CUET PG 2023 Question Paper COQP12 Shift-2

A tirade is a long, angry speech of criticism or accusation. Therefore, Option is the correct answer.

Option D is the correct answer.

The last sentence in the passage, 'Add to this the art of persuasion, and you have a winning combination.' implies that we need to be persuasive.

The sentence 'While aggressive communication makes people withdraw from you' implies that we should not be assertive. Hence, Option B is incorrect.

Options A and C could not be inferred from the passage.

Note: The passage has certain grammatical errors and typos in the original CUET paper.

Note: The question options have errors in the original CUET paper.

The correct answer is Option D

The passage mentions that nearly everyone in the restaurant stared at the guests, some in disbelief. This indicates that the guest's behaviour was noticeable and perceived as aggressive by others present. Therefore, Statement C is correct.

Statement A. The passage does not explicitly state whether the guest was treating the waiter. It only describes the guest's behaviour and interaction with the waiter, focusing on the guest's demands and demeanour. Therefore, option A cannot be considered correct.

Statement B. While it's true that the guest demanded good food, the passage also emphasizes that he demanded the highest order of respect from the waiter. The focus is not solely on the quality of the food but also on the guest's insistence on being treated with respect. Thus, statement B is not entirely accurate.

Statement D. The passage describes the guest's behaviour as loud, angry, and demanding, which aligns with aggression. However, it also mentions that there's an important difference between being aggressive and being assertive. While the guest's behaviour may be perceived as aggressive, there's no indication that he was exhibiting assertiveness in a positive manner. Therefore, statement D, stating that the guest was both aggressive and assertive, is not entirely accurate.

From the passage, we can infer that:

Aggressive behaviour can cause people to withdraw, while assertiveness can inspire people to follow. Persuasiveness can be a winning element in communication, and politeness is often seen as a refined quality.

Therefore,

• Aggressiveness matches with People withdraw from you
• Assertiveness matches with People follow you
• Persuasiveness matches with A winning element
• Politeness matches with Refined

The 'winning combination' mentioned in the passage is inferred from the sentence: "While aggressive communication makes people withdraw from you and want to avoid you, assertiveness makes people want to follow you.  Add to this the art of persuasion, and you have a winning combination."

So, based on the passage's statement, the winning combination includes being assertive and persuasive, making option c) Assertive and Persuasive the correct answer.

Option A is the correct answer.

• Gene Expression (A) matches with A process of lifetime (III). This could be inferred from the sentence, 'Gene expression is a process in which certain genes are turned on or off during one's lifetime.'
• Cortisol (B) matches with Turns on a series of bad genes (II). This could be inferred from the sentence, 'Long-term stress increases the production of cortisol, a stress hormone. Like a domino effect, cortisol switches on a series of bad genes that can lead to heart disease, cancer and immunological disorders.
• Reduced stress matches with A by product of good habits (IV). This could be inferred from the sentence,' The by product of good habits is reduced stress resulting from financial independence, happiness, good health, etc.'
• DNA (D) matches with Changing of genome (I). This could be inferred from the sentence, 'Habits are not harmless. They can alter your DNA by changing your genome.'

Statement A is true, as the passage mentions that bad habits can lead to immunological disorders.

Statement B states: “The altered DNA gets passed on to our children.” While the passage does not directly state this, it discusses the concept of gene expression or epigenetics, which involves changes in gene activity that do not involve alterations to the genetic code but still get passed down to at least one successive generation.

Statement C is partially true. The passage mentions that bad habits can be harmful, but it also states that good habits can have positive effects. So, saying “habits are harmful” is too broad and not entirely accurate according to the passage.

Statement D is true. The passage mentions that habits can alter your DNA by changing your genome.

Statement E, "The DNA can make your children better or worse", is true. While the passage does not directly state this, it does discuss how our habits can alter our DNA and potentially lead to various health issues. If we consider the broader context of genetics, it is known that parents pass on their genes to their offspring. Therefore, if our habits have altered our DNA for better (through good habits) or for worse (through bad habits), these changes could potentially influence the genetic makeup of our children.

So, the statements A, B, D, and E are consistent with the information provided in the passage, making option D the correct answer.

Note: The question should have been 'epigenetics' instead of 'epileptics' to find the correct answer

Option D is the correct answer.

We can infer this from the sentence, 'Did you know that your daily habits can turn genes on or off? It's known as gene expression or epigenetics.'

The correct answer is option C.

We can infer this from the sentence, 'Bad habits can create long-term stress in the form of financial problems, job loss, health issues, etc.'

Note: The answer options had typographical errors in the original CUET question paper.

Option A is the correct answer.

The passage mentioned that 'Bad habits can turn off good genes and turn on bad genes. Consuming too much sugar is an example of such a bad habit.

Option B is incomplete and wrong.

Options C and D are not inferred directly from the passage.

Option C is the correct answer.

In the given context of the passage, it is mentioned that people came from all places to seek the Wazir’s judgement. The Wazir was known for his wisdom and fair judgement, which is why he was sought after by people from various regions. This implies that he was a ‘wise judge’ (Statement E). 

The other characteristics such as being ‘very famous’ (Statement A), an ‘old judge’ (Statement B), an ‘old Wazir’ (Statement C), or a ‘very patient listener’ (Statement D) are not explicitly stated in the context. Therefore, these statements do not form the basis for people seeking his judgment. Hence, the correct answer is ‘E only’ (Option C). This is because people were drawn to him due to his reputation as a wise judge and not necessarily because of the other characteristics mentioned in the statements.

The correct answer is option D (which is point E only).

The story demonstrates the wisdom and intelligence of the judge, who used a clever method to determine the true owner of the horse.

The other statements do not directly relate to the main point of the story. The beauty of the horse (Statement D) is  mentioned, but it’s not what the story proves. The cleverness of the court (Statement A) or the horse (Statement C) is not demonstrated in the story. While the judge (Statement B) used a clever method, the emphasis of the story is more on his wisdom and intelligence (Statement E). Therefore, the answer is E only.

The correct answer is Option D.

The story suggests that the tall man was impressed by the Wazir’s wisdom in determining the horse's true owner.

The other options (A, C, D, E) are not supported by the details of the story. The tall man was not consoled, embarrassed, undecided, or confused, according to the information provided. Therefore, the answer is Option D, which states B only.

Option B is the correct answer.

Arresting the Other Man (Statement A): The other man's arrest was a consequence of the Wazir’s discovery, not the method of discovery itself. Therefore, statement A is incorrect.

From the Appearance and Good Manners of the Tall Man (Statement B): While the Wazir did note the tall man’s appearance and manners, he did not base his decision solely on these observations. He used them as initial impressions but sought further evidence to make his judgement. Therefore, statement B is incorrect.

By Patiently Listening to the Case of Theft (Statement C): Although the Wazir patiently listened to the case, the listening itself did not reveal the true owner. The discovery was made by observing whom the horse followed. Therefore, statement C is incorrect.

Knowing Whom the Horse Followed (Statement D): This is the key piece of evidence that led the Wazir to the real owner. The horse chose to follow the tall man, indicating a familiarity and bond that typically exists between a pet and its owner.

Leaving the Horse Free (Statement E): The Wazir left the horse free, but this action alone didn’t reveal the true owner. It was a method of gathering more information.

While both actions (D and E) were part of Wazir’s process, the actual discovery of the real owner came from knowing whom the horse
followed (Statement D). Therefore, the correct answer is Option b) D only.

Option A is the correct answer.

Although the passage doesn't explicitly describe the other man, it could be inferred from the story that the tall man was described as well-dressed and soft-spoken, implying that the other man had contrasting characteristics.

The story does not provide information about the other man’s build or manners, so options b), c), and d) are less likely.

The correct answer is option C.

• A. Retreat matches with II. Advance. These are antonyms; ‘retreat’ means to move back or withdraw, while ‘advance’ means to move forward.
• B. Vivacious matches with I. Languid. These are antonyms; ‘vivacious’ means lively and energetic, while ‘languid’ refers to displaying a disinclination for physical exertion or effort; slow and relaxed.
• C. Evidence matches with III. Confutation. ‘Evidence’ supports a claim or argument, while ‘confutation’ refers to the action of proving a statement or theory to be wrong or false.
• D. Exult matches with IV. Lament. These are antonyms; ‘exult’ means showing elation or jubilation, especially as the result of a success, while ‘lament’ is an expression of grief or sorrow.

Option B is the correct answer.

1. Schism—Split: The term ‘Schism’ refers to a division or split, especially one into two groups, caused by a disagreement about ideas, particularly in a religious organization. This is why it matches ‘Split’ from List II.

2. Quixotic—Unrealistic: ‘Quixotic’ is an adjective that describes someone who is overly idealistic, unrealistic, or impractical. It’s often used to describe people who pursue noble ideals but in an infeasible or unrealistic way. Hence, it matches ‘Unrealistic’ from List II.

3. Relegate—Demote: ‘Relegate’ is a verb that means to assign an inferior rank or position to someone or something. It involves lowering someone or something in rank or position. Therefore, it matches with ‘Demote’ from List II.

4. Incognito—Secretly: ‘Incognito’ is an adjective that describes someone who avoids recognition, usually by changing their name or appearance. It’s often used when someone wants to remain anonymous or secret. Therefore, it matches ‘Secretly’ from List II.

Option B is the correct answer.

The original sentence is: "Holding the fatal telegram in her closed first, the distraught mother fell back on the couch."

Using Option B would make it "The distraught mother fell on the couch."

"Fell on" means to collapse or drop onto a surface, which accurately reflects what the mother did in the context of the sentence. The telegram caused her distress, leading her to collapse onto the couch. This option effectively conveys the same meaning as the original sentence without altering it significantly. Thus, option B is the appropriate substitution.

Note: There is typographical error in the question in the original CUET question paper

Option B is the correct answer.

The error in part 2 should be corrected. "Convinced with" is incorrect and should be "convinced of." Therefore, the correct sentence is "The principal was convinced of his innocence in the act." The answer is 2.

Option B is the correct answer.

A. Beneath the skin: The one-word substitution for this is “Subcutaneous.” The term “subcutaneous” refers to something located or occurring under the skin.

B. Too old for work: The appropriate word here is “Superannuated”.The word “superannuated” is used to describe someone who is retired or no longer fit for work due to old age.

C. Wise and full of deep knowledge: The single word that fits is “Sapient”.The term “sapient” refers to someone who is wise, knowledgeable, and possessing great wisdom.

D. One who lives in a cave: The term for this is “Troglodyte”.It describes a person who dwells in a cave or a dark, secluded place. In a broader sense, it can also refer to someone who is reclusive or prefers solitude.

Option C is the correct answer.

A. She despised none of her lovers: This means that she didn’t dislike any of her lovers.

B. She did not despise any of her lovers: This is another way of expressing the same idea as in A.

C. She seldom or ever has sweet talks with her son: This sentence is a bit confusing. The word “ever” seems redundant here. It would make more sense without it: “She seldom has sweet talks with her son.”

D. She seldom or never has sweet talks with her son: This sentence means that she rarely or almost never engages in sweet conversations with her son.

E. He ran fast tremendously: This sentence is grammatically incorrect. The correct form would be: “He ran tremendously fast.”

Therefore, The correct statements are A,B and D

Option B is the correct answer.

When transforming direct speech to indirect speech, you typically shift the verb tenses back one step in time, especially when reporting something that occurred in the past.

In the original direct speech, "passed" is in the past tense. When converting it to indirect speech, we shift the tense of the verb "passed" to its past perfect form "had passed" to indicate that the crisis occurred before the time of the reporting.

So, "ten years ago" becomes "ten years before" to maintain the same relative time frame. Therefore, the correct indirect speech version is:

b) He said that the country had passed through a crisis ten years before.

Option B is the correct answer.

1. Tut! - III. Slight disapproval: Tut is an exclamation used to express mild disapproval or annoyance.
2. Ahem! - I. Express doubts: “Ahem!” is often used to get someone’s attention or to subtly express doubt or hesitation before making a statement.
3. Preto! - IV. While performing a magic trick: This mysterious-sounding word could be uttered by a magician during a performance to add an element of intrigue.
4. Ahoy! - II. Cry of greeting: Sailors and seafarers traditionally use “Ahoy!” as a friendly greeting or to attract attention across distances.

Option B is the correct answer.

The most logical order of sentences to construct a coherent paragraph is:

C. The revolutionary spirit of Netaji was never dampened ever after the surrender of Japan. This sentence sets the stage by highlighting Netaji’s unwavering commitment to India’s cause, even in challenging circumstances.

B. “Japan” surrender is not India’s surrender," he said. This statement reinforces Netaji’s perspective that India’s fight for independence was distinct from Japan’s surrender. It connects to the introduction by emphasizing the need to separate the two events.

D. He knew that a war of liberation demanded great spirit, sacrifice, courage, and patience. This sentence builds on the previous one by explaining Netaji’s understanding of the essential qualities required for a successful struggle for freedom. It connects to the introduction by reinforcing Netaji’s unwavering determination.

A. It was with this invincible spirit that Netaji opposed Wavell’s offer. This final sentence ties everything together by illustrating how
Netaji’s refusal to accept Lord Wavell’s proposal exemplified his unyielding commitment to India’s cause.

Therefore, the correct order is C, B, D, A.

Option A is the correct answer.

Sentence C introduces the context that India has been involved in multiple wars. Sentence A highlights India’s strategic significance.Sentence D specifies the second country involved in multiple wars, and sentence B explains that despite the wars, India did not achieve clear political objectives.

Therefore, the correct sequence is A, C, D, B

Option A is the correct answer.

Option A arranges the sentence parts as follows:

1. Those that have seen the Hindus 
2. P. have naturally no more doubt 
3. S. of their existence than own country 
4. Q. of the existence of other person 
5. R. among them in their own country
6. whom they have met

When we put these together, the sentence reads:

“Those that have seen the Hindus have naturally no more doubt of their existence than own country of the existence of other person among them in their own country whom they have met.”

This sentence means that people who have seen Hindus in their own country have as much certainty of their existence as they do of the existence of any other person they have met in their own country. This makes logical sense and is grammatically correct, which is why option A is the correct answer. The other options do not form a coherent sentence when arranged in the given order.

The correct answer is Option A.

“Cottoned on to”: This informal expression means to realize or become aware of something. It implies that someone has understood a situation, fact, or idea. In the context provided, Mahendra has grasped the fact that the speaker is not interested in his ideas.

Option C is the correct option.

The original sentence contains an error in the subject-verb agreement. The correct form should be “intend” (plural) instead of “intends” (singular) because the subject “candidates” is plural.

Additionally, the pronoun “I” should be replaced with the objective form “me” in this context.

So the revised sentence would be: “All of the candidates except Manindra and me intend to choose cricket as a hobby.

Option A is the correct answer.

• A: The central part of a wheel → II: Hub
• B: Without a body → I: Incorporeal
• C: A great work of art → IV: Magnum opus
• D: A lie told on purpose → III: Perjury

Assume the P and Q investments are $$9x$$ and $$10x$$ respectively.

And their profits are $$4y$$ and $$5y$$ respectively.

Given that P invested for 8 months

So, $$8\times9x=4y$$

or, $$72x=4y$$

$$y=18x$$ . . . (1)

Now assume that Q invested for $$m$$ months

So, his profit $$5y=m\times10x$$ . . . (2)

put eqn (1) in (2) we get

$$5\times18x=m\times10x$$

$$90x=m\times10x$$

$$m=9$$

Hence, the answer is 9 months.

Let us say the sum is X. 

Compound interest at 10% for three years will be, $$((1.1)^{3}-1)X$$=$$0.331X$$

We are told, 0.331X=33100, X=100000

Simple interest on the same sum will be (100000)((10/100)(3))=30,000. 

Hence, the answer is 30,000. 

Let us assume that the interest rate is r. And the principal amount is P. 
The sum after three years would be, $$P\left(1+\frac{r}{100}\right)^3$$, we are told that this value is 13380. 

Similarly, the sum after six years would be, $$P\left(1+\frac{r}{100}\right)^6$$, we are told that this value is 20,070. 

Let us divide the latter by the former, we get, 

$$\frac{P\left(1+\frac{r}{100}\right)^6}{P\left(1+\frac{r}{100}\right)^3}=\frac{20070}{13380}=1.5$$

Therefore, $$\left(1+\frac{r}{100}\right)^3=1.5$$

Substituting this value in the first equation we have, $$P\left(1.5\right)=13380$$

We get P = 8920. 

Hence, the answer is Option D. 

Let us say the vendor bought 24 apples. Since he is buying them at a rate of 8 apples for 12 rupees, the total price he would have paid is 36 rupees. 
While selling these 24 apples, he is selling them at a rate of 6 apples for 10 rupees. The total money he would receive from the sale is 40 rupees. 

Profit made is 4 rupees. 

Profit percentage will be (4/9)(100)=11.11%

We are given that the list price of the trouser is ₹300, and after two successive discounts, the final price is ₹210. The second discount is 12.5%.

Let the first discount be x%

After the first discount, the price becomes $$300\times\left(1-\dfrac{x}{100}\right)$$

After applying the second discount of 12.5%, the price becomes $$300\times\left(1-\dfrac{x}{100}\right)\times\ 0.875\ =\ 210$$

Upon solving, we get x = 20

Let us assume the total amount of marks is X. 

If P scores 30% of the marks, P will score 0.3X. And we are told that this is 30 marks less than the passing marks. 
So, Passing marks will be 0.3X+30.

And at the same time, we are told that with 40% of the marks, Q got 40 more marks than the passing marks. 
So, Passing marks will be 0.4X-40

Equating the two equations, we get X = 700. 

Passing marks will be 240. 

The percentage required to pass will be 240/700. Which is 12/35 or 34.28%. 

Let the income of the person be 2S; if he spends 50% of it, then he is saving 2S - S = S.

If his income increases by 20%, then the income becomes $$2S\ +\ \dfrac{20}{100}\left(2S\right)\ =\ \dfrac{12}{5}S$$

Initially, his expenses were S, and if they increase by 10%, the expenses become $$S\ +\ \dfrac{10}{100}\left(S\right)\ =\ \dfrac{11}{10}S$$

So, his savings in the second case  = $$\dfrac{12}{5}S\ -\ \dfrac{11}{10}S\ =\ \dfrac{\left(24\ -\ 11\right)}{10}S\ =\ \dfrac{13}{10}S$$

The savings increased by a percentage of $$\dfrac{\left(\ \dfrac{13}{10}S\ -\ S\right)}{S}\times\ 100\ =\ \dfrac{3}{10}\ \times\ 100\ =\ 30\%$$

Hence, the correct answer is option B.

Let the volume of the tank be 6V litres. 

If the pump takes 2 hours to fill the tank, then the capacity of the pump is $$\dfrac{6V}{2}=\ 3V\ $$litres/hour.

In 2 hours 20 minutes $$\ =\ 2\ +\ \dfrac{20}{60}\ =\ \dfrac{7}{3}$$ hours, the water produced by the pump is $$3V\ \times\ \dfrac{7}{3}\ =\ 7V$$.

We know that the tank has a volume of 6V litres. So, the leak in $$\dfrac{7}{3}\ $$hours removed 7V - 6V = V litres of water. So, in 1 hour, the leak removes $$\dfrac{3V}{7}$$ litres.

The capacity of the leak is $$\dfrac{3V}{7}$$ litres/hour. So, the time taken for the leak to empty the whole tank is 

$$6V\ \times\ \dfrac{7}{3V}\ =\ 14$$ hours.

Hence, the correct answer is option A.

Let the speed of the lady be 4S and the time taken to reach the office be T. 

So, the distance can be calculated as 4S * T = 4ST.

In the second case, when she walks at 3/4 of her speed, the speed of the lady becomes 3S. The time taken is given as T + 30. 

So, the distance covered in this case is 3S * (T + 30) = 3ST + 90S.

We know that the distance to the office remains constant and must be the same in both cases. 

Equating them, we get,

4ST = 3ST + 90S

ST = 90S

T = 90 minutes.

So, the usual time taken by the lady is 90 minutes.

Hence, the correct answer is option C. 

Given that the bus covers 1125 km in 15 hours

So, the speed of the bus is $$\dfrac{1125}{15}=75$$

Given that avg. speed of car is one-third that of the bus

So, avg speed of car is = $$\dfrac{75}{3}=25$$

The distance it will cover in 30 min or half hour is $$25\times\dfrac{1}{2}=12.5$$ km

Hence, the answer is Option B

Firstly, we can solve this question by assuming that the length of the man is negligible and that only the length of the train matters. 
If the man and the train move in opposite directions, the relative velocity will increase.

200m is 0.2km. The speed of the train is 50 kmph, and that of the man is 5 kmph. 
Effective relative velocity will be 55 kmph.  

Time taken to cover 0.2km will be 0.2/55=1/275 hours. 

An hour has 3600 seconds. 3600/275=144/11 seconds. 

Hence, the answer is Option C. 

P and B can do the work in 10 and 15 days, respectively. 

Let the total units of work be LCM(10,15) = 30 units.

So, P can do 30/10= 3 units per day

B can do 30/15 = 2 units per day

If they work together, they would do 3+2 =5 units per day.

Therefore, in 5 days, they will do $$5\times\ 5=25\ $$units

Then Work left = 30-25 = 5 units.

R can do this work in 2 days, therefore he does 5/2 = 2.5 units per day.

If they are getting Rs.1500 for 30 units of work, then they get $$\ \frac{\ 1500}{30}=Rs.\ 50$$ per unit.

B and R will do 2 + 2.5 = 4.5 units per day. 

Therefore, they will earn $$4.5\times\ 50$$= Rs. 225

Let us say the work is 36 units big. 
This means that P, who can finish the work in 9 days, does 4 units a day, and Q, who can finish the work in 12 days, does 3 units a day. 

Working alternatively means that every two days (4+3) units of work will be done. 
So, 5 cycles of this will ensure 35 units of work is completed, 5 cycles means 10 units of work. 
The last unit is completed by the person who starts work first, which is P. P does 4 units a day so that P can finish 1 unit in 0.25 days. 
Hence, the answer will be 10.25 days. 

Assume that A, B and C can do $$a$$, $$b$$ and $$c$$ units of work per day.

So, the total work is $$10\times\left(a+b\right)=10a+10b$$ . . . (1)

Similarly, the total work is $$15\times\left(b+c\right)=15b+15c$$ . . . (2)

Equate eqn(1) and eqn (2) we get

$$10a+10b=15b+15c$$

Given that A is twice as good a workman as C or $$a=2c$$

Putting in above equation we get

$$20c+10b=15b+15c$$

or, $$5c=5b$$

or, $$b=c$$

So, the efficiency of B and C is the same

If they together complete the work in 15 days, B alone will complete it in 30 days.

The average of ten numbers is 8. If each number is multiplied by 15, then the average of the set of numbers is:

Let us assume the numbers are $$x_1,x_2,......x_{10}$$

Thus, $$\dfrac{x_1+x_2+x_3+....x_{10}}{10}=8$$

Each number is multiplied by 15, So the average will also be 15 times.

$$\dfrac{15\left(x_1+x_2+x_3+....x_{10}\right)}{10}=15\times\ 8\ =\ 120$$

The average of the men is solely changing due to the change in the weight of the person being replaced. No other person in the group is coming in or going out. 
This means the change in the average of 1.5kg, which is calculated over 10 men, is solely due to the heavier person coming in. 
The change in average is 1.5kg, which means the change in the total amount of weight will be 15 kg.

This means the new man coming in is 15kgs heavier than the old man. The old man weighs 70kgs, this means the new man will weight 85kgs.   

Let the four consecutive even numbers be A, B, C and D.

Since they are consecutive even numbers, we can express them in terms of A as:

B = A + 2

C = A + 4 

D = A  + 6 

We are given that their average is 61.

Hence, ( A + B + C + D)/4 = 61

Or, A + B + C + D = 244

Replacing B, C and D

A + A + 2 + A + 4 + A + 6 = 244

4A = 232

A = 58

Hence, B, C and D are respectively 60, 62 and 64.

We need to find A * D

Hence, 58 * 64 = 3712

Let the cost price of 1 litre of milk be C

Now, assume that we mix x litres of milk with y litres of water.

The total cost price of the mixture = C × x (water is free).

The selling price must be 16.67% more than the cost price, i.e. 7/6 of the cost price

For the mixture to sell at the cost price per liter, the selling price should be equal to the cost price per liter.

Solving the equation, we get, x : y = 6 : 1

To find the probability of getting at most three heads, we will use the complement rule (P(not A)

At most three heads means we can get 0, 1, 2, or 3 heads.

The complement of this event is getting exactly 4 heads.

Since four unbiased coins are tossed, the total number of possible outcomes is:

2^4 = 16

The only way to get 4 heads is HHHH, which is 1 outcome.

P(exactly 4 heads)=1/16

P(at most 3 heads)=1−P(exactly 4 heads)

=1−1/16 = 15/16

DETAIL is a six-letter word with three vowels and three consonants. 
This means there will be three odd places and three even places. 
This means we must fit the three vowels in the three odd places. And the three consonants can fit into the three even places. 
The number of ways to arrange three items in three places will be 3!. 

We can arrange three vowels in three odd places in 3! ways, and three consonants in three even places in 3! ways. 

Total ways to arrange it will be (3!)(3!)=36. 

In triangles, the length of the sides is proportional to the sine of the angle opposite to the. 

The angle opposite AB is 55 degrees while the angle opposite BC will be 45 degrees. 

Since sin 55 > sin 45, AB>Bc

Therefore, Option A is the correct answer. 

The volume of a cone can be written as $$\pi r^2h$$. 
Where r is the radius of the base of the cone and h is the height of the cone.

The heights of two right circular cones are in the ratio 1 : 2, 
Let us say, H1 is 1X and H2 is 2X

Perimeters of their bases are in the ratio 3 : 4, 
Let us say, $$\2pi r_1$$ is 3Y and $$\2pi r_1$$ is 4Y. 

$$r1=\frac{3Y}{2\pi\ }$$ and $$r2=\frac{4Y}{2\pi\ }$$

Volume of cone 1 will be, $$\pi\left(\frac{3Y}{2\pi\ }\right)^2\left(X\right)$$

Volume of cone 2 will be, $$\pi\left(\frac{4Y}{2\pi\ }\right)^2\left(2X\right)$$

The ratio will hence be 9:32. 

The surface area of a sphere is, A = $$4\pi r^2$$

Let the radii of the two spheres be a and b. Given that their surface areas are in the ratio:

A1:A2= $$\dfrac{4}{25}$$

Substituting the formula for surface area:

$$4\pi a^2$$:$$4\pi b^2$$ = 4:25

Canceling 4π from both sides:

$$a^2:b^2=4:25$$

Taking the square root on both sides:

a:b = 2:5

Now, the volume of a sphere is V = $$\dfrac{4}{3}\pi r^3$$

The ratio of their volumes is:

V1:V2= $$a^3:b^3$$ = 8:125

Let's rewrite the equation:

$$a^2+\dfrac{1}{a^2}+b^2+\dfrac{1}{b^2}=4$$

We know that $$x^2+\dfrac{1}{x^2}\ge\ 2$$

If we compare, we get,

$$a^2+\dfrac{1}{a^2}=\ 2$$ and $$b^2+\dfrac{1}{b^2}=\ 2$$

This is possible when $$a^2=1\ \&\ b^2=1$$

Hence, $$a^2+b^2\ =\ 1\ +\ 1\ =\ 2$$

a + b + c = 6
Squaring on both sides:
$$a^2+b^2+c^2+2\left(ab\ +\ bc\ +\ ca\right)=36$$.
$$a^{2} + b^{2} + c^{2} = 14$$
This gives: ab + bc + ca = 11.
$$a^3+b^3+c^3-3abc=\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ca\right)$$
Putting in all the given values, we get:
36 - 3abc = 6(14 - 11)
abc = 6.

$$2x^{2} + 3x - 35 = 0$$

This can be written as

$$2x^2+10x-7x-35=0$$

$$2x\left(x+5\right)-7\left(x+5\right)=0$$

$$\left(2x-7\right)\left(x+5\right)=0$$

Thus, x = 7/2 or -5

Similarly, for $$4y^{2} + 10y - 104 = 0$$

This can be written as

$$4y^2-16y+26y-104=0$$

$$4y\left(y-4\right)+26\left(y-4\right)=0$$

y = 4 or -26/4

Therefore, x and y are unequal, and no relation can be established between them.

The given information can be shown in an image as follows,

We can see that for the outer square, the length of the side is equal to the diameter of the circle. So, the side of the outer square is 2a, and the area of the outer square is $$2a\ \times\ 2a\ =\ 4a^2$$

We can see that for the inner square, the length of the diagonal is equal to the diameter of the circle. So, the area of the inner square is $$\dfrac{1}{2}\ \times\ 2a\ \times\ 2a\ =\ 2a^2$$.

So, the difference between the areas of the outer and the inner squares  = $$4a^2\ -\ 2a^2\ =\ 2a^2$$

Hence, the correct answer is option B.

If PQ and RS are two diameters of a circle of radius r, then they are mutually perpendicular.

RS = 2r (Where r is the radius of the circle)

RP = RS = $$r\sqrt{2}$$

Area of circle = $$\pi r^2$$

Triangle SPR is a right-angled triangle, right-angled at P.  (Angle RPS is 90 degrees as RS is the diameter)

Area of $$\triangle PRS$$ = $$\dfrac{1}{2}\times PR\times\ PS$$ = $$\dfrac{1}{2}\times r\sqrt{2}\times\ r\sqrt{2}$$ = $$r^2$$

Thus, the ratio is $$\pi r^2$$:$$r^2$$ = $$\pi:1$$

The value of $$\dfrac{1}{4 \times 5} + \dfrac{1}{5 \times 6} + \dfrac{1}{6 \times 7} + ....... + \dfrac{1}{10 \times 11}$$:

The terms can be written as

$$\Sigma\ \dfrac{1}{\left(n+3\right)\left(n+4\right)}$$

=> Where sigma means the summation of all terms where n = 1 to n = 7

$$\Sigma\ \dfrac{1}{\left(n+3\right)\left(n+4\right)}$$

=> $$\Sigma\ \dfrac{\left(n+4\right)-\left(n+3\right)}{\left(n+3\right)\left(n+4\right)}$$

=> $$\Sigma\ \left[\dfrac{1}{\left(n+3\right)}-\dfrac{1}{\left(n+4\right)}\right]$$

=> $$\dfrac{1}{4}-\dfrac{1}{5}$$ + $$\dfrac{1}{5}-\dfrac{1}{6}$$ + .....$$\dfrac{1}{10}-\dfrac{1}{11}$$

=> All other terms will get cancelled, and only 1/4 and -1/11 will left.

Thus, $$\dfrac{1}{4}-\dfrac{1}{11}=\dfrac{7}{44}$$

We know that $$\left(a\ +\ b\right)^2\ -\ \left(a\ -\ b\right)^2\ =\ 4ab$$

So,

$$\left(x\ +\ \frac{1}{x}\right)^2\ -\ \left(x\ -\ \frac{1}{x}\right)^2\ =\ 4\times\ x\ \times\ \frac{1}{x}\ =\ 4$$

$$\left(x\ -\ \frac{1}{x}\right)^2\ =\ \left(\frac{17}{4}\right)^2\ -\ 4$$

$$\ \left(x\ -\ \frac{1}{x}\right)^2\ =\ \frac{\left(289\ -\ 64\right)}{16}\ =\ \frac{225}{16}$$

$$\ x\ -\ \frac{1}{x}\ =\ \frac{15}{4}$$

Hence, the correct answer is option B.

Let the number of 1-rupee coins, 50-paise coins, and 25-paise coins in the bag be 5x, 6x, and 8x respectively, where x is a common factor.

The total value of the coins is ₹250.

The value of 1-rupee coins = 5x × 1 = 5x rupees.

The value of 50-paise coins = 6x × 0.50 = 3x rupees.

The value of 25-paise coins = 8x × 0.25 = 2x rupees.

The total value is the sum of all these values:

5x + 3x + 2x = 250

10x = 250

x = 25

Number of 50-paise coins = 6 × 25 = 150

Assume the money with P, Q, R and S to be $$3x$$, $$4x$$, $$9x$$ and $$10x$$ respectively.

So, the difference between R and Q is $$9x-4x=5x=2580$$

or, $$x=516$$.

So, the total amount with Q and S together is $$4x+10x=14x=7224$$

Hence, the answer is 7224.

Given that the total number of marbles is 15 and we have to select 4 of them

Probability of Selecting atleast one red marble = 1 - Probability of selecting no red marble

P(No red marble) = $$\dfrac{^{11}C_4}{^{15}C_4}=\dfrac{330}{1365}$$

So, P(Atleast one red marble) = $$1-\dfrac{330}{1365}=\dfrac{1035}{1365}=\dfrac{69}{91}$$

Hence, the answer is $$\dfrac{69}{91}$$

He sold X quantity at 8% profit and (500-X) at 18% profit. 

Total money received after sale will be, 
(1.08)(X)+1.18(500-X)=1.14(500)

1.08X+590-1.18X=570
20=0.1X

X will be 200kg. 

Hence, the quantity sold at 18% profit will be 300kg. 

The number of ways to select a committee of 5 members consisting 3 men and 2 women are,

Selecting 3 men out of the 7 men in $$^7C_3\ =\ 35$$ ways

Selecting 2 women out of the 5 women in $$^5C_2\ =\ 10$$ ways

Total number of ways = 35 * 10 = 350 ways.

Hence, the correct answer is option D.

To find the odd group, let us check each option-

A) 2, 3, 5, 7 → All are prime numbers.

B) 17, 19, 23, 29 → All are prime numbers.

C) 53, 59, 61, 67 → All are prime numbers.

D) 37, 41, 43, 49 → 49 is not a prime number (since 49=7*7)

Since all other groups consist entirely of prime numbers, the odd group is D) 37, 41, 43, 49, because 49 is not a prime number.

63 is the only number in the group of given numbers that is not prime. 
71, 23, 17, 13, all of them are prime numbers. 

The person started walking from S and stopped at E.
To calculate SE, we need to find the length of hypoteneuse in the triangle SAE where SA = 5 m and AE = 30 - 15 - 10 = 5 m.
Length of SE = $$\sqrt{\ 5^2+5^2}=5\sqrt{\ 2}$$ m.

80 = $$9^2-1$$
? = $$100^2-1=9999$$.