CAT Mock Test 8

6. If 12P + 3R + 4Q = 16, where P, Q and R are positive real numbers, then what is the maximum possible value of P³R³Q²?

7. The route taken by a bus from Delhi to Jaipur has ‘n’ stops, including the source and the destination. When ‘m’ new stops are added on the route of the bus (where m > 1) the number of different tickets that can be issued between two stops on the route increases by 11. What is the value of ‘n’?

8. Yamini and Zora are standing 25 km apart. Zora starts moving towards Yamini. After 40 minutes Yamini also starts moving towards Zora. By the time Yamini covers 5 km, Zora has covered 15 km. They meet at a point 7 km from the starting point of Yamini. What is the speed of Yamini?

9. A cube of edge 12 cm is cut into 64 equal cubes. All the cubes are now arranged on a table such that one face of each cube touches the table. The resulting figure is a solid cuboid whose length and breadth are in the ratio 4 : 1 respectively. What is the total surface area of the table occupied by the
cuboid?

10. If log₁₆5 = m and log₅3 = n, then what is the value of log₃6 in terms of ‘m’ and ‘n’?

Directions for questions 11 to 13: Answer the questions on the basis of the information given below.

The table given below shows the various costs (in Rs. lakhs) incurred on the production of one ton of five different crops and the Selling Price (in Rs. lakhs) per ton of each crop. 

Note: Profit = Selling Price – Total Cost

11. For which crop is the profit percentage per ton the highest?

12. For how many of the given crops is the Irrigation cost more than 20% of the total cost?

13. If 1 kg of raw material of Cotton costs Rs. 54 and 200 grams of raw material is sown in 10 m² of land, then what is the area of land required for producing 1 ton of Cotton?

14. What are the last two digits of 9483⁶⁷⁴⁸³ ?

15. In the figure given below ABCD is a rectangle. The ratio of the length of EB to the length of BF is 2 : √3. What is the ratio of the length of BF to the length of FC?

16. Two sets A and B are given below.

A = {2⁰, 2¹, 2², 2³, 2⁴}

B = {3⁰, 3¹, 3², 3³, 3⁴}

How many different proper fractions can be made by picking the numerator from one of the sets and the denominator from the other set?

17. Two six-faced unbiased dice are thrown simultaneously. What is the probability that the sum of the numbers that appear on the two dice is a prime number?

18. The question given below is followed by two statements, A and B. Mark the answer using the following instructions:

Mark (a) if the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

Mark (b) if the question can be answered by using either statement alone.

Mark (c) if the question cannot be answered even by using both the statements together.

Mark (d) if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.

Q. If p and q are natural numbers, then what is the remainder when (p + q) is divided by 7?

A. 6q – p = 5

B. 8q + p = 45

19. Two operations, for real numbers x and y, are defined as given below.

(i) x




 y = (x + y)²

(ii) x Δ y = (x − y)²

If x²  
y² = 169 and x² Δ y² = 25, then what is the value of x²y²?​

20. Two lines P and Q intersect at point (3, 2) in the x-y plane. The slope of line P is 45° and line Q is parallel to the x-axis. What is the area (in sq. units) of the triangle formed by P, Q and a line perpendicular to P and passing through point (5, 4) ?

21. There are four lines in a plane and exactly two of them are parallel. If P is the number of points of intersection of these lines, then how many different values of P are possible?

22. Which of the following number(s) is/are not prime?

(i) 2⁵⁰⁰¹ + 1    (ii) 2⁵⁰⁰² + 1      (iii) 2⁵⁰⁰³ + 1

23. Pawan and Qureshi working together can do a piece of work in 10 days whereas Qureshi and Rohit working together can do the same work in 12 days. All three work together to do a job for which they are paid Rs. 300. If Qureshi’s share is Rs. 140, then what is Pawan’s share?

24. How many positive integer pairs (x, y) satisfy √x + √y = 2003 ?

Directions for questions 25 and 26: Answer the questions on the basis of the information given below.

Travelabad is famous for its vast railway network. It has three types of trains – Super Fast, Express and Passenger – and each type of train has two classes of travel – Sleeper and Air Conditioned. The train fare in Travelabad has two components – fixed fare and variable fare. The fixed fare is based on the class of travel – Rs. 60 for Sleeper and Rs. 100 for Air Conditioned. The variable fare depends on the distance of the journey, the type of train and the class of travel. The table given below shows the variable fare (in Rs.) for different distance ranges from the source station to the destination station.

AC = Air Conditioned Class
SL = Sleeper Class

25. Ghumakkad Das travels only in the Sleeper class of Super Fast trains. He travelled from Delni to Bhokal and then took another train from Bhokal to Mumtai. Next day he returned to Delni directly from Mumtai. The total train fare while going to Mumtai from Delni via Bhokal exceeded the train fare while coming back to Delni from Mumtai by Rs.125. If Bhokal lies on the only rail route connecting Delni and Mumtai, in which range does Delni-Mumtai rail distance fall?

26. One day Yatri Kumar travelled in the Sleeper Class of a train. Next day he travelled in the Air Conditioned Class of the same type of train for a different journey. If the train fare on the two days was exactly the same, in which type of train did he travel?

27. From a vessel containing 160 litres of milk, ‘x’ litres is drained out and replaced with water. Then ‘x’ litres of milk-water solution is drained out and replaced with water. If the quantity of milk left in the vessel is 90 litres, then what is the value of ‘x’?

28. In the figure given below ABCD is a square of side 4 cm. P is the midpoint of AD and is joined with vertex B. A perpendicular is drawn from vertex C on BP, which intersects BP at point E. What is the area of ΔBEC?

29. The sum of thirty-two consecutive natural numbers is a perfect square. What is the least possible sum of the smallest and the largest of the thirty-two numbers?

30. The question given below is followed by two statements, A and B. Mark the answer using the following instructions:

Mark (a) if the question can be answered by using either statement alone.

Mark (b) if the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

Mark (c) if the question cannot be answered even by using both the statements together.

Mark (d) if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.

Q. What is the sum of a, b and c?

A. The numbers a, b and c are in Arithmetic Progression.

B. a2 + b2 + c2 = 83, where a, b and c are natural numbers.

Directions for questions 31 to 34: The passage given below is followed by a set of four questions. Choose the most appropriate answer to each question.

Three judgments by the Supreme Court in the month of July mark a sharp departure from pedantic legalism and point to the possibilities of a transformative constitutionalism that sustains and elaborates the idea of constitutional morality developed in the Naz Foundation judgment of the Delhi High Court in 2009. The three cases are also very different pieces that speak to different realities in similar fashion: Ram Jethmalani v Union of India (SIT); Nandini Sundar and Others v State of Chhattisgarh (SJ); and Delhi Jal Board v National Campaign for Dignity and Rights of Sewerage and Allied Workers (DJB). It might be argued, and rightly too, that radical jurisprudence by the Supreme Court is not a recent phenomenon — it has an older
history rooted in struggles for civil and political rights. While that is the genealogy of this jurisprudence, we need yet to celebrate each signpost in the development of deliberative jurisprudence that responds not merely to the manifestations of a case, narrowly construed, but sees the larger socio-political context as an inextricable part of the bare facts, so to speak.

The guarantee of public goods — security, infrastructure for governance, law making and enforcement, provision of material and cultural goods especially for classes that lack the power, privilege and status to secure these for themselves — is state obligation. Neither markets (which cater to self-centered activities of individuals and groups) nor purely private social action can be expected to stand in for the state and provide public goods. Central to the delineation of the problem in these cases is the opening out of the idea of constitutionalism to include a broader idea of justice that enables the mapping of injustice in all its complexity. Tracing the link between the existence of perennial channels for unaccounted monies abroad and the erosion of developmental goals of the state, the Supreme Court contextualizes the need to reign in cash flows and ensure total accountability with reference to the structure of a neo-liberal economy. Gunnar Myrdal’s caution about the dangers of a “soft state” that spawns the “unholy nexus between the law maker, the law keeper, and the law breaker” is immediately relevant.

“Carried away by the ideology of neo-liberalism, it is entirely possible that the agents of the State entrusted with the task of supervising the economic and social activities may err more on the side of extreme caution, whereby signals of wrongdoing may be ignored even when they are strong. Instances of the powers that be ignoring publicly visible stock market scams, or turning a blind eye to large-scale illegal mining have become all too familiar, and may be readily cited.”

The framework of justice by this token stretches illimitably beyond the narrow confines of constitutional law and decided cases to the letter and spirit of the constitution.

“Modern constitutionalism posits that no wielder of power should be allowed to claim the right to perpetrate state’s violence against anyone, much less its own citizens, unchecked by law, and notions of innatehuman dignity of every individual.”

31. Which of the following options correctly sums up the areas that the author seeks to cover through the passage?

32. “Central to the delineation of the problem in these cases is the opening out of the idea of constitutionalism to include a broader idea of justice that enables the mapping of injustice in all its complexity.” Which of the following statements would correctly paraphrase the above line?

33. How does the author develop the central idea?

34. It can be inferred that the tone of the author in the third paragraph is

35. The question given below is followed by two statements, A and B. Mark the answer using the following instructions :

Mark (a) if the question can be answered by using Statement A alone, but cannot be answered by using Statement B alone.
Mark (b) if the question can be answered by using Statement B alone, but cannot be answered by using Statement A alone.
Mark (c) if the question can be answered by using either statement alone.
Mark (d) if the question cannot be answered by any of the two statements.

Q. Four friends – Ajay, Bikas, Chetan and Deepak – have different surnames among Rathore, Agarwal, Yadav and Sharma, not necessarily in the same order. They are standing in a queue one after the other. Either Rathore or Agarwal is standing immediately in front of Ajay and the other is standing immediately behind Ajay. Bikas and Chetan are standing at the two ends of the queue.

What is the surname of Ajay?
A. The surname of Chetan is Agarwal.
B. The surname of Bikas is Yadav.

36. There are two gaps in the sentence given below. From the pairs of words given, choose the one that fills the gaps most appropriately.

To call their fervor a …………….. of the media was a/an ……………… of an out-of-touch intellectual elite, and an insult to basic human integrity and intelligence.

37. There are two gaps in the sentence given below. From the pairs of words given, choose the one that fills the gaps most appropriately.

What distinguishes the book from many other collective volumes with similar ………….. coverage is its unifying theme of regional disparities, and a common methodological ………...

Directions for questions 38 and 39: Answer the questions on the basis of the information given below.

Four teams – Alveston, Blackpool, Chelsea and Dunstable – reached the semifinal stage in a football tournament. Two of the four teams played against each other in the first semifinal and the rest two played against each other in the second semifinal. The winners of these two matches played the final and the winner of the final match was declared the Champion of the tournament. The following observations were made during the semifinals and the final match:

(i) Ten goals were scored in the three matches. At least one goal was scored by each of the four teams. Each team scored a distinct number of goals.
(ii) The team that scored the maximum number of goals in the three matches was not the Champion of the tournament.
(iii) Alveston did not play against Blackpool but Chelsea played against Dunstable.
(iv) Neither Blackpool nor Dunstable was the Champion of the tournament. The absolute difference between the total goals scored by these two teams in the three matches was 2.

38. How many goals were scored in the final match of the tournament?

39. How many goals did the Champion of the tournament score in its semifinal match?

Directions for questions 40 and 41: The passage given below is followed by a set of two questions. Choose the most appropriate answer to each question.

Meditation is the natural process of withdrawing attention from environmental, physical, and mental processes and consciously directing it inward to a chosen focus of attention. But not many people know how to practice meditation for personal benefit and spiritual growth.

The beneficial side-effects of regular meditation practice include stress reduction, strengthening of the body’s immune system, more orderly thinking, improvement in power of concentration, and a slowing of the biological ageing process. For these reasons, meditation practice is recommended by an increasing number of doctors as a harmless way for patient-clients to be more responsible for their own total wellbeing. The primary purpose of meditation practice, however, is to bring forth clear states of awareness that will make authentic spiritual growth easier to experience.

Cultivation of inner contentment prevents us from getting swept away by circumstances. Engaging in selfexamination and self-discipline is important in order to clear away any of the psychological conflicts that might pose a problem. Study of ‘lower’ or secular knowledge helps us function effectively in the world. Many get educated so that they can live more effectively. But also important is the acquisition of higher knowledge or metaphysics to inquire about God, cosmic mind, manifestation of universes, our relationship with God — why are we here, and for what purpose?

When engaged in daily activities and relationships, endeavour to maintain a state of mental calmness and Self-awareness. Cultivate cheerfulness and optimism. Maintain your emotional balance. Adhere to wholesome routines of activity and rest. Maintain a healthy lifestyle: choose a nutritious diet and exercise regularly. Let all of your thoughts, feelings, and actions be wholesome and constructive. You will then be empowered to live enjoyably, effectively, and successfully.

40. Which of the following sums up the central idea of the passage most effectively?

41. According to the passage, what is the most important purpose of meditation?

42. Given below are five sentences. Each sentence has a pair of words that are italicized. From the italicized words, select the most appropriate words (A or B) to form correct sentences. The sentences are followed by options that indicate the words, which may be selected to correctly complete the set of sentences. From the options given, choose the most appropriate one.

A man came floundering (A) / foundering (B) through the snow towards us.
For some persevere (A) / perverse (B) reason he is refusing to see a doctor.

His mordent (A) / mordant (B) wit appealed to students.
She set off at a cantor (A) / canter (B).
The fire chard (A) / charred (B) the paper.

43. Given below are five sentences. Each sentence has a pair of words that are italicized. From the italicized words, select the most appropriate words (A or B) to form correct sentences. The sentences are followed by options that indicate the words, which may be selected to correctly complete the set of sentences. From the options given, choose the most appropriate one.

The white marble sculpture of the saint in the throes of divine ecstasy is strikingly offset by a gilt aureole (A) / oriole (B).

Conflicts among the various groups do not auger (A) / augur (B) well for the future of the peace talks. Sometimes shipbuilders sheath (A) / sheathe (B) a ship’s bottom with copper for extra protection from barnacles and other threats.

She was so tired, her eyelids were beginning to drupe (A) / droop (B).
She developed complications (A) / complexities (B) after the surgery.

Directions for questions 44 to 46 : Answer the questions on the basis of the information given below.

The figure given below shows the plan of a housing complex, which has eight houses – P1, P2, P3, P4, P5, P6, P7 and P8. Each house is owned by a different person among Aadi, Bina, Cara, Diya, Ema, Fiza, Gauri and Hari, not necessarily in the same order. The houses are of two types – Bungalows and Quarters. All the Bungalows are identical; similarly, all the Quarters are also identical. P3, P6 and P8 are the Bungalows and each of them is owned by a different officer. Each Quarter is owned by a different servant. Two persons are called neighbours if their houses share a common wall. E.g. the one who lives in P1 is a neighbour of those who live in P2 and P6.

It is also known that:
(i) The number of neighbours of Aadi is equal to the number of neighbours of Cara.
(ii) Diya is a neighbour of both Aadi and Fiza.
(iii) Ema is an officer and is a neighbour of Gauri who does not live in P7.
(iv) Bina and Hari are not neighbours.
(v) Fiza lives in P8 and Aadi is not her neighbour.

44. Who lives in P7?

45. How many neighbours does Aadi have?

46. Who among the following is definitely not a neighbour of Diya?

47. The paragraph given below is followed by a question. Choose the most appropriate answer to the question.

People repeatedly complain that they see advertisements everywhere, but advertisers should not be blamed for this. No one is forced to advertize his property - for many companies it is an important part of their income. Football teams would have much less money if they were not sponsored. And
no one is forced to look at advertising - you can turn the TV off between shows, or just flick past adverts in newspapers. If you don’t want to see the adverts, then just ignore them.

Which of the following statements would weaken the above argument?

48. The paragraph given below is followed by a question. Choose the most appropriate answer to the question.

Anorexia Nervosa is an eating disorder defined as severe, self- inflicted starvation and loss in body weight to at least 15% below that expected for the individual’s sex and height. Anorexia is typically associated with women and body image and is classified as a mental illness. Mortality varies between 5% and 18%. Patients who are dangerously thin are sometimes force-fed through a nasogastric (through the nose) tube. This force-feeding is undignified. The patient’s right to refuse treatment should be respected even if they are mentally ill.

Which of the following statements would weaken the above argument?

49. The question given below is followed by two statements, A and B. Mark the answer using the following instructions :

Mark (a) if the question can be answered by using Statement A alone, but cannot be answered by using Statement B alone.
Mark (b) if the question can be answered by using Statement B alone, but cannot be answered by using Statement A alone.
Mark (c) if the question can be answered by using either statement alone.

Mark (d) if the question cannot be answered by any of the two statements.

Q. Five people having different ages are standing in a row. They are Engineer, Professor, Manager, Doctor and Lawyer respectively by profession. The oldest among them is standing in the middle of the row and he is not a Lawyer. The youngest among them is an Engineer and he is not standing at
any of the two ends of the row. The Professor is younger than exactly three people and he is standing at one of the ends of the row. The Doctor is standing beside the Engineer. The Lawyer is standing beside the Doctor. The Manager is standing beside the Lawyer. How many people are younger than the Manager? 

A. The Lawyer is younger than the Doctor.
B. The Manager is younger than the Lawyer.

Directions for questions 50 to 52: The passage given below is followed by a set of three questions. Choose the most appropriate answer to each question.

”The lions had escaped, but the tiger was there. He was starving; one soldier tried to feed it and the other soldier shot and killed it after it bit the soldier’s hand off.” In brief, that is the play’s first scene.

From there, the action bursts into a plethora of issues, each more disturbing than the next. On one level, it’s a political drama about the war in Iraq, on another, an existential tract with the tiger as a contemporary Godot, and on still another, it’s a ghost story. When I ask Joseph about the ghosts, he is finally at home and easily forthcoming as he delves into the story line. “The Tiger explains in his first monologue as a ghost that suddenly the knowledge and the stuff of the universe is floating into him.

This is a basic reality of dying in this world that I’ve created, that once you’re dead and you’re a ghost, you learn at an accelerated pace. Suddenly, the ghost knows about Dante and suddenly Kev (the Marineturned- ghost) knows about the bones in his hand, about the Arabic roots of the word algebra, and all of a sudden he’s praying in Arabic.”

In Bengal Tiger emotional reality is clouded by the problems of translation. By using Arabic dialogue (without subtitles), Joseph underlines the failure of communication. As he points out, “US soldiers, by and large, don’t speak Arabic. When you’re in a very stressful and violent situation, the act of translation takes on huge importance. And yet, because those situations are so stressful, what is lost in translation in those moments can be grave.”

Indeed, the language barrier leads to a harrowing scene when Kev (Brad Fleischer), the Marine, who shot the tiger, enters an Iraqi home in pursuit, he imagines, of the enemy. Upon entering, Kev draws his gun and starts shouting at the women in English while they respond by screaming at him wildly in Arabic. The miscommunication and the mass confusion it fuels make for a situation much more frightening than any ghost story.

Much as I try to probe for the psychological roots to Joseph’s often disturbing work, the playwright diverts me from his personal experience to his aesthetic. “Story-telling”, he imparts, “can get boring if you’re not dealing with the issues of life or death, or on the edge of something. Now that doesn’t mean that every story has to have violence in it, but I’m attracted to it for a number of reasons, and part of it is the movies that I was raised on, most of which employed violence in some way.”

50. It can be inferred that the purpose of the first paragraph is

51. Which of the following describes a technique that the author frequently uses in the passage?

52. According to the passage, why does Joseph refer to disturbing issues in his work?

53. A paragraph is given below from which the last sentence has been deleted. From the given options, choose the one that completes the paragraph in the most appropriate way.

The answers to these questions about reality were many, but in Germany they tended to posit the idea of an evolving harmony, a movement towards equilibrium between the two poles of an objective reality and subjective human consciousness. The work of Mommsen, Eucken and Heyse was
characterized by this spirit of willingness to see reality in an explicable, idealized light, whereas Hauptmann, the consummate naturalist, rejected all attempts to embellish reality. Like other naturalists he adopted a critical position, under the banner of “truth”, towards hypocrisy and convention and under the banner of “modernity”, towards the fashion for historical themes and subjects within literature.

54. A paragraph is given below from which the last sentence has been deleted. From the given options, choose the one that completes the paragraph in the most appropriate way.

Policy failures come in many shapes and sizes. But they are almost invariably accentuated by the choices that have to be made in periods of financial shortage. Yesterday the coalition government found itself confronted by two of them, one in policing policy and the other in higher education. The
failures are radically different in many details. But they have this in common: they are both serious failures, and they were both foreseeable. They could both have been mitigated by clearer policymaking at an earlier stage.

Directions for questions 55 to 57: Answer the questions on the basis of the information given below.

Four people – Alfred, Buckley, Cherry and Dirk – went to a museum on a Sunday. No two of them reached the museum at the same time. They were wearing shirts of different colours among Purple, Red, White and Yellow, in no particular order. It is also known that :

(i) Cherry was not the first one to reach the museum and he was wearing the Red shirt.
(ii) The person wearing the Yellow shirt reached the museum earlier than Buckley.
(iii) The person wearing the White shirt was not the last one to reach the museum.
(iv) Alfred was not wearing the Yellow shirt.
(v) The person wearing the Purple shirt reached the museum earlier than the person wearing the White shirt.
(vi) Alfred reached the museum before Dirk.

55. Who among the four was wearing the White shirt?

56. Who among the four was the last to reach the museum?

57. Which of the following statement(s) is/are correct?
I. Dirk was wearing the Yellow shirt and he reached the museum before Cherry.
II. Alfred was wearing the White shirt and he reached the museum before Cherry.

58. The word given below has been used in sentences in four different ways. Choose the option corresponding to the sentence in which the usage of the word is incorrect or inappropriate.

Wash
(a) He decided to wash down the meal with a glass of red wine.
(b) The first day of the play was washed out after only 90 minutes.
(c) The body was found washed over on a beach.
(d) She always helps to wash up after dinner even if she is the guest.

59. The word given below has been used in sentences in four different ways. Choose the option corresponding to the sentence in which the usage of the word is incorrect or inappropriate.

Whip
(a) She had the whip hand and it was useless to resist.
(b) However difficult the task she will always whip through it.
(c) Shivi whipped up a delicious dinner for us in 10 minutes.
(d) The police officer whipped at her radio and called for back-up.

60. The word given below has been used in sentences in four different ways. Choose the option corresponding to the sentence in which the usage of the word is incorrect or inappropriate.

Zip
(a) The sleeping bags can zip together.
(b) This jacket zips up right to the neck.
(c) I put out my hand to ask the auto rickshaw driver to stop but he just zipped past me.
(d) She zipped into class as if nothing had happened and she was not 45-minutes late!

Solutions

1. b

f(0) = 10 = c                               …(i)

f(1) = a + b + c and f(–1) = a – b + c

∴ b = –b = 0                              …(ii)

f(2) = 4a + 2b + c = 14

∴ a = 1                                      …(iii)

From equations (i), (ii) and (iii), we get

f(10) = 100a + 10b + c = 110.

2. c

Let the hundreds digit be n.
The tens digit will be 2n.
The unit digit will be 4n.
The possible values of ‘n’ are 1 and 2 and hence the
possible numbers are 124 and 248 respectively.
On converting 248 in base 8 and base 9, the given
condition gets violated.
On converting 124 in base 8 and base 9, we get
(174)₈ = (147)₉ . 
Required sum = 4 + 7 = 11.

3. a

Absolute percentage change in the total sales of Naruti Kuzuki Ltd. from April to July

= (5670 - 5250)/5250 X 100 =  8%

Absolute percentage change in sales of Dwift from April to July

= (75 - 69)/75 x 100 = 8%

4. d

Sales of the other car models of Naruti Kuzuki Ltd. in

May 2010 = 549000 – (50 + 72 + 51 + 52)×1000 = 324 × 10³

Sales of the other car models of Naruti Kuzuki Ltd. in July 2010 = 567000 – (42 + 63 + 33 + 69) × 1000 = 360 × 10³

Percentage increase

= (360 - 324)/324 x 100 = 11.11%

5. b

The ratio of the sales of Sezire to the total sales of cars by Naruti Kuzuki Ltd. in :

April = (49x1000)/(5250x100) = 7/75

May = (72 x 1000)/(5490 x 100) = 8/61

June = (72 x 1000)/(5580 x 100) = 8/62

July = (63 x 1000)/(5670 x 100) = 1/9

So the ratio is the highest for May.

6. a

Note: A.M. ≥ G.M.

7. d

^n+mC₂ = ⁿC₂ + 11

(n + m)(n + m +1)/2 = n(n - 1)/2 + 11

n² + 2nm – n + m² – m = n² – n + 22
m² + (2n – 1)m = 22
m(m + 2n – 1) = 22
Hence, m = 2 and n = 5.

8. a

If Yamini covers 5 km in ‘t’ hours, Zora will cover 15 km in t + (2/3) hours.

The distance between the two at this moment is 5 km, and Yamini will cover 2 km more and Zora will cover 3 km more till they meet.

Therefore, the ratio of the speeds of Yamini to Zora is 2 : 3.

(5/t) / 15/(t + (2/3)) = 2/3

Solving the above equation, we get t = 2/3

Speed of Yamini = 7.5 km/hr.

9. c

Volume of each smaller cube

= (12 x12 x12)/64 = 27 cm³

Edge of each smaller cube = 3 cm

Let the number of cubes along the length and the breadth of the cuboid be 4x and x respectively.

4x × x = 64 or x = 4

Length of the cuboid = 4x × 3 = 48 cm
Breadth of the cuboid = x × 3 = 12 cm
Required surface area = 48 × 12 = 576 cm²

10. a

log₁₆5 = 1/4 x log5/log2 m                …(i)

log₅3 = log3/log5 = n                       …(ii)

From equations (i) and (ii), we get

m x n = log5/log2 x 1/4 x log3/log5 or log2/log3 = 1/4mn

Let log₃6 be equal to k; therefore,

log₃6 = log6/log3 = (log3 + log2) / log3 = 1 + log2/log3 = k

∴ k = (1 + 4mn)/4mn

For questions 11 to 13: The table given below can be formed from the data given in the question.

11. b

Profit percentage per ton for:

Maize = 30/90 x 100 = 33.33%

Rice = 15/75 x 100 = 20%

SugarCane = 20/105 x 100 = 19.05%

Cotton = 15/160 x 100 = 9.375%

Mustard seeds = 40/140 x 100  = 28.57%

So the profit percentage per ton is the highest for Maize.

12. c

Two - Sugar Cane and Cotton.

13. c

Total quantity of raw material used in production of 1 ton of Cotton

= (27 x10⁵)/54 = 50,000 kg

The total area of land required

= 10/200 x 50, 000 x 10³ 

= 2500000 m² = 2.5km² 

14. b

If N is a natural number such that N = a^pb^qc^r... where a, b, c etc are prime numbers, then Euler’s Totient function is given by φ(N) = N(1 - (1/a))(1 - (1/b))(1 - 1/c)

If P is some other natural number which is prime to N, then the remainder when Pφ(N) is divided by N is 1. To find the last two digits we need to find the remainder when 948367483 is divided by 100. 

φ(100) = 100(1 - (1/2))(1 - (1/5)) = 40

Required remainder

= 83⁶⁷⁴⁸³ = 83^40k+3 = 83³ = 87.

15. c

Let the length of EB be 2x units.

Therefore, the length of BF = √3x units.

Let the length of FC be a units.

Therefore, the length of DC = √3a units.

(Since triangle DFC is 30°- 60°- 90° triangle.)

In triangle AED,

∴ √3(√3a − 2x) = √3x + a
=> (√3x)/a = 2/3
Required ratio = 2 : 3.

16. a

A = {1, 2, 4, 8, 16}
B = {1, 3, 9, 27, 81}
The number of possible proper fractions when denominator is equal to 2, 4, 8 and 16 are 1, 2, 2 and 3 respectively.
The number of possible proper fractions when denominator is equal to 3, 9, 27 and 81 are 2, 4, 5 and 5 respectively.
Since no two of these fractions can be equal, the answer = 24.

Alternate method: All the combinations can result in a proper fraction except when 1 is chosen from both the sets. So the answer = 5 × 5 – 1 = 25 – 1 = 24.

17. b

The total number of possibe outcomes = 6 × 6 = 36.
The favourable values of the sum are 2, 3, 5, 7 and 11.
Favourable cases when the sum is:
I) 2 = (1, 1)
II) 3 = (1, 2) and (2, 1)
III) 5 = (1, 4), (4, 1), (2, 3) and (3, 2)
IV) 7 = (1, 6), (6, 1), (2, 5), (5, 2), (3, 4) and (4, 3)
V) 11 = (5, 6) and (6, 5)
The total number of favourable cases = 15.

Required probability = 15/36 = 5/12

18. b

From Statement A :
6q – p = 5
p = 6q – 5
p + q = 7q – 5
(7q – 5) when divided by 7 leaves remainder 2.
This statement alone is sufficient to answer the question.

From Statement B :

8q + p = 45
p = 45 – 8q
p + q = 45 – 7q
(45 – 7q) when divided by 7 leaves remainder 3.
This statement alone is sufficient to answer the question.

19. b

(x² + y² )² = 169
x² + y²  = +13                                                               ..(i)
(since x² + y² ≥ 0 )

(x² - y² )²  = 25

x² - y² = ±5                                                                  ..(ii)

Case I :
x² + y² = 13
x² – y² = 5
Solving the equations, we get x² = 9 and y² = 4.

Case II :

x² + y² = 13
x² – y² = –5
Solving the equations, we get x² = 4 and y² = 9.
In both the cases, x²y² = 4 × 9 = 36.

20. d

As slope of line P is 45°, ∠ABC = 45°.
(Corresponding angles)

In triangle ABC, length of AB

= √((5 − 3)² + (4 − 2)²) = 2√2 units

Therefore, length of AC = 2√2 units

Required area = 1/2 x 2√2 x 2√2 = 4 sq.units

21.a

Only two cases are possible :

Case I:

Points of intersection = 3

Case II:

Points of intersection = 5

Hence, possible values of P are 3 and 5.

22. d

(aⁿ + bⁿ)/ (a +b) => Remainder 0, if n is odd.

∴ 2⁵⁰⁰¹ + 1 and 2⁵⁰⁰³ + 1 are divisible by 3.

Now, 2⁵⁰⁰² + 1 can be written as 4²⁵⁰¹ + 1 .

∴ 4²⁵⁰¹ + 1 is divisible by 5.

Hence, none of the given numbers is a prime number.

23. a

Let the work (in units) done in a day by Pawan, Qureshi and Rohit be P, Q and R respectively. Let the total work done be (L.C.M. of 10 and 12) 60 units.

∴ P + Q = 6 units and Q + R = 5 units.

Let Pawan’s share be Rs. x. So Rohit’s share will be

Rs. (160 – x).

Ratio of the amount received by Pawan and Qureshi together to the amount received by Qureshi and Rohit together

= (x + 140)/(140 + 160 - 5) = 6/5 or x = 100

24. a

√x = √2003 − √y

Squaring both the sides, we get

x = 2003 + y − 2 (√2003 × y)

For x to be an integer, y must be of the form 2003a², where ‘a’ is a natural number.

Similarly, we can say that x must be of the form 2003b², where ‘b’ is a natural number.

∴ √2003a² + √2003b² = √2003

⇒a + b = 1

Hence, no solution is possible.

25. c

We can say that the total fare of :

Delni-Bhokal + Bhokal-Mumtai = Mumtai-Delni + Rs.125.

Hence, the variable fare of :

Delni-Bhokal + Bhokal-Mumtai = Mumtai-Delni + Rs.65.

This is possible only if Mumtai-Delni falls in the distance range 1001 – 1800 km (Rs. 340). One of Delni-Bhokal and Bhokal-Mumtai falls in the range 151 – 500 km (Rs. 155) and the other falls in the range 501 – 1000 km (Rs. 250).

26. c

Yatri Kumar must have travelled in a Passenger train.

First day : Fare in the Sleeper Class for the distance range 1001 – 1800 km = Rs. 160 + Rs. 60 = Rs. 220.

Second day : Fare in the Air Conditioned Class for the distance range ≤150 km = Rs. 120 + Rs. 100 = Rs. 220.

27. b

After the first operation :

The amount of milk (in litres) left = 160 – x

After the second operation :

The amount of milk (in litres) left

= (160 - x) - (160 - x)/160 X x = 90

⇒ x² – 320x + 70 × 160 = 0

⇒ (x – 40)(x – 280) = 0

Therefore, x = 40.

(Since x cannot be equal to 280.)

28. c

In right triangle PDC, using Pythagoras theorem, 

PD² + DC² = PC²

⇒PC = 2√5 cm                                             …(i)

Area ΔPBC = 1/2 area sq. ABCD

= (4 x 4)/2 = 8cm²                                          ..(ii)

Also, area ΔPBC = 1/2 x CE x PB

From equations (i) and (ii), we get

1/2 x CE x 2√5 = 8 or CE = 8/√5

In right triangle CEB, by Pythagoras theorem,

BE² + CE² = BC²

=> BE = 4/√5 cm

Required area = 1/2 x CE x BE = 3.2 cm²

29. c

Let the numbers be a, a + 1, a + 2, ……, a + 31.

Sum of these numbers = 32a + (31x32) = 16(2a + 31)

As 16 is a perfect square, the least possible value of 2a + 31 = 49.

Therefore, a = 9 and a + 31 = 40.

The least possible sum = 49.

30. d

From Statement A:

Statement A alone is clearly insufficient to answer the question.

From Statement B:

a² + b² + c² = 83

Case I :

(a, b, c) = (1, 1, 9)

Case II :

(a, b, c) = (3, 5, 7)

Statement B alone is also not sufficient to answer the question.
From Statements A and B:
The values of (a, b, c) are (3, 5, 7) and the sum of a,
b and c is 15.

31. a

The author makes reference to three judgments by the Supreme Court and asserts the significance of social action. She draws an important connection among courts, social sciences and social movements. The second paragraph also makes a reference to the importance of the State in social development - that in certain areas it cannot be substituted by the private
sector or the private social sector. The last two paragraphs also bring out the importance of the constitution and for the legal framework to include "the letter and the spirit of the constitution". Option (a) is the answer. Options (b) and (c) can be ruled out because there is not reference to politics - to the socio-political context only. Option (d) can also be
ruled out because though the author hints at correct governance or strict governance (when he refers to a "soft state") it does not talk about enforcement of justice.

32.d

The second paragraph provides the answer to this question. Option (d) is the best paraphrasing of the highlighted text which indicates that the understanding of constitutionalism needs to be widened so that a broader understanding of justice can be included. And this will help cover all complexities of injustice. Option (a) is incorrect as it is incorrect to infer that the
understanding of constitutionalism and justice need to be merged. Option (b) is incorrect as it states that the understanding of constitutionalism and justice should include aspects of injustice – not all complexities of injustice. Option (c) is ambiguous as from it one can infer that aspects of injustice are to be included/ a part of an understanding of constitutionalism and
justice.

33. c

The first paragraph starts with a reference to three recent judgments with a reference to a previous judgment (Naz foundation). In the next few sentences the author asserts that these pronouncements have a lineage in jurisprudence. She also indicates that every such case that is viewed and judged from the socio-political context is to be celebrated. Option (c)
is the answer. Option (a) is incorrect – the three cases do not form the core of the discussion. Similarly option (b) is also incorrect. Option (d) can be ruled out as the author does not state that jurisprudence has a lineage that includes neo-liberalism. In fact, she states that agents of the state are carried away by the ideology of neo-liberalism – this is with reference to the problem of a “soft state”.

34. c

The third paragraph is in inverted commas indicating that it is quoted from some other source. The paragraph envisages a situation where the State, “carried away by the ideology of neo-liberalism” and overly cautious, ignores the signals of wrongdoing even when they are strong. The tone of paragraph is cautionary and objective. It is not particularly critical of anything in particular nor does it have a disparaging tone. Option (c) is the correct answer.

35. b

The given information can be shown as :

Therefore, the surame of Ajay is either Yadav or Sharma.

From Statement A:

The surname of Chetan is Agarwal; but we still cannot conclude anything about the surname of Ajay. This statement alone is not sufficient to answer.

From Statement B:

The surname of Bikas is Yadav; therefore, the surname of Ajay is Sharma. This statement alone is sufficient to answer.

36. c

The lines talk about the response of the media to a particular issue (the issue has not been mentioned). The author has a good opinion about the response of the media as understood by the word ‘fervor’. The elites have presented their views about the response but their opinion is disliked by the author as revealed by the words ‘insult to the basic integrity and
intelligence’. So, we need a negative word for the first as well as the second blank.

The word ‘gimmick’ and ‘contrivance’ are apt for the first blank. ‘Gimmick’ means an unusual trick or unnecessary device that is intended to attract attention or to persuade people to buy something. ‘Contrivance’ is (usually disapproving) something that causes things to happen in a story in a way that does not seem natural or believable; a clever trick or plan. ‘Cachet’
which means ‘prestige’ makes option (a) unfit for the blanks. ‘Illusion’ which means a false idea or belief, especially about somebody or about a situation is apt for the second blank. Thus, option (c) is the correct option.

‘Torrid’ means emotional and passionate, so ‘torridity’ is incorrect for the first blank. ‘Pun’ means the clever or humorous use of a word that has more than one meaning, or of words that have different meanings but sound the same; double-meaning. Thus, option (b) and (d) are negated.

37. d

The author is speaking on a positive note about the book and mentions its goodness. The author talks about the regional disparities related to the subject that are covered with a unifying theme in the book. ‘Sundry’ which means various is inappropriate is the given context. ‘Turnpike’ which refers to a wide road, where traffic can travel fast for long distances and that drivers must pay a toll to use is inappropriate. Thus, options (b) and (c) are negated.

‘Disparate’ which means made up of parts or people that are very different from each other (example: a disparate group of individuals) matches with the theme of the sentence. ‘Distinct’ means easily or clearly heard, seen, felt, etc; clearly different or of a different kind is less apt than disparate for the first blank.

‘Heuristic’ means involving or serving as an aid to learning, discovery, or problem-solving by experimental and especially trial-and-error methods; also : of or relating to exploratory problem-solving techniques that utilize self-educating techniques to improve performance. Thus, ‘heuristic’ is the apt word for the second blank. Option (d) is the correct answer.

For questions 38 and 39:
Let Alveston, Blackpool, Chelsea and Dunstable be represented by A, B, C and D respectively

From statement (iii), we can conclude that C and D played the final match. From statement (iv), D was not the Champion, so D must have lost to C in the final and C was the Champion. In the three matches, as each team scored a different total number of goals, the number of goals scored by the teams must be 1, 2, 3 and 4, in no particular order. As A and B lost the
semifinals, they must have scored 1 and 2 goals, in no particular order. Also, as C was the Champion of the tournament, it must have scored 3 goals and D must have scored 4 goals.

As C played two matches and won both the matches, it must have scored at least 2 goals in the semifinal, as the least number of goals scored by any team was 1. Also, to win each
match, C must have scored at least 1 goal in each match. So C must have scored 1 goal in one match and 2 goals in the other. C must have won by a margin of 2 – 1 against A in the semifinal and by a margin of 1 – 0 against D in the final. The table given below illustrates the situation :

38. a

1

39. b

Chelsea, the Champion of the tournament, scored 2 goals in the semifinal.

40. c

The last line of the first paragraph states that meditation can be used for personal benefit and spiritual growth. The rest of the paragraphs all present information to the reader on how this is so. Option (c) is the answer. Option (a) is incorrect as it mentions the side effects of meditation indicating a negative connotation. But the passage only refers to positive
side effects. Option (b) is incorrect as the passage does not imply that meditation is necessary for enjoying life. It only argues why and how meditation is beneficial. Option (d) does not fit in with the scope of the passage. The option itself could have been considered had there been reference only to a specific spiritual journey in the passage.

41. c

The last line of the second paragraph states the primary purpose of meditation - “The primary purpose of meditation practice, however, is to bring forth clear states of awareness that will make authentic spiritual growth easier to experience.” Link this with the last paragraph and option (c) emerges as the answer. Option (a) can be ruled out as there is no mention that
meditation improves biological processes – it only strengthens of the immune system and leads to slowing of the biological ageing processes. These are also mentioned as beneficial side effects and not the main purpose of meditation. Option (b) has been mentioned in the passage but not as the main purpose of meditation – they are benefits of meditation and
elements of living a wholesome life. Option (d) can be ruled out because the ultimate goal of a follower has not been mentioned and only acquisition of knowledge is not the main purpose of meditation.

42. c

ABBBB

In the given context, ‘flounder’ means to struggle to move or get somewhere in water, mud, etc. ‘Founder’ as a verb means to fail because of a particular problem or difficulty. For example: The peace talks foundered on a basic lack of trust. It also means to fill with water and sink. For example: Our boat foundered on a reef. So ‘floundering’ is the apt word for the first sentence. ‘Persevere’ means to continue trying to do or achieve something despite difficulties. ‘Perverse’ means showing deliberate determination to behave in a way that most people think is wrong, unacceptable or unreasonable. Thus, ‘perverse’ is apt for the second sentence. ‘Mordent’ means a musical decoration in which either the note above or below is played as well as the written note; a musical ornament made by a quick alternation of a principal tone with the tone immediately below it. ‘Mordant’ means critical and unkind, but funny. Thus, ‘mordant’ is the apt word for the third sentence. ‘Cantor’ refers to the person who leads the singing in a synagogue or in a church choir. ‘Canter’ as a noun means a movement of a horse at a speed that is fairly fast but not very fast; a ride on a horse moving at this speed. So, ‘canter’ is apt for the fourth sentence. ‘Chard’ refers to a vegetable with large leaves and thick white, yellow or red stems. ‘Charred’ means burnt and black. So ‘charred’ is the apt word for the fifth sentence.

43. d

ABBBA

‘Gilt’ refers to a thin layer of gold, or something like gold that is used on a surface for decoration. ‘Aureole’ means a circle of light. ‘Oriole’ refers to a bird. In the context of gilt, the word ‘aureole’ is appropriate. ‘Auger’ refers to a tool that looks like a large corkscrew and is used for making holes in wood. ‘Augur’ means to be a sign that something will be successful or not
successful in the future; bode. Thus, ‘augur’ is apt for the second sentence. ‘Sheath’ refers to any covering that fits closely over something for protection. It is a noun. ‘Sheathe’ on the other hand is its verb form and means to cover something in a material, especially in order to protect it. As the sentence requires a verb, ‘sheathe’ is the apt word. ‘Drupe’ is a noun and refers to one-seeded indehiscent fruit having a hard bony endocarp, a fleshy mesocarp, and a thin exocarp that is flexible (as in the cherry) or dry and almost leathery (as in the almond). ‘Droop’ means to bend, hang or move downwards, especially because of being weak or tired. In the given context, ‘droop’ is the apt word. ‘Complication’ in the given context means a new problem or illness that makes treatment of a previous one more complicated or difficult. ‘Complexity’ means the state of being difficult to understand example: the complexities of the system. One develops complications after surgeries; complexities is inappropriate in the given context.

For questions 44 to 46 :

Let Aadi, Bina, Cara, Diya, Ema, Fiza, Gauri and Hari be represented by A, B, C, D, E, F, G and H respectively. The number of neighbours of the person living in :
P1 and P5 = 2;
P2, P4 and P7 = 3;
P6 and P8 = 4;
P3 = 5.

From statement (v), it can be concluded that A lives in P1 or P2 or P6. From statement (i), A cannot live in P6 as then A and C will not have the same number of neighbours. From statement (ii), A and F have a common neighbour – D – and hence it can be concluded that A lives in P2 and D lives in P3. From statement (iii), E lives in P6 and hence G lives in P1. From statements (iv) and (i), it can be concluded that C lives in P4. Thus it can be concluded that one between B and H lives in P5 and the other lives in P7. The following figure illustrates these conclusions :

44. d

Either Bina or Hari lives in P7.

45. b

Aadi has three neighbours.

46. a

Gauri is not a neighbour of Diya.

47. b

The author argues that the consumers have a choice weather or not to view advertisements and therefore, they should not complain about increasing adverts. Option (b) weakens this argument. If people are not aware that the piece of art or public information they are viewing is a form of adverts, then it is impossible to consciously avoid it.

48. a

The argument revolves around a patient’s right to choose weather or not a treatment should be administered to him/her. Option (a) states that in case of mental illness, a patient loses the ability to exercise this right as he/she is unable to take rational decisions. Hence, option (a) weakens the argument.

49. b

Let the ages of the five people, from youngest to oldest, be represented by A1, A2, A3, A4 and A5 respectively. From the given information it can be concluded that the age of the Engineer is A1 and the age of the Professor is A2. As the age of the Lawyer is not A5 and he is standing between the Manager and the Doctor, the Manager must be standing at one of
the ends of the row and the Professor must be standing at the other end of the row. The tables given below show the two possible cases.

From Statement A:

The given information is already present in the root of the question. This statement alone is not sufficient to answer.

From Statement B :

As the Manager is younger than the Lawyer, the age of the Manager must be A3. Hence, exactly two people are younger than him. This statement alone is sufficient to answer.

50. b

The first paragraph starts with a narration of an incident between the tiger and the soldiers. It ends by saying that this is the first scene of the play. Option (b) is correct. Option (c) is incorrect as the second paragraph takes forward the thread of thought (discussing the structure of the play). Option (d) is incorrect as there is no assertion or tone in the first paragraph itself. Option (a) is incorrect since the passage does not mention whether the scene described is based on a real-life incident or not.

51. c

A careful reading of the passage will help identify that the author uses the analysis and quotation approach. She makes her point and then uses a quote from Joseph to substantiate that point. This can be seen from the second, third, fourth and sixth paragraphs. Option (c) is the answer. Options (a) and (b) are
incorrect as the author never moves from specific to general or vice versa.

52. d

The last paragraph has the answer. Refer to the lines ““Story-telling”, he imparts, “can get boring if you’re not dealing with the issues of life or death, or on the
edge of something.”” Option (a) is incorrect as violence has not been explicitly linked to contemporary political realities. Option (c) is incorrect as Joseph never states this. Option (b) can’t be inferred as there is no reference to critiques of social realities.

53. a

The paragraph discusses the idea of reality – on one hand an idealized reality and on the other a naturalistic reality. This paragraph indicates a dichotomy in viewpoints. Option (c) can be ruled out because there is no reference to a third view in the paragraph. Option (d) is ruled out as the educated bourgeoisie are not
the subject of the paragraph – it is the works and the views of artistes (writers). Option (b) does not match with the central idea of the passage as this option
talks about beauty and not reality. Option (a) is the best answer as it considers the dichotomy as well as the works of the German artistes with respect to reality.

54. b

The paragraph is about policy failures – specifically the policing policy and the higher education policy. The paragraph has a negative tone. Option (c) can be
ruled out as it has a tone of relief – a positive tone. Options (a) and (d) can be ruled out as they are only specific to the policing policy. Option (b) is the answer
as it refers to both the policing and higher education policies. It also follows from the penultimate line in the paragraph that states that both failures could have
been mitigated – option (b) logically completes the paragraph by stating that instead they were allowed to fester.

For questions 55 to 57:

From statements (i), (ii) and (vi), it can be concluded that Alfred was the first person to reach the museum. From statements (i), (ii) and (iv), it can be concluded that Dirk was wearing the Yellow shirt.

Hence, either Alfred or Buckley was wearing the Purple shirt and the other one was wearing the White shirt. From statement (v), it can be concluded that Alfred was wearing the Purple shirt while Buckley was wearing the White shirt. Further analysis leads to the following table:

55. b

Buckley

56. c

Cherry

57. a

Only statement I is correct.

58. c

To wash over means to suddenly affect somebody strongly, so that they are not aware of anything else or to happen to or around somebody without affecting them. This is incorrect in the given context. The correct sentence should be “The body was found washed up on a beach”. Washed up here means to carry something onto land. So (c) is incorrect.

Wash down means to drink in order to swallow something solid. So, (a) is correct. Wash out means to make a game, an event, etc. end early or prevent it from starting. Thus (b) is correct. Wash up means to clean the plates and dishes after a meal. Thus, (d) is correct.

59. d

Sentence (d) is incorrect. The correct phrasal verb is whip out which means to remove quickly. The correct sentence is “The police officer whipped out her radio
and called for back-up.”

Have/hold the whip hand (over somebody/something) means to be in a position where you have power or control over somebody/something. So (a) is correct.
To whip through means to do something quickly. Thus, (b) is correct. To whip up is to make food quickly. So (c) is correct.

60. d

Zip somebody/yourself into something means to fasten clothes, bags, etc. with a zip/zipper. For example: The children were safely zipped into their sleeping bags. However, in the context given in (d) zip into is incorrect. The correct usage should have been strode into which means to walk in with long strides sometimes indicating confidence. Thus option (d) is incorrect.

Zip together means to be fastened with a zip/zipper. So (a) is correct. Zip up or zip somebody/something up means to be fastened with a zip/zipper; to fasten
something with a zip/zipper. So (b) is correct. Zip past means to move very quickly or to make something move very quickly in the direction mentioned. Thus,
(c) is correct.