainders 2, 3 and 4 respectively. What is the smallest such number?

• (A) 58
• (B) 62
• (C) 86
• (D) 74

What is the maximum possible number of intersection points of 15 lines in a plane, assuming no two lines are parallel and no three are concurrent?

• (A) 105
• (B) 210
• (C) 91
• (D) 120

There are 4 roads between towns A and B, and 3 roads between towns B and C. How many different ways can a person travel from A to C via B and return to A without using the same road more than once in each direction?

• (A) 144
• (B) 12
• (C) 72
• (D) 24

(A) But as access to other texts is enjoyed more widely, some of the dominance textbooks now enjoy will wane.
(B) As indeed will the power of teachers—whose prejudices may often be just as ingrained as those found in textbooks, and rather harder to pin down.
(C) It won’t be long before children, will be able to access, by way of smartphones, the textbooks prescribed for their courses.
(D) As long as textbooks in one form or another are used and as long as they are issued or approved by the state, they will remain a political issue.

A major difference between the points of view expressed by Freud and Jung as discussed in the passage is:

• (A) One considered ailments of the mind to be the result of conflict between the conscious and the unconscious, while the other considered them to be inherent in the unconscious.
• (B) One considered that ailments of the mind are grounded in the conscious, while the other considered them to be triggered by the unconscious.
• (C) One considered that the evil qualities of human beings resided in the unconscious mind, while the other considered that the unconscious mind repressed desired feelings.
• (D) One considered that ailments of the mind are grounded in the unconscious, while the other considered them to be triggered by the conscious.

Which of the following statements are logically consistent with the paragraph?
(I) Idle thoughts can sometimes illuminate the situation of the person as valuable messages from the unconscious.

(II) Emotionally dishonest clients are very poor communicators and suffer from psychological problems.

(III) Dissociative identity disorder is primarily due to denied emotions.

(IV) Dreams can help effect, in us, better understanding and development of the spirit.

(V) Honest communication and open interaction can positively influence a psychotherapeutic process.

• (A) I, III, IV
• (B) I, IV, V
• (C) I, II, IV
• (D) II, III, V

If a paragraph were to be inserted between the first and second paragraphs, it would most likely deal with which of the following?

• (A) Dreams can be instrumental in gauging a person's emotional state.
• (B) Emotions are, very often, the substance of a person's idle thoughts.
• (C) It is very difficult to gauge emotional honesty.
• (D) Dreams, often, are indicative of emotions that remain unexpressed.

In saying "It is tempting to wish petulantly that the unconscious would speak to us more clearly..." the author intends to suggest:

• (A) The inability to understand the unconscious can irritate psychotherapists when pursuing their objectives.
• (B) The inability to understand the unconscious can puzzle psychotherapists in pursuit of their objectives.
• (C) The inability to understand the unconscious can frustrate psychotherapists when pursuing their objectives.
• (D) The inability to understand the unconscious can divert psychotherapists from their objectives.

If W and U do not live on the same floor, then which of the following cannot be true?

• (A) V lives on the third floor
• (B) Q lives on the third floor
• (C) R lives on the second floor
• (D) P lives on the second floor

If S and R are living on the first and sixth floor respectively, which of the following must be true?

• (A) T is living on the same floor as X
• (B) R is living on the second floor
• (C) T is living on the third floor
• (D) W is living alone on his floor

If Q lives on the third floor, then how many combinations of persons could live on the second floor?

• (A) 8
• (B) 6
• (C) 5
• (D) 7

(a) Leonardo da Vinci was a self-taught man and began teaching himself Latin at the early age.
(b) He became a great engineer and was the first to discover that blood circulated through the body.
(c) He believed that coarse people of bad habits and shallow judgments did not deserve so beautiful an instrument and such a complex anatomical equipment than the human body.
(d) They should merely have a sack for taking in food and letting it out again, for they are nothing but the alimentary canal.
(e) Very fond of animals, he was himself a vegetarian and had the habit of buying caged birds from the market and setting them free immediately.

• (A) Only a and c
• (B) b and d
• (C) Only a
• (D) Only e

[(a)] Although thoughts are primary, thoughts in themselves have no method of transmission and are therefore dependent on speech.
[(b)] If we were to summarize the logo-centric approach to meaning, we should state that what emerges is that speech is the original signifier of meaning.
[(c)] Language, the cornerstone of humanity, emerges as a process to allow our thoughts to travel across space and between people.
[(d)] Language can then be viewed as a system of verbal signs that signify individual thought.
[(e)] Language produces speech to transmit thoughts and writing to transmit speech.

• (A) cabed
• (B) baced
• (C) beacd
• (D) caedb

MELT

• (A) The crowd melted away after the prayer meeting.
• (B) Even the sternest mother’s heart melts at the sight of her baby crying.
• (C) His anxiety melted away when he received an SMS from his daughter confirming that she had reached her destination safely.
• (D) The cries of opposition suddenly melted to cheers when the principal agreed to the demands of the students.

[(a)] Generally speaking, in pre-capitalist societies people produced things directly for other people, not for sale on a market – in Marx’s language, they produced for use, not exchange.
[(b)] However, producing things for sale (or exchange) creates a new dynamic, different from societies that produce directly for use.
[(c)] Capitalism is very different from past modes of production.
[(d)] Under capitalism, nearly all of the products of human labor are commodities, that is, they are produced for sale.
[(e)] Every system of production has to regulate how much of people’s labor is spent producing one thing versus another, so that the society does not end up using labor on things that are useless.
[(f)] Marx called this “generalized commodity production”—people obtain their needs not by producing what they need, but by purchasing them on a market, and people produce what other people need and want by selling things on a market.

If Lewis participated in two sports, which of the following is definitely false?

• (A) Mike did not participate in Skiing.
• (B) John participated in Paragliding.
• (C) Lewis participated in Skiing.
• (D) Mike participated in Paragliding.

If John participated in Paragliding, which of the following statements is definitely true?

• (A) Mike participated in Rock Climbing.
• (B) John participated in Bungee Jumping.
• (C) Lewis did not participate in Skiing.
• (D) Peter did not participate in Rock Climbing.

Which of the following is not a possible combination of number of sports taken up by John, Mike, and Lewis?

• (A) John – 1, Mike – 2, Lewis – 2
• (B) John – 1, Mike – 1, Lewis – 1
• (C) John – 1, Mike – 2, Lewis – 1
• (D) John – 2, Mike – 1, Lewis – 2

Eight men have their first names, as Ratan, Rama, Ramesh, Ramu, Rakesh, Rajan, Rishabh and Rohit and their surnames are Kulkarni, Arora, Jain, Dutta, Singh, Sharma, Sen and Murthy, not necessarily in the same order. These eight persons are sitting around a circular table as per the following instructions:
[(i)] Ramu is sitting opposite Kulkarni and to the left of Singh.
[(ii)] Rajan is sitting opposite Sharma and next to Murthy, who is sitting to the left of Rama.
[(iii)] Arora is sitting opposite Ratan and Rohit sits adjacent to Dutta.
[(iv)] Rama, who is next to Rishabh and Ramesh, sits opposite Sen.
If Rishabh Arora sits between Kulkarni and Sharma, and opposite Singh, then who sits opposite Rakesh Dutta?

• (A) Ramesh Murthy
• (B) Rama Murthy
• (C) Rajan Jain
• (D) Rishabha Arora

Which of the following most accurately represents the author's criticism of 'Homo economicus'?

• (A) It gives an inaccurate picture of consumer behaviour in real economic transactions.
• (B) The ideal person who makes choices in conservative economic models is, in fact, the opposite of 'homo economicus'.
• (C) It is nowhere close to the unpredictable consumer in real economic situations.
• (D) It is the economists' mythical Everyman.

The author of the passage mentions the observations of Hall, Zhao and Sharif in order to:

• (A) Demonstrate that people take pride in their achievements even in hard times.
• (B) Demonstrate how empathy can play a significant role in persuasion.
• (C) Provide support for the assertion that dignity is a powerful factor in decision-making.
• (D) Illustrate that authorities would be able to implement policies more effectively if they understand their citizens.

The view mentioned in the last paragraph (“Taking the path… real life”) refers to which of the following?

• (A) People are loath to make any choice when faced with a plethora of options.
• (B) Consumers prefer to seek expert guidance when making a choice.
• (C) Employers coax workers to accept pension plans with fixed contribution rates.
• (D) The view that more choice is good for consumers should be regarded with skepticism.

The scientist and the artist are both concerned to change the world — the one the external world of man's objective relations with nature, the other the internal world of his subjective relations with his fellow men. The scientist discovers a contradiction in his consciousness of the external world and resolves it in a scientific hypothesis; the artist discovers a contradiction in his consciousness of the internal world and resolves it in a work of art. Both are creative acts. The scientist extends our knowledge and hence also our control of nature —

• (A) The artist takes complex explanations and renders them simple.
• (B) In doing so, he proves that there is nothing we cannot do - everything is brought within our command.
• (C) The artist heightens our sense of ourselves as social beings and so advances the class struggle.
• (D) The artist teaches us to think for ourselves.

In the passage the author is primarily concerned with?

• (A) Critically examining Proust’s “In Search of Lost Time.”
• (B) Providing a synopsis of Proust’s reading tastes.
• (C) Evaluating Proust’s position in the great literary tradition.
• (D) Discussing the intellectual influence Proust’s contemporaries had on his works.

The author quotes an example of Proust’s maxims to highlight his (Proust’s):

• (A) Grasp of the metaphysical.
• (B) Penchant for the philosophical.
• (C) Belief in a Supreme Being.
• (D) Exceptional choice of thought and word.

The passage implies that Proust subscribes to which of the following views?
(a) Reading a good book is like having a conversation with a classical writer.
(b) Reading is a virtuous pastime and it leaves an indelible impression on one’s mind.
(c) Literature imitates life.
(d) A reader can invest in the feelings for characters in a book.
(e) Dostoyevsky’s “The Idiot” was appreciated by him for the unanticipated turns in the plot.
(f) Dostoyevsky’s “The Idiot” was known for its aesthetics, its gripping pace and its unlikely element of surprise.

• (A) a, c, d
• (B) a, b, c, e
• (C) a, b, c, e, f
• (D) a, b, c, d, e

If \( g = 9 \), then what is the minimum possible number of times for which the weighing machine is to be used?

• (A) 1
• (B) 2
• (C) 3
• (D) 4

If \( g = 7 \), what is the minimum possible number of times for which the weighing machine is to be used?

• (A) 1
• (B) 2
• (C) 3
• (D) 4

If \( g = 3 \), what is the minimum possible number of times for which the weighing machine is to be used?

• (A) 2
• (B) 3
• (C) 4
• (D) 5

If \( g = 2 \), what is the minimum possible number of times for which the weighing machine is to be used?

• (A) 2
• (B) 3
• (C) 5
• (D) 4

(A) The trade in iron ore makes it the second-largest commodity market by value after crude oil.
(B) The metal provides the backbone of skyscrapers, bridges and motorways, and the carapace and internal organs of cars, fridges and washing machines.
(C) Given steel’s ubiquity — it makes up 95% of global metal production — iron ore, the raw material from which it is made, attracts strangely little attention.
(D) The development of a process to turn raw earth into steel merits a high spot on a list of mankind’s most ingenious achievements.