CMAT 2019 Question Paper

Given Speed of surya = 25 km/hr = $$25\times \frac{5}{18} = \frac{125}{18}$$ m/s.

Time taken(T) = Distance Travelled/ Speed

$$\Rightarrow T =\frac{500}{\frac{125}{18}} = 72$$ sec 

Hence the time taken by Mr. Surya is '72 sec' or '1.2 min'. 

As per the empirical rule, approximately 99.7% of the data in a bell-shaped distribution lies within three standard deviations of the mean, or $$\mu \pm 3\sigma$$.  $$\mu \pm 6\sigma$$ will have approximately 99.99967% of the data. Hence, option C.

The topper of the class is the one who gets a highest overall score. Let us check the options, who has got the overall score.

Option A:

The overall score of Maya = 90 + 50 + 90 + 60 + 70 + 80 = 440 marks 

Option B:

The overall score of Arya = 100 + 80 + 88 + 60 + 80 + 70 = 478 marks

Option C:

The overall score of Rupesh = 80 + 55 + 85 + 95 + 50 + 90 = 455 marks

Option D:

The overall score of Riya = 90 + 72 + 70 + 72 + 91 + 70 = 465 marks

So, the topper of the class is Arya, with a overall score of 478 marks.

Given, Rajesh can check the quality of 1000 items in 5 hours

$$\Rightarrow$$ Efficiency of Rajesh = 200 items/hr.

Also given, Rakesh can complete the 75% of same job in 3 hours

$$\Rightarrow$$ time taken by Rakesh to complete 100% of the job = $$\frac{100}{75}\times 3$$ = 4 hours.

$$\Rightarrow$$ Efficiency of Rakesh = 250 items/hr.

Given in the process of checking 1300 items, Rakesh spends only 2 hours. Let say time spent by Rajesh be 't' hours, which is also the total time taken.

Total Work = Efficiency $$\times$$ time taken 

$$\Rightarrow 1300 = 250\times 2 + 200\times t$$

$$\Rightarrow 200t = 800$$

$$\Rightarrow t = 4$$

Hence the time taken in the process of checking 1300 items is 4 hours.

Let the cost of each orange, banana and apple be Rs. 'o' , 'b' , and 'a' respectively.

Given, Two oranges, three bananas and four apples cost Rs. 15

$$\Rightarrow$$ 2o + 3b + 4a = 15..........(1)

Also given, Three oranges, two bananas and one apple cost Rs. 10

$$\Rightarrow$$ 3o + 2b + a = 10............(2)

Adding (1) and (2), we get,

5o + 5b + 5a = 25

$$\Rightarrow$$ o + b + a = 5

Then the cost of three oranges, three bananas and three apples is given as

3o + 3b + 3a = 3 [o + b + a] = 3$$\times$$ 5 = Rs. 15 

$$360\sqrt?$$ + 4500 = 19700 - 9800

$$\Rightarrow 360\sqrt? + 4500 = 9900$$

$$\Rightarrow 360\sqrt? = 5400$$

$$\Rightarrow \sqrt? = 15$$

$$\Rightarrow ? = 15^2$$

$$\Rightarrow ? = 225$$

Curved surface area of cylindrical pillar is given as A = 2$$\pi$$rh, where 'r' is base radius and 'h' is height of the cylinder.

So curved surface area of each pillar A = $$2\times \pi\times 0.35\times 5 = 11 m^2$$

Given there are 30 cylindrical pillars.

The curved surface area of half the number of pillars = 15 * A = 165 $$m^2$$.

Given rate of painting is Rs. 10 per $$m^2$$

The cost of painting curved surface of half the number of pillars = Curved surface area * rate of painting

= $$165\times 10$$

= Rs. 1650. 

Probability = Expected number of outcomes/ Total number of outcomes.

Total number of outcomes =  The number of ways of selecting 3 professors at random from a total of 10 professors.

= 10C3 = 120 ways.

Expected number of outcomes = Selecting 3 professors so that at least one of the junior professor is selected.

The possible cases are,

Case(1): Selecting 1 junior professor out of 4 and Selecting 2 senior professor out of 6 = 4C1 * 6C2.

Case(2): Selecting 2 junior professor out of 4 and Selecting 1 senior professor out of 6 = 4C2 * 6C1.

Case (3): Selecting 3 junior professor out of 4  = 4C3.

So Expected number of outcomes = 4C1 * 6C2 + 4C2 * 6C1 + 4C3 = $$4\times 15 + 6\times 6 + 4$$ = 100 ways.

Probability = $$\frac{100}{120} = \frac{5}{6}$$ 

In a clock, 

In one revolution the minute hand covers 60°

$$\Rightarrow$$ 60 minutes = 360°

$$\Rightarrow$$ 1 minute = 6°.

$$\Rightarrow$$ for every minute the minute hand covers 6°.

Similarly In one revolution the hour hand covers 12 hours.

$$\Rightarrow$$ 12 hours = 360°

$$\Rightarrow$$ 1 hour = 30°.

$$\Rightarrow$$ for every hour, the hour hand covers 30°.

So at 5.20 P.M. the hour hand must have covered 5 * 30° = 150° + 20*1/2 = 160

and minute hand must have covered 20 * 6° = 120°.

So the angle created by two hands of the clock when the time is 5.20 P.M. = 160 - 120 = 40°.

Given, Total volume of soaps sold = 680 lakh units.

Volume of Lux sold = 136 lakh units.

$$\Rightarrow$$ Percentage of Lux sold = $$\frac{136}{680}\times 100$$ = 20% 

Also given,

percentage of Lifebuoy sold is 30%,

 percentage of Camay 10%,

 percentage of Liril 15% and 

percentage of Mysore Sandal 10% 

From the pie chart

The percentage of Lux + Lifeboy + Camay + Liril + Mysore Sandal + Others  sold = 100%

$$\Rightarrow$$ The market share of others = 100 - 20 - 30 - 10 - 15 - 10 = 15%

In a triangle, the angular bisector divides the side which it intersects in the ratio of other two sides.

So, In the triangle ABC, the angular bisector AD divides the side BC in the ration of AB and AC

$$\Rightarrow$$ BD : DC = AB : AC

Given BC = 10 cm and DC = 6 cm 

$$\Rightarrow$$ BD = BC - DC = 10 - 6 = 4 cm

Then $$AB =\frac{BD}{DC}\times AC = \frac{4}{6}\times 4.2 = 2\times 1.4 = 2.8$$ cm 

Based on the given constraints, there will be two cases in which task 1 is either assigned to one among person 3 or 4 or to one among person 5 or 6

Case 1:

Assigning Task 1 to either Person 3 or 4.

No. of ways of assigning task 1 = 2 ways

No. of ways of assigning task 2 = 1 way 

Remaining 4 tasks can be assigned among the remaining 4 persons in 4! ways.

Therefore, Total number of ways = 2 x 1 x 4! = 48

Case 2:

Assigning Task 2 to either Person 5 or 6.

No. of ways of assigning task 1 = 2 ways

No. of ways of assigning task 2 = 2 ways 

Remaining 4 tasks can be assigned among the remaining 4 persons in 4! ways.

Therefore, Total number of ways = 2 x 2 x 4! = 96

Hence, total number of possible arrangements= 48 + 96 = 144

Let us consider the fucntion f(x) = $$a\cos x + b\sin x + c$$ 

The range of f(x) if given as $$c - \sqrt{a^2 + b^2} \leq f(x) \leq c + \sqrt{a^2 + b^2}$$

Then the maximum value of  3 $$cosx+4 sinx+8$$  is = 8 + $$\sqrt{3^2 + 4^2}$$ 

= 8 + 5 = 13

Let the number be 'x'

one-fourth of the number = $$\frac{1}{4}\times x = \frac{x}{4}$$

one-third of one-fourth of the number = $$\frac{1}{3}\times \frac{x}{4} = \frac{x}{12}$$

Given, one-third of one-fourth of the number is = 15

$$\Rightarrow \frac{x}{12} = 15$$

$$\Rightarrow x = 180$$

Hence the number is 180.

Then three-tenth of the number = $$\frac{3}{10}\times x = \frac{3}{10}\times 180 = 54$$

Let the number of men be 'm' and number of women be 'w' in the class.

Given Average score of men = 70

$$\Rightarrow$$ Total score of men$$\div$$number of men = 70

$$\Rightarrow$$ Total score of men = 70$$\times$$m

Also, Average score of women = 83

$$\Rightarrow$$ Total score of women$$\div$$number of women = 83

$$\Rightarrow$$ Total score of women = 83$$\times$$w

Given the class average = 76

$$\Rightarrow$$ (Total score of men + Total score of women)$$\div$$(number of men + number of women) = 76

$$\Rightarrow \frac{70\times m + 83\times w}{m + w} = 76 $$

Let the ratio of number of men to women $$\frac{m}{w} = k$$

$$\Rightarrow$$ 70k + 83 = 76k + 76

$$\Rightarrow$$ 6k = 7 

$$\Rightarrow$$ k = 7 : 6.

Hence the ratio of men to women in the class is 7 : 6.

Probability of A or B = Probability of A + Probability of B - Probability of A and B.

$$\Rightarrow$$ Probability of drawing king or heart = Probability of drawing king + Probability of drawing heart - Probability of drawing kings which are hearts from the deck of cards.

A deck of cards contain 52 cards, of which there are 4 kings and 13 hearts and 1 king which is heart also. 

Probability of drawing a king = $$\frac{4}{52}$$

Probability of drawing a heart = $$\frac{13}{52}$$

Probability of drawing a king which are heart also = $$\frac{1}{52}$$

$$\Rightarrow$$ Probability of drawing king or heart = $$\frac{4}{52} + \frac{13}{52} - \frac{1}{52}$$

= $$\frac{16}{52}$$

= $$\frac{4}{13}$$

Let the three consecutive odd numbers be 'x-2', 'x' and 'x+2'

Given the sum of three consecutive odd numbers is 20 more than the first number

$$\Rightarrow$$ x-2 + x + x+2 = 20 + x-2

$$\Rightarrow$$ 2x = 18

$$\Rightarrow$$ x = 9

Therefore the three consecutive odd numbers are 7,9 and 11.

The middle number is 9.

When a pair of dice are thrown simultaneously the maximum sum possible is 12.

The possible cases of getting a sum of 9 are:

                    dice 1     dice 2

                    four         five.....................(1)

                    five          four.....................(2)

                     six          three....................(3)

                   three         six.......................(4)  

So a total of 4 cases are possible

The possible cases of getting a sum of 10 are:

                    dice 1     dice 2

                     four        six......................(1)

                      six         four.....................(2)

                     five        five.....................(3)

So a total of 3 cases are possible

The possible cases of getting a sum of 11 are:

                   dice 1       dice 2

                    five           six...................(1)

                     six           five..................(2)

So a total of 2 cases are possible

The possible cases of getting a sum of 12 are:

                  dice 1      dice 2

                   six           six.....................(1)

So a total of 1 case is possible.

Total number ways of getting a sum of 9 or more = 4 + 3 + 2 + 1 = 10 ways

Total outcomes when two dice are rolled simultaneously = 6 * 6 = 36 ways

Probability of getting a sum of 9 or more = Expected number of outcomes/ Total outcomes

= $$\frac{10}{36}$$

= $$\frac{5}{18}$$

Given the length, breadth and height of a rectangular cuboid are in the ratio 1: 2 : 3.

Let the length, breadth and height be k, 2k, and 3k units where 'k' is a constant.

Volume of the cuboid(V') = $$l\times b\times h$$ units = $$k\times 2k\times 3k$$  = $$6k^3$$ units

Given the length, breadth and height are increased by 100% each .

Then the new length, breadth and height will be doubled.

So new length, breadth and height of the rectangular cuboid are 2k, 4k, and 6k units.

New Volume of the cuboid (V') = $$2k\times 4k\times 6k = 48k^3$$ units.

Increase in the volume of the cuboid = V' - V = $$48k^3 - 6k^3 = 42k^3 = 7 [6k^3] = 7V$$

Therefore the volume has increased 7 times the initial volume.

let the length of the halls be 'a' and 'a+1' m respectively and height of the halls be 'h' m.

Area of 4 walls of first square hall (A1) = $$(4\times a\times h) m^2$$

Given, cost of painting is Rs. 5 per sq.m

$$\Rightarrow$$  cost of painting 4 walls of the first square hall = A1 * 5 = $$4\times a\times h\times 5 = Rs. 20*a*h$$.

Given that this cost of painting = Rs. 6000

$$\Rightarrow$$ 20*a*h = 6000...........(1)

Similarly,

Area of 4 walls of second square hall (A2) = $$(4\times a+1\times h) m^2$$

$$\Rightarrow$$  cost of painting 4 walls of the second square hall = A2 * 5 = $$4\times a+1\times h\times 5 = Rs. 20*(a+1)*h$$.

Given that this cost of painting = Rs. 6100

$$\Rightarrow$$ 20*(a+1)*h = 6100............(2)

Dividing (2) with (1), we get

$$\frac{a+1}{a} = \frac{6100}{6000}$$

$$\Rightarrow 1 + \frac{1}{a} = \frac{61}{60}$$

$$\Rightarrow a = 60$$

Substituting this value in equation (1), we get

20*60*h = 6000

$$\Rightarrow$$ h = 5 m.

So, the height of the two walls is 5 m.

Volume left out in the rectangular box = Total volume of the rectangular box - Volume of the cylinder placed within it.

Total volume of the rectangular box of width(a), length(b), and height(c) is given as (V) = $$a\times b\times c$$ cubic units.

= $$6\times 8\times 10$$

= 480 cubic units.

Volume of the solid cylinder of height 'c' and of diameter 'a' is given by (V') = $$\frac{\pi}{4}*a^2*c$$ cubic units.

= $$\frac{\pi}{4} * 6^2 * 10$$

= 90$$\pi$$ cubic units.

Therefore left out volume = 480 - 90$$\pi$$ cubic units.

Given f(x) = $$x^3 - 4x + p$$ and  f(0) and f(1) are of opposite signs.

$$\Rightarrow f(0)\times f(1) < 0$$

$$f(0) = 0^3 - 4*0 + p = p$$

$$f(1) = 1^3 - 4*1 + p = p-3$$

$$\Rightarrow (p)(p-3) < 0$$

$$\Rightarrow 0 < p < 3$$.

Given, speed of a boat in still water (V) =  5 km/hr

Let speed of the stream be V' km/hr.

time taken to go 20km downstream (t) = distance travelled$$\div$$relative speed of the boat 

= $$\frac{20}{V + V'}$$

=$$\frac{20}{5 + V'}$$ hours

time taken to go 20 km upstream (t') =  distance travelled$$\div$$relative speed of the boat 

= $$\frac{20}{V - V'}$$

= $$\frac{20}{5 - V'}$$ hours

Given that t' = 3*t

$$\Rightarrow \frac{20}{5 - V'} = 3\times \frac{20}{5 + V'}$$

$$\Rightarrow 4V' = 10$$

$$\Rightarrow V' = 2.5$$ km/hr.

So the speed of the stream is 2.5 km/hr.

Whenever some cubes are melted to form a single larger cube, the total volume always remains constant.

So, Sum of the volumes of three small cubes = Volume of the larger cube.

Let the side of the lager cube so formed be 'a' cm.

Then $$1^3 + 6^3 + 8^3 = a^3$$

$$\Rightarrow a^3 = 729$$

$$\Rightarrow a = 9$$ cm.

Surface area of cube so formed = 6*$$a^2$$ = $$6\times 9^2 = 6\times 81 = 486  cm^2$$

Speed = Distance travelled$$\div$$time taken

So, for the same distance travelled, Speed is inversely proportional to time taken.

$$Speed\propto \frac{1}{time taken}$$

Given ratio of speeds of three cars  is 5 : 4 : 6.

So, ratio of the time taken to travel same distance is $$\frac{1}{5} : \frac{1}{4} : \frac{1}{6}$$

= 12 : 15 : 10

The given statement indicates a question about the ban of political parties, the first argument is weak as there is no context about teaching the lesson to the political parties.

But the second argument is strong, because if the parties are banned, it will definitely lead to an end of democracy.

Hence, only II is strong.

=> Ans - (B)

Small squares = 6 (ABKD, BCEK, DKLF, KEGL, FLIH, LGJI)

Big squares = 2 (ACGF, DEJH)

Total squares = 8

=> Ans - (C)

Cup is used to drink something with the help of lips. Similarly birds collects grass with the help of beak to make her nest.

=> Ans - (C)

The given statement indicates that if any student is found to use unfair or unethical means in an exam will be disqualified, hence the first conclusion follows since it also debars the student from using unfair means in the exam. But second conclusion does not follow since there is no context about the examination system.

Thus, only conclusion I follows.

=> Ans - (A)

A well is located at one corner and a cabin at another corner opposite to the gate.

Lemon and Coconut trees are on either side of the gate

The mango tree is not at the corner where the cabin is located, => Mango Tree and Well are at the same corners, also Neem Tree and Cabin are at same corners

Thus, only possible combination at diagonally opposite ends is Neem Tree and Lemon Tree.

=> Ans - (D)

JAPAN is coded KCSES

Similarly, for Castle :

=> Ans - (C)

Clearly, each statement alone is not sufficient to find Deepa's age as on 30th October 2018.

Now, if we combine last two statement, we can find Prabha's age and if we add it to first statement, then we can also find Deepa's age.

Thus, all the three statements are required.

=> Ans - (B)

The pattern followed is that '4' and '2' are alternatively added.

24 + 4 = 28

28 + 2 = 30

30 + 4 = 34

34 + 2 = 36

=> Ans - (D)

Retina, cornea and pupil are parts of a human eye, while vision is a functionality of an eye, hence it does not belong with others.

=> Ans - (A)

Though all are musical instruments, but violin, cello and guitar are played with hands while a flute is used with mouth hence it is the odd one.

=> Ans - (B)

It is a known fact that Copper has a very low electric resistance, and that's why it is used to make electric wires.

Thus, R is the correct explanation of A.

=> Ans - (D)

Alternatively, the arrows are facing downwards, and towards the right. Also, it gets decrease by 1 in each alternate figure. Thus, in the fifth figure, there will be 3 arrows facing downwards as shown in 3rd figure.

=> Ans - (A)

Let us assume that vashista is walking in morning

so, sun would be in east

positioning back to sun means he was walking towards west

from there he turned left, then turned right, and then towards left again. so he is now walking towards south.

Let us now assume that he is walking in evening.

so, sun will be on west side.

positioning back to sun means he was walking towards east.

from there he turned left, then turned right, and then towards left again. so he is now walking towards North.

Therefore the answer is north or south.

Hence answer is option D

The numbers are of the form $$2^n$$ where $$n$$ is in decreasing order starting from 1.

$$2^{1}=2$$

$$2^{0}=1$$

$$2^{-1}=\frac{1}{2}$$

$$2^{-2}=\frac{1}{4}$$

$$2^{-3}=\frac{1}{8}$$

=> Ans - (B)

Only son of her grandfather = Shruti's father

Now, Ankit's father is also Shruti's father, => Ankit is Shruti's brother.

=> Ans - (D)

(A) : T (+1) = U (+2) = W (+2) = Y

(B) : G (+1) = H (+2) = J (+3) = M

(C) : A (+1) = B (+2) = D (+2) = F

(D) : N (+1) = O (+2) = Q (+2) = S

=> Ans - (B)

If the employees have confidence in the management, it follows that they are hostile.

=> Ans - (C)

Given that 123 means "he is talented"----(a)

               3456 means "talented people earn more"------(b)

               45678 means "people earn more to enjoy".------(c)

Now we will decode what number means what word.

1---- He

2---- is

3---- the number 3 is in sentence a and b , so from these two sentences, the number 3 is common and the word Talented is common

so 3 is talented.

But 456 in sentence b and c implies the same sentence people earn more so we cant determine the particular code for earn.

so, the answer will be cant be determined.

X(m), Y and P are siblings.

Z is their mother and Q is father, => Z is wife of Q.

Hence, second and fourth are definitely true.  First can be true if Y is a male.

But third option can never be true, since X is brother of P.

=> Ans - (C)

R is the father of S, S is the father Q, 

which implies R is the grand father of Q

P is the daughter of R

Thus P is the aunt of Q

Swimming is the practice that is done only in water, hence water is absolute necessary to perform swimming.

=> Ans - (D)

The little one of a hen is called chick, similarly amphibian of a frog is called tadpole.

=> Ans - (A)

Total students = 33

Akshay's rank in the class = 13th

Ajay's rank (5 students below him) = 28th

Number of students between them = $$(28-13)-1=14$$

=> Ans - (C)

Code for each letter is given as :

P -> 3
I -> 1
L -> 8
L -> 8
E -> 2
R -> 6

=> PILLER : 318826

=> Ans - (A)

In the problem figure, the second image is mirror image of first when horizontal mirror is placed, similarly the first option is the correct mirror image of the question figure.

In the second figure, number of lines are not equal, and the fourth image is the mirror replica when vertical mirror is placed.

=> Ans - (A)

The author in the paragraph talks about endangered languages. In the first line of the passage, he defines an endangered language as one " that is likely to become extinct in the near future". 

Thus, the "these" mentioned in the given sentence refers to "endangered languages".

Hence, option C is the correct answer.

In the second last line of the passage, the author states that "Latin slowly evolved into modem Italian, Spanish, French, Romanian, and other languages."

Thus, the Spanish language evolved out of Latin and hence, option D is the correct answer.

The first line of the paragraph defines an endangered language as "An endangered language is one that is likely to become extinct in the near future.".

Hence, the answer is option B.

The third sentence of the paragraph states, "However, other members can challenge the decision of a member to make use of provisions available to developing countries."

Hence, the answer is option B.

The second sentence of the paragraph states, "Members announce for themselves whether they are "developed" or "developing" countries."

Hence, the answer is option D.

"Developing country status in the WTO brings certain rights. There are for example provisions in some WTO Agreements which provide developing countries with longer transaction periods before they are required to fully implement the agreement and developing countries can receive technical assistance."

From the above-mentioned sentences from the passage, we can infer that option A is the required answer to this question.

The fifth sentence of the passage states, " It is like the nourishment that is necessary for a sapling to grow into a big and fruitful tree.".

Thus, parenting is compared with "nourishing a plant".

Hence, the answer is option C.

The second-last line of the passage states, "the value system stands divided on some of the major facets of parenting". 

Hence, option A is the answer to this question.

The passage mentions, "Parenting styles vary from culture to culture. The world is a big place comprising of a variety of people having different ways of living. Although culture is the key ingredient...".

From this, we can infer that parenting is dependent on the culture of a region and varies with it.

Hence, the answer is option C.

In the passage, the author quotes Steve jobs in the lines "Remembering that I'll be dead soon, ... what is truly important" Jobs, used to say.

Hence, the "I" in the above-mentioned sentence refers to Steve Jobs and thus, option B is the answer.

"And yet, death is the destination, we all share. No one has ever escaped it, and that is how it should be, because death is very likely the single best invention of life."

From the above-mentioned lines from the passage, we can observe that options B, C and D are true. Option A is not mentioned in the passage and hence, is the answer.

The author mentions, "He was such a perfectionist that there was a period when he had no furniture in his house at all, because he could not decide what to buy".

From this line, we can infer that Steve Jobs believed in perfectionism.

Hence, the answer is option D.

The passage talking bout Steve Jobs mentions that Jobs was an ardent perfectionist. On several occasions, his house had no furniture because he could not decide what to buy. 

Option A: Jobs could not find the perfect furniture for his house. 
Option B: This is the correct answer. The passage does not mention anything about Jobs not having money to purchase furniture. 
Option C and D: Jobs was a perfectionist, and due to this reason, he could not decide what to buy.

From the statement mentioned by the author ', I would like to share a few little known facts about the man who pretty much changed the world with one small technological device', we can say that the paragraph is in first-person narrative.

In the third line of the passage, the author mentions ' I would like to share a few little known facts about the man...". The passage provides lesser-known facts about Steve Jobs, such as his habit of working barefoot, his strict dietary choices, his fascination with Zen Buddhism, and his perfectionism in selecting furniture.

It does not primarily emphasize his business management skills (option B) or provide his complete life story (option C). Moreover, as the passage highlights "little known facts," option D is also incorrect.

A: Incorrect due to the redundant "but," awkward "that Mathematics".

B. It is grammatically correct and the required answer.

C. Incorrect due to the incorrect use of "that" after "although" and the redundant "but."

D. Incorrect due to the improper use of "that" in the main clause.

Hence, the answer is option B.

The correct sentence is "did he realize / that he had been / helped by a man / he never respected"

Thus, the correct order of sentences is PRQS.

Hence, the answer is option A.

The phrase "reinventing the wheel" means to engage your time in finding/doing something that is already known/done.

Hence, the correct answer is option D.

Oligarchy: Small group people having control of a country.

Aristocracy: Government by a privileged noble class.

Monarchy: Rule by a single king, queen, or similar royal figure.

Autocracy: Absolute rule by one person with unrestricted power.

Therefore, Option A is the correct answer. 

Abridging means to shorten or reduce the length of something

Of the given options, only option B is the one that comes close to it in meaning. 

Hence, Option B is the correct answer.

The correct phrases are "to work something out" and "to hand something over". Hence, the answer is option D.

Section C of the given sentence contains an error. The right phrasing would be "there was still a little tea". 

Hence, the answer is option D.

Pacify means to calm, soothe, or bring peace.

Aggravate means to worsen, intensify, or provoke, which is the opposite of pacify. Therefore, Option A is the correct answer.

Discourage: Means to dishearten, but not necessarily the opposite of pacify.

Slow down: Refers to reducing speed, which is unrelated to pacifying.

Encourage: Means to motivate, which is not the opposite of pacify.

"Leaving in a lurch" means to "leave without help". Among the options, option C is the correct answer.

prima facie - based on the first impression

Answer is option A.