SRCC GBO 2022 Question Paper

Option D: Correct.

 This is a direct question that can be answered by pointing to the sentence in the passage that discusses the drawbacks of solar paint. The second sentence of the second paragraph, "Despite the promise of solar paint, there are still some problems. While the paint only converts about one per cent of light to energy..." answers the question. 

From here, we know that the only disadvantage of the solar paint mentioned in the passage is that it converts about one per cent of light to energy.

Option A: Incorrect. There is no mention of the manufacturing time of the solar paint.

Option B: Incorrect. The cost of paint is not mentioned, but a low cost is an advantage.

Option C: Incorrect. The second paragraph, in fact, mentions that scientists are actively working to improve quantum dots. There is no mention that the scientists cannot achieve the same.

Option C: Correct. It is mentioned a couple of times in the last paragraph that discusses WtE method that the problem it causes is of "pollution". As visible through the direct sentences from the passage: "the burning process causes pollution and creates more problems. ..."
"these types of energy plants still emit carbon dioxide (CO2), which contributes to other environmental problems..."

Option A: Incorrect. Though it might seem relevant to the passage but notice the word that has been used in the passage, that is, controversial; "Waste to Energy plants remain somewhat controversial among scientists and environmental activists...." a controversy does not imply a debate and moreover the scientists and environmentalists both agree upon the fact that WtE method causes pollution.

Option B: Incorrect. Energy efficiency of WtE plants is not discussed at all.

Option D: Incorrect. New types of WtE plants is infact neither a proposed solution nor a problem in fact the passage mentions that new types of WtE plants still cause the same pollution problem; Some new energy plants use a cleaner method of converting waste to energy. However, these types of energy plants still emit carbon dioxide (CO2),...

Option B: Correct. Looking at the question stem is necessary here to eliminate other likely answers. The question stem is what the author "suggests" in the last paragraph, so we have to look at inferences rather than facts from the same. From the last paragraph; "Building the turbines on the ocean is more effective than building them on land because there tends to be a steadier and stronger wind on the ocean....." and the passage also ends with highlighting the advantage of floating wind farms. That is what the author is suggesting, remaining things are facts.

Option A: Incorrect. Though the last paragraph does mention this particular fact but it is not what the author suggests, hence it does not answer the question stem.

Option C: Incorrect. No where in the passage it is mentioned that there will be lesser floating wind turbines in the future.

Option D: Incorrect. This will appear as a strong contender for the right answer, it fits the question stem as well, but, notice the use of the word "must"- it is an extreme word and the author is merely suggesting that building wind farms on ocean will help save space for crowded countries. Moreover, the option says wind as a source of energy saves space, whereas floating wind farms save the space as clearly mentioned in the last line of the passage. 

To answer this particular question we have to just focus on the relevant paragraph that talks about conventional energy sources as asked.

Option D: Correct. "Traditional energy sources such as oil and natural gas are dwindling rapidly...." directly mentioned in the first paragraph.

Option A: Incorrect. "Disappeared" serves as a wrong and an extreme word here. The conventional energy sources have dwindled, not disappeared.

Option B: Incorrect. It is nowhere mentioned that the traditional energy sources have become more easily available.

Option C: Incorrect. The passage mentions that the extraction of these resources is at the expense of environment, this does not imply that they are difficult to extract. "In many countries, this has meant extracting natural resources at the expense of the environment..."

We have to look into the paragraphs talking about fables and understand what a fable does as the question stem is "objective" of a fable.

Option B: Correct. As we skim through the lines mentioning what does a fable do, we find; "The purpose of a fable is to convey moral messages to the readers ..." this line particularly mentions the clear objective/ purpose of a fable which is to convey moral messages which ultimately aim at upliftment of character, this option fits and no other options fit the objective of moral teachings.

Option A. Incorrect. Though a line mentions about the role of animals and birds in fables that; "The purpose of a fable is to convey moral messages to the readers and this objective is usually achieved through animals, birds or trees..." but here the animals and birds and trees are used a "medium" to convey moral messages, they are not the message being conveyed.

Option C: Incorrect. No where the problems of contemporary society is mentioned or discussed.

Option D: Incorrect. No where the past is mentioned or discussed.

Here since a line from the passage is mentioned, we trace where it is exactly present in the passage and skim around it to understand its implication.

Option D: Correct. The line clearly talks about how a fabulist dons many hats and sounds appreciative of the fabulist. Since a fabulist is a writer and their writing fulfills many purposes, this option fits well.

Option A: Incorrect. There is no mention of the need for more fabulists even though the passage appreciates their role.

Option B: Incorrect. Fabulists must be honored can be a correct inference, but, they must be respected "above" other writers is a wrong and extreme implication that is not mentioned.

Option C: Incorrect. The passage does mention that a fabulists is  multifaceted, but to infer that they can replace teachers is not right, neither is it mentioned in the passage.

To answer this question correctly we have to navigate to the part of the passage that talks about parables and tales. 

Option A: Correct. The line where comparison is drawn between fables, tales and parables, it is mentioned about fables that; "It will contain, like the tale, a short but real narrative; it will seek, like the parable, to convey a hidden meaning..." This line draws the difference between a tale and a parable- that is a parable has a concealed or a hidden meaning while a tale does not have it, a tale has short and real narrative.

Option B: Incorrect. Depiction of facts is not a difference between a tale and a fable. As mentioned in the passage both tale and parable are narration of stories through different methods.

Option C: Incorrect. Length of the narrative is not mentioned as a comparative point between a tale and a fable.

Option D: Incorrect. The choice of characters is not mentioned as a difference between tale and fable, in fact choice of characters is mentioned with regards to fables, which has animals, birds and trees. 

To answer the "main idea" of the passage, we must skim through and especially focus on the first and the last paragraphs, and try to compare options and then choose the best fit.

Option B: Correct. "It is in this that the fable scores a point over the tale and the parable...." This is directly mentioned in the passage and it says that fable is superior to tale and parable, preceded by an explanation for the same. The other parts of the passage talk about the qualities of a fable after introducing what tales, parables and fables are. Hence, the passage builds up to the main idea of how fables are better.

Option A: Incorrect. The passage does indirectly imply that each of these formats is distinguished, creative pursuits and hence should be respected. But, it is not explicitly mentioned, and hence it cannot be the "main idea".

Option C: Incorrect. The purpose of a fable is to convey moral messages to the readers ...it is mentioned that conveying moral messages is in fact purpose of a fable and that these messages maybe hidden is not stated in the passage. Moreover, this is not the main idea of the passage. As the passage is more focused on the "qualities of the fable".

Option D: Incorrect. The main idea of the passage is not to highlight the main difference between the three modes. They are introduced to build to the fact that how fables are better. Moreover, the difference between the three is not in the portrayal of characters but in their objectives and styles. 

To answer the "main idea" of the paragraph correctly, we have to skim through the passage and especially pay attention to the concluding paragraph, and make sure it is encapsulated in the main idea answer.

Option C: Correct. The passage mentions about "subnivium" which is the hidden world beneath snow, the concluding paragraph mentions that climate change is adversely affecting winter snow. This option encapsulates both the aspects and hence, is right.

Option A: Incorrect. "Thanks to the emerging field of winter ecology, we now know that snowy environments have lives of their own..." this line does mention that winter ecology which has subnivium is an emerging field and new researchers are studying it- the paragraph does not explicitly mention any "creative approaches", moreover, it is not the main idea, it is used to introduce a topic.

Option B: Incorrect. The last paragraph mentions sufficient information about survival of plants and animals beneath the snow and nowhere it is mentioned in the passage that we know "very little" about them.

Option D: Incorrect. It is not mentioned that the field of "winter ecology" has emerged because of climate change. Winter ecology is also mentioned above as a field to study subnivium as well. So it is clear that winter ecology as a field did not emerge to study climate change as it studies other things as well.

Option C: Correct. The last paragraph mentions how the snow cover in winter helps in the survival of many life forms like - fungi, invertebrates, soil bacteria and plant roots-...the paragraph also mentions about climate change but we have to analyse and compare other options as well and check if they are right inferences.

Option A: Incorrect. There is no mention of animals feeling "more comfortable" during snowfall.

Option B: Incorrect. It is mentioned that the tiniest lifeforms can survive beneath snow and fulfill their nutritional requirements but it is not mentioned that they "depend" upon frozen surfaces for their food, moreover there is no mention of large lifeforms specifically.

Option D: Incorrect. The temperature in subnivium is higher than that of the frozen surface, it is mentioned. But, it enables the organisms to survive.

We have to focus primarily on the last paragraph here.

Option B: Correct. The last paragraph talks about the impact that climate change will have on the subnivium and that it is being studied "climate change is upsetting that chilly balance. Winter ecologists are studying how the lack of snow cover directly affects the ecology of many subnivium ecosystems...". Hence, it is the right answer.

Option A: Incorrect. The statement might be right, but the last paragraph does not talk about access to water resources at all.

Option C: Incorrect. The paragraph does not mention the mechanism of the formation of subnivium at all.

Option D: Incorrect. While the statement might be true but this statement is not being discussed in the last paragraph. 

To answer this question focus on what the second paragraph is talking about. 

Option C: Correct. The second paragraph mentions how the traditional belief that snowy environments are inactive is challenged through the study of winter ecology, which shows that snowy environments "have lives of their own". As depicted by the extract;" This microhabitat turns traditional thinking about snow on its head...."

Option A: Incorrect. It is nowhere mentioned that the winter ecologists do not know much about the subnivium, neither a reasoning for the same is provided.

Option B: Incorrect. It is nowhere mentioned what is the best time to see the subnivium.

Option D: Incorrect. It is nowhere mentioned that there was ever any reason because of which scientists did not study the winter environment. The passage does mention that this study field is fresh and there were traditional beliefs about the winter environment, but no historical reasons are provided for not studying the field earlier. 

Option B: Correct. Swim "across" the English Channel is correct because, across is the preposition that indicates movement from one side to another, which is what swimming is. Hence, it is the most appropriate.

Preposition "over" refers to movement to a "higher level". Hence, it is not right, since swimming is sideways movement.

Preposition "against" refers to moving opposite something. Like against the river current. Hence, it is not valid here.

Preposition "through" refers to movement from one side to another, in an enclosed space. Since English Channel is not enclosed, hence through is not valid here.

Option C is the most appropriate choice because it provides additional information that directly supports the context of the paragraph.

Throughout the paragraph, the focus is on the revival of businesses in 2021 and how companies have been investing in up-skilling and re-skilling their workforce. The missing sentence needs to complement this theme by providing more details about where these investments have been directed.

Option C does exactly that by specifying some of the sectors where these investments have increased, such as IT, e-commerce, pharma, and EdTech. By mentioning these sectors, it gives a clearer picture of where the up-skilling efforts have been concentrated, highlighting areas of growth and importance in the business landscape during the specified time period.

Therefore, Option C serves to enhance the coherence and relevance of the paragraph by providing specific examples that align with its central theme.

Option D: Correct.

From the first glance we can understand that the paragraph is talking about an action that has happened in the past and the impact of which is in the present. In such cases "Present Perfect" tense and its forms are used.

has returned- present perfect

has been trying- present perfect continuous 

Option C: Correct.

It is known that "opportunity knocks" is a common phrase. Hence, it is the right choice for the first blank.

The partner choice for the second blank "convert" also fits as "convert to success"

Option A: Correct.

Sumptuously, plentiful and richly are all synonymous- as they all mean- "in abundant quantity"

Selectively, is the odd one out as it means- choosing few things among other many things.

Option B: Correct.

This question uses common phrases/ idioms

The right idioms used here are- ruffled the feathers, cool their heels and cool it.

Now we have to use the right combination on the basis of the sentence. 

Ruffled the feathers is appropriate for the first blank because it means "to annoy" or "upset".

Cool their heels means to wait for a significant amount of time, mostly for someone else, therefore cool their heels is a misfit here, since the members are likely being asked to calm down and not wait.

Cool it means to calm down and hence it is the right choice.

Option C: Correct. 

We have to first understand and make a rough sense of what the entire paragraph is trying to convey. We can understand that it talks about seeing a strange animal -> describes the strange animal -> tells the purpose/ function of that animal -> as given in the final sentence; ascertains what the animal is.

The first sentence mentions that a man was noticed by the gaoler, so the follow up sentence should be "B. The gaoler sent for him and I saw something between a lizard and crocodile, about two feet long with claws and a scaly covering." Him being the cue here, it is naturally the follow up sentence.

The next sentence following the end of the previous sentence should describe how the animal looked, which is done by option A.

Since there is one more sentence further explaining the features and appearance, so the next sentence would be D.

The sentence C fits at last, which describes, what is supposed to be done with the animal, after its features and appearance are described.

Option A: Correct.

Saunter, Amble and Stroll, all three are synonymous, meaning "to walk in a slow or relaxed manner."

Hence, option A, scurry is the odd one out, which is an antonym of these words and means; "to walk rapidly".

Option A: Correct.

Despite her busy schedule is the correct sentence. Despite is never followed by "of". 

Option A: Correct. 

Impenetrable means something that cannot be "passed through" or hard to get through.

Impassable means the same thing.

Also note that in vocabulary knowing what certain prefixes mean, can assist in predicting word meanings.

The prefix "im" used here means- "not", "without", "opposite of".

Option D: Correct.

Understanding the meaning of idioms and phrases is the key to this question. Also, identifying, if the idiom is correct is important.

On the air- broadcasting

On the cards- a future event likely to happen

On call- being available usually outside the designated working time

On the boil- on the verge or at peak

So, option D fits best, as the sentence tries to convey that a new project in Central Delhi is being worked upon and the speaker's father is expected to be available even on the weekends. 

Option A: Correct. 

To describe a planned action happening tomorrow.

A combination of present perfect and future tense will be used.

has promised- present perfect tense

will drop- simple future

Option A: Correct.

The third sentence or sentence C is an outlier.

The paragraph is clearly talking about literacy rates in the country and how many of literates are present gender wise. 

The sentence talking about Panipat city is irrelevant here.

Option B: Correct.

This question is about understanding that when a sentence refers to a person, grammatically "which" is never used for a person, it is used for things. "Whom" is how a person should be referred to. This information, eliminates all other options. 

Option C: Correct.

Understanding the tone of the sentence is the key here.

When referring to an economic crisis, followed by a comment about expenditure, it becomes clear that the expenditure at the time of crisis will be condemned, criticized or questioned upon. 

The only option doing so is C.

Going through the sentences, we can see that C sets the context of the discussed event. 

A and D would make a good chronological pair; the ostrich and emu fell into the pit (A), and then they tried to jump out of the pit but could not as it was too deep (D)

B serves as the conclusion of the paragraph, as after the ostrich and emu were trapped in the pit, their squawking brought other animals to the pit. 

CADB is the sequence in these sentences that should be arranged in order to make a logically coherent paragraph. 

Therefore, option C is the correct answer. 

Option A: Correct.

Going through the options we can clearly see that humane, patient and forgiving are all words denoting positive aspects of a person's nature.

Vicious is hence the odd one out. 

Vicious means deliberately cruel, but even if one does not know the meaning, one can eliminate it by grouping other similar words together.

Option A: Correct.

Understanding the meaning of the phrases is the key here. 

When something is being passed from generation to generation, it indicates, that it is "passing down", because there is a transfer from a senior to new comer, indicating a hierarchy. 

Hence, handed down is the right choice here.

Option D: Correct.

Knowing the meaning of the word in the question is the key to answer here.

Repulsive means to be drawn away from, disinterest. 

Attractive is hence the right choice since it means being drawn towards something. 

Option B: Correct.

Knowing the meanings is important here.
Contemplate means to think or ponder upon something, hence the word consider is closest in meaning to it, and is therefore the synonym. 

Option A: Correct.

Understanding the relationship between the words in the question is the key here.

Drum: Beat means - a drum which is an instrument is beaten (an action) to generate sound/ effect, that's how a drum functions.

Similarly among the options, Trumpet: blow means - a trumpet which is an instrument is blown (an action) to generate sound/ effect, that's how a trumpet functions.

The other options rightly place the instruments but they are not followed by actions that generate sound from them, but, rather, the objects or body parts used to play them, hence they are incorrect.

Statements B, C, and D talk about how attendance in India has increased overall, with B providing a good introduction to the topic and D expanding the discussion to include even the rural areas. 

Statement A, on the other hand, talks about how teacher attendance is low. This not only introduces the context of teachers being considered in terms of attendance but also goes against the general theme of attendance records improving. 

Hence, Statement A is out of context among the given sentences.

Therefore, Option A is the correct answer. 

Statement B sets the passage's context: an English passenger drawing someone into a conversation.
The natural follow-up to this is statement D, which clarifies what conversation is being talked about here.

At this point, we can mark option C as our answer, but it is always good to look at the complete sequence and see if it is logically coherent. From D, we go to A, which mentions one more thing the Englishman brought up during his conversation; after which comes statement C, which continues with the responses to the previous question posed by the Englishman. 

BDAC is a logically coherent sequence

Therefore, Option C is the correct answer. 

To solve this analogy, we need to understand the relationship between "shrug" and "indifference."

A shrug is a gesture that typically expresses indifference.
We need to find a pair where the first word is a gesture that typically expresses the second word.

Let's analyze the options:

A wave : fatigue - A wave is a gesture that does not typically express fatigue.
B blink : scorn - A blink is an involuntary action, not a gesture expressing scorn.
C scowl : desire - A scowl is a facial expression that typically expresses anger or displeasure, not desire.
D nod : assent - A nod is a gesture that typically expresses assent (agreement or approval).

Hence, only the relationship in option D matches the relationship in the given pair: a gesture expressing a specific feeling or state.

Therefore, option D is the correct answer. 

The phrase "good classroom strategies encourage" should be "good classroom strategies that encourage" or "good classroom strategies to encourage"

Hence, this part of the sentence is incorrect and therefore, Option D is the correct answer. 

Option A: "for which she has applied"; this option correctly uses "for which" to refer back to the secretarial job. It indicates that she has applied for the job. The preposition "for" is necessary here to indicate the action of applying for something.

Option B:  "which she has read" The phrase "which she has read" suggests she simply read the advertisement but does not imply any further action.

Option C: "That she bought." this option is incorrect because it does not make sense in the context of a job advertisement. You cannot buy a job. 

Option D: "for which she has written." this option could make sense in a different context, such as if she wrote the job advertisement herself. However, it does not fit the common scenario where someone applies for a job. The typical and expected action related to a job advertisement is applying, not writing the advertisement.

Overall, A would be a better fit over D

Therefore, Option A is the correct answer. 

Option C: Correct.

The correct usage of prepositions is the key here.

We can take up the second blank first and understand that if one is resting in the periphery of a tree, one rests "under" it, so now we are left with option C and D. 

Now we check the first blank. Feeling tired "after" a long journey is right. 

Option A: drop off means to take someone or something to a particular place, usually by car, as you travel to a different place

Option B: drop by means to pay a brief, casual visit

Option C: drop out means to withdraw from participation or membership

Option D: Drop-in means to come for a visit, especially without having received an invitation for a specific time

Of all the given options, only option C fits in the context of the sentence, implying that every year, some boys, stop their participation or leave in the middle of the course. 

Therefore, Option C is the correct answer. 

Total number of Bronze and Silver medals won by Country C = 42 - 16 = 26 and the ratio of silver medals to bronze medals = 6:7.
So, the number of silver medals = $$\frac{6}{13}\times\ 26\ =\ 12$$.
Similarly, Silver medals won by D and F are 8 and 15 respectively.
Total Silver medals won by C, D and F = 12 + 8 + 15 = 35.

Total medals won by A, B and C together = 40 + 38 + 42 = 120.
Required percentage = $$\frac{35}{120}\times\ 100=29.16\%\approx\ 29.2\%$$.

The number of gold medals won by B, D, E = 14+10+12=36.

Now calculate the bronze medals won by C and F.

Bronze medals won by C:

16+6x+7x=42

13x=26

x=2

7x=14

Bronze medals won by F :

13+5y+6y=46

11y=33

y=3

6y=18

Bronze medals won by C and F=14+18=32

The percentage by which 36 is more than 32.

$$\frac{\left(36-32\right)}{32}\cdot100$$=12.5%

Silver medals won by A = $$\frac{3}{5}\times\ 25=15$$
Silver medals won by E = $$\frac{4}{9}\times\ 27\ =\ 12$$

Bronze medals won by D = $$\frac{3}{5}\times\ 20=12$$
Bronze medals won by F = $$\frac{6}{11}\times\ 33\ =\ 18$$
Required ratio = 15+12 : 12+18 = 27:30 = 9:10

It is giving that 1800 students are studying five different courses -A, B, C, D and E.

The number of male students is $$57\frac{1}{7}\%$$ more than that of female students.

Let number of female students be 100x, thus number of male students will be 100x+(400/7)x = 1100/7x

Total students = 1800

100x+1100x/7 = 1800

1800x/7 = 1800

x = 7

Thus, number of female students = 700 and number of male students = 1100

It is given that Out of male total students, 24% are studying course B = 24% of 1100 = 264

the ratio of the number of female students to male students studying this course is 5:6.

Number of female students studying course B = (264/6)*5 =220

Total students studying course B = 264+220 = 484

It is given that the total number of students studying course C is 342, out of which female students are 104. Hence, number of male students = 342 - 104 = 238

It is given that 18% of females are studying course A = 18% of 700 = 126

Also, the ratio of male students to female students studying A is 4:3.

Hence, the number of male students = (126/3)*4 = 168

Total students studying A = 168+126 = 294

It is also given that One-fifth of total males are studying course D = 20% of 1100 = 220

Also, the number of female students studying D is 25% less than that of males studying D = 220*0.75 = 165

Total number of students studying D = 165+ 220 = 385

Therefore, we make a table from the above information-

The average number of female students studying courses A, B and C = (126+220+104)/3 = 150

The total number of male students studying courses D and E = 220+210 = 450

It is giving that 1800 students are studying five different courses -A, B, C, D and E.

The number of male students is $$57\frac{1}{7}\%$$ more than that of female students.

Let number of female students be 100x, thus number of male students will be 100x+(400/7)x = 1100/7x

Total students = 1800

100x+1100x/7 = 1800

1800x/7 = 1800

x = 7

Thus, number of female students = 700 and number of male students = 1100

It is given that Out of male total students, 24% are studying course B = 24% of 1100 = 264

the ratio of the number of female students to male students studying this course is 5:6.

Number of female students studying course B = (264/6)*5 =220

Total students studying course B = 264+220 = 484

It is given that the total number of students studying course C is 342, out of which female students are 104. Hence, number of male students = 342 - 104 = 238

It is given that 18% of females are studying course A = 18% of 700 = 126

Also, the ratio of male students to female students studying A is 4:3.

Hence, the number of male students = (126/3)*4 = 168

Total students studying A = 168+126 = 294

It is also given that One-fifth of total males are studying course D = 20% of 1100 = 220

Also, the number of female students studying D is 25% less than that of males studying D = 220*0.75 = 165

Total number of students studying D = 165+ 220 = 385

Therefore, we make a table from the above information-

Number of male students studying course B = 264

Number of female students studying course D = 165

The ratio of the number of male students studying course B to that of female students studying course D = 264:165 = 88:55 = 8:5 

It is giving that 1800 students are studying five different courses -A, B, C, D and E.

The number of male students is $$57\frac{1}{7}\%$$ more than that of female students.

Let number of female students be 100x, thus number of male students will be 100x+(400/7)x = 1100/7x

Total students = 1800

100x+1100x/7 = 1800

1800x/7 = 1800

x = 7

Thus, number of female students = 700 and number of male students = 1100

It is given that Out of male total students, 24% are studying course B = 24% of 1100 = 264

the ratio of the number of female students to male students studying this course is 5:6.

Number of female students studying course B = (264/6)*5 =220

Total students studying course B = 264+220 = 484

It is given that the total number of students studying course C is 342, out of which female students are 104. Hence, number of male students = 342 - 104 = 238

It is given that 18% of females are studying course A = 18% of 700 = 126

Also, the ratio of male students to female students studying A is 4:3.

Hence, the number of male students = (126/3)*4 = 168

Total students studying A = 168+126 = 294

It is also given that One-fifth of total males are studying course D = 20% of 1100 = 220

Also, the number of female students studying D is 25% less than that of males studying D = 220*0.75 = 165

Total number of students studying D = 165+ 220 = 385

Therefore, we make a table from the above information-

The number of male students studying course A is what per cent of the total number of
students studying course D (correct to one decimal place)?

The number of male students studying course A  = 168

The total number of students studying course D = 385

The number of male students studying course A is per cent of the total number of students studying course D = (168/385)*100 = 43.6%

Option C is the correct answer.

It is giving that 1800 students are studying five different courses -A, B, C, D and E.

The number of male students is $$57\frac{1}{7}\%$$ more than that of female students.

Let number of female students be 100x, thus number of male students will be 100x+(400/7)x = 1100/7x

Total students = 1800

100x+1100x/7 = 1800

1800x/7 = 1800

x = 7

Thus, number of female students = 700 and number of male students = 1100

It is given that Out of male total students, 24% are studying course B = 24% of 1100 = 264

the ratio of the number of female students to male students studying this course is 5:6.

Number of female students studying course B = (264/6)*5 =220

Total students studying course B = 264+220 = 484

It is given that the total number of students studying course C is 342, out of which female students are 104. Hence, number of male students = 342 - 104 = 238

It is given that 18% of females are studying course A = 18% of 700 = 126

Also, the ratio of male students to female students studying A is 4:3.

Hence, the number of male students = (126/3)*4 = 168

Total students studying A = 168+126 = 294

It is also given that One-fifth of total males are studying course D = 20% of 1100 = 220

Also, the number of female students studying D is 25% less than that of males studying D = 220*0.75 = 165

Total number of students studying D = 165+ 220 = 385

Therefore, we make a table from the above information-

The difference between the number of male and two times the female students studying course E is x

=> 210-2*85 = x

=> 210-170 = x

=> x = 40

Option C is correct answer.

Imports in 2015,17, and 19 is 520, 400, 480. Exports in 2014, 15, and 17 are 300, 240, 360.

Imports = 520+400+480=1400

Exports = 300+240+360=900

1400:900=14:9

We need to find the difference between imports and exports as a percentage of Imports for each year:

2014: Difference = 120

Percentage = (120/420)*100 = 28.57%

2015: Difference = 280

Percentage = (280/520)*100 = 53.84%

2016: Difference = 150 

Percentage = (150/430)*100 = 34.88%

2017: Difference = 40

Percentage = (40/400)*100 = 10%

2018: Difference = 130

Percentage = (130/450)*100 = 28.89%

2019: Difference = 80

Percentage = (80/480)*100 = 16.67%

So the change in percentage for 2014 and 2018 is between 25% to 30%.

Percentage changes (2017 to 2018)

Imports: From 400 to 450

Increase = 50/400 = 12.5%

Exports :From 360 to 320

Decrease = 40/360 = 11.11%

Exports in 2020

2019 value = 400

Decrease by 11.11%

400×(1−0.1111)=355.6

Imports in 2020

2019 value = 480

Increase by 12.5%

480×1.125=540

Difference = 540 - 355.6 = 184.4

The percentage by which exports were less than imports (2020)

(184.4/540)*100 = 34.2%

average exports (per year) in 2015, 2018 and 2019 : (240+320+400)/3 = 320

Imports in 2018: 450

Difference = 130

Difference percentage = (130/450)*100 = 28.9%

It is given that total expenditure in January = ₹54,000

And, the expenditure is December is 20% more than that in January = 20% of 54000 + 54000 = ₹ 64800

Expenditure on items A,B,C,D,E and F in January

A = 20% of 54000 = 10800

B = 15% of 54000 = 8100

C = 18% of 54000 = 9720

D = 25% of 54000 = 13500

E = 12% of 54000 = 6480

F = 10% of 54000 = 5400

Similarly, Expenditure on items A,B,C,D,E and F In December.

A = 18% of 64800 = 11664

B = 12% of 64800 = 7776

C = 16% of 64800 = 10368

D = 21% of 64800 = 13608

E = 20% of 64800 = 12960

F = 13% of 64800 = 8424

The question is "The expenditure on item D in December is ₹108 more than the total expenditure in January over items:"

The expenditure on item D in December is = 13608

Option A) Expenditure of item C and E in January = 9720 + 6480 > 13608

Option B) Expenditure of item B and C in January = 8100 + 9720 > 13608

Option C) Expenditure of item B and F in January = 8100 + 5400 = 13500

Thus, we can see that The expenditure on item D in December is ₹108 more than the total expenditure in January.

Hence, Option C is the correct answer.

It is given that total expenditure in January = ₹54,000

And, the expenditure is December is 20% more than that in January = 20% of 54000 + 54000 = ₹ 64800

Expenditure on items A,B,C,D,E and F in January

A = 20% of 54000 = 10800

B = 15% of 54000 = 8100

C = 18% of 54000 = 9720

D = 25% of 54000 = 13500

E = 12% of 54000 = 6480

F = 10% of 54000 = 5400

Similarly, Expenditure on items A,B,C,D,E and F In December.

A = 18% of 64800 = 11664

B = 12% of 64800 = 7776

C = 16% of 64800 = 10368

D = 21% of 64800 = 13608

E = 20% of 64800 = 12960

F = 13% of 64800 = 8424

The average expenditure on items A, C and D together in January is what per cent less than the expenditure on item E in December?

The average expenditure on items A, C and D together in January is = (10800+9720+13500)/3 = 11340

Tthe expenditure on item E in December = 12960

It is less by [(12960- 11340)/12960]*100 = 12.5%

Option D is the correct answer.

It is given that total expenditure in January = ₹54,000

And, the expenditure is December is 20% more than that in January = 20% of 54000 + 54000 = ₹ 64800

Expenditure on items A,B,C,D,E and F in January

A = 20% of 54000 = 10800

B = 15% of 54000 = 8100

C = 18% of 54000 = 9720

D = 25% of 54000 = 13500

E = 12% of 54000 = 6480

F = 10% of 54000 = 5400

Similarly, Expenditure on items A,B,C,D,E and F In December.

A = 18% of 64800 = 11664

B = 12% of 64800 = 7776

C = 16% of 64800 = 10368

D = 21% of 64800 = 13608

E = 20% of 64800 = 12960

F = 13% of 64800 = 8424

It is given that in January the income of the family is 20% more than the total expenditure.

Thus, income in January = 1.2*54000 = 64800

Savings in January = 64800 - 54000 = 10800

It is also given that in December the income of the family is 15% more than the expenditure.

Thus, the income in December = 1.15*64800 = 74520

Savings in December = 74520 - 64800 = 9720

The savings in January are more than that in December by = 10800 - 9720 = 1080

=> [(1080)/9720]*100 = 11.11%

Approx 11% (Option B is the correct answer)

Total Expenditure for January = 54000.
December's expenditure is 20% more than January's i.e. 1.2*54000 = 64800.
Now, we calculate month wise distribution of expenditures on the given items.

The item on which there is 4% decrease in December as compared to January is B.

If 25% of the male employees in offices A are transferred to office C, then the number of male employees in Office C are 128 + 25% of 384 = 224.
And, if 35% of female employees in D are transferred to office E, then the number of female employees in E are 16 + 35% of 240 = 100.
The required percentage = $$\frac{100}{224}\times\ 100\approx\ 44.6\%$$

Male employees in Office E = $$\frac{50.4}{360}\times\ Total$$. 
This gives the total number of male employees = 1600.
Total male employees in offices C and F = $$\frac{28.8+32.4}{360}\times\ 1600\ =\ 272$$.

Total employees in Office C = $$\frac{43.2}{360}\times\ Total$$.
This gives the Total number of employees = 2400.
Total employees in Office B = $$\frac{64.8}{360}\times\ 2400\ =\ 432.$$
The required ratio = 272:432 = 17:27.

Using the table, 

the number of female employees as a percentage for male employees is: 31.25%, 80%, 125%, 50%, 7.14% and 50% for the offices A, B, C, D, E and F respectively.
The number of female employees as a percentage of male employees is second lowest in office A.

Number of male employees in E = $$\frac{50.4}{360}\times\ Total\ Male$$ i.e. 224.
This gives the number of Total male employees = 1600.
And Total employees in C = $$\frac{43.2}{360}\times\ Total$$ i.e. 288.
This gives the Total number of Employees = 2400.
Using these values, we can calculate Total number of Employees and Total number of Female employees for all the offices.

average number of male employees in offices A, D and F = 336 and the total number of female employees in offices B, E and F are 280.
The required percentage = $$\frac{336-280}{280}\times\ 100\ =\ 20\%$$.

Total Production of Rice in 2016 and 2018 = 320 + 280 = 600.
Total Production of Maize in 2015 and 2019 = 250 + 500 = 750. 
The required ratio = 600:750 = 4:5.

Increase in maize production = $$\frac{Current\ -\ \Pr evious}{\Pr evious}\times\ 100$$.
Increase in Production in the following years are:
2016 = 20%,
2017 = 26.66%,
2018 = 5.26%,
2019 = 25%.
The 2nd highest increase is in year 2019.

Production of Wheat in 2015, 2017 and 2019 is 240, 330 and 360 respectively.
The average will be: $$\frac{240+330+360}{3}=310$$.
Production of Maize in2018 = 400.
The difference is 400 - 310 = 90. 
The percentage by which the average is less than the Maize production = $$\frac{90}{400}\times\ 100\ =\ 22.5\%$$.

Percentage by which wheat production increased in 2018 over 2017 = $$\frac{400-330}{330}\times\ 100\ =\ 21.21\%$$.
Production in 2020 = (1 + 21.21%)*Production in 2019 = 1.2121*360 = 436.36.

16.5% of this production is exported which means that 83.5% was left for domestic use i.e. 0.835*436.36 = 364.36 $$\approx\ $$ 364.4

The following points are given in the question.

i)The total units of all these products produced by X and Y together are 5500, and company Y produces 20% more units than company X.

Let x be the number of products from company X. Then the number of products from company Y will be x+$$\frac{20}{100}$$ = 1.2x

x+1.2x=2.2x=5500

$$\Rightarrow$$ x =2500

The number of products from company x is 2500, and that from y is 1.2*2500=3000

ii) Out of the total units of the products produced by company Y, 12% are of product B, and company X produces 30% more units of B than Y.

Given that 12% of Y products are B.

12% of 3000 = 360. Company Y produces 360 products of type B.

company X produces 30% more units of B than Y.

Company X produces 468 products of type B.

iii) The ratio of the units of product A produced by companies X and Y is 5: 6, and the total number of units of A is 990.

Let's say the constant proportionality of the given ratio is k. 5k+6k = 11k = 990.

$$\Rightarrow$$ k = 90

Company X produces 450 products of type A, and Company Y produces 540 products of type A.

iv) The number of units of product D produced by company X is 650, and company Y produces 40% more of it.

The number of units of product D produced by company X is 650.

Company Y produces 40% more than company X. That will be 910.

v) company X produces 550 units of C, and Company Y produces 55 more.

Company X produces 550 units of C. And Company Y produces 605(55 more).

vi) The units of the products left with companies X and Y are of product E.

The product left for company X is 382, and that for company Y is 585.

The number of units of product C produced by company Y is 605.

The number of units of product B and E produced by company X is 468+382 = 850

605 is what percent of 850?

$$\frac{605}{850}$$*100 = 71.2

The following points are given in the question.

i)The total units of all these products produced by X and Y together are 5500, and company Y produces 20% more units than company X.

Let x be the number of products from company X. Then the number of products from company Y will be x+$$\frac{20}{100}$$ = 1.2x

x+1.2x=2.2x=5500

$$\Rightarrow$$ x =2500

The number of products from company x is 2500, and that from y is 1.2*2500=3000

ii) Out of the total units of the products produced by company Y, 12% are of product B, and company X produces 30% more units of B than Y.

Given that 12% of Y products are B.

12% of 3000 = 360. Company Y produces 360 products of type B.

company X produces 30% more units of B than Y.

Company X produces 468 products of type B.

iii) The ratio of the units of product A produced by companies X and Y is 5: 6, and the total number of units of A is 990.

Let's say the constant proportionality of the given ratio is k. 5k+6k = 11k = 990.

$$\Rightarrow$$ k = 90

Company X produces 450 products of type A, and Company Y produces 540 products of type A.

iv) The number of units of product D produced by company X is 650, and company Y produces 40% more of it.

The number of units of product D produced by company X is 650.

Company Y produces 40% more than company X. That will be 910.

v) company X produces 550 units of C, and Company Y produces 55 more.

Company X produces 550 units of C. And Company Y produces 605(55 more).

vi) The units of the products left with companies X and Y are of product E.

The product left for company X is 382, and that for company Y is 585.

The number of units of product B produced by company X is 468.

The number of units of product E produced by company Y is 585.

The ratio is 468:585 = 4:5

The following points are given in the question.

i)The total units of all these products produced by X and Y together are 5500, and company Y produces 20% more units than company X.

Let x be the number of products from company X. Then the number of products from company Y will be x+$$\frac{20}{100}$$ = 1.2x

x+1.2x=2.2x=5500

$$\Rightarrow$$ x =2500

The number of products from company x is 2500, and that from y is 1.2*2500=3000

ii) Out of the total units of the products produced by company Y, 12% are of product B, and company X produces 30% more units of B than Y.

Given that 12% of Y products are B.

12% of 3000 = 360. Company Y produces 360 products of type B.

company X produces 30% more units of B than Y.

Company X produces 468 products of type B.

iii) The ratio of the units of product A produced by companies X and Y is 5: 6, and the total number of units of A is 990.

Let's say the constant proportionality of the given ratio is k. 5k+6k = 11k = 990.

$$\Rightarrow$$ k = 90

Company X produces 450 products of type A, and Company Y produces 540 products of type A.

iv) The number of units of product D produced by company X is 650, and company Y produces 40% more of it.

The number of units of product D produced by company X is 650.

Company Y produces 40% more than company X. That will be 910.

v) company X produces 550 units of C, and Company Y produces 55 more.

Company X produces 550 units of C. And Company Y produces 605(55 more).

vi) The units of the products left with companies X and Y are of product E.

The product left for company X is 382, and that for company Y is 585.

The number of units of product A produced by company X is 450.

40% of the number of units of products D produced by company Y is $$\frac{40}{100}$$*910 = 364

450 - 364 = 86

So, k is 86. 

The following points are given in the question.

i)The total units of all these products produced by X and Y together are 5500, and company Y produces 20% more units than company X.

Let x be the number of products from company X. Then the number of products from company Y will be x+$$\frac{20}{100}$$ = 1.2x

x+1.2x=2.2x=5500

$$\Rightarrow$$ x =2500

The number of products from company x is 2500, and that from y is 1.2*2500=3000

ii) Out of the total units of the products produced by company Y, 12% are of product B, and company X produces 30% more units of B than Y.

Given that 12% of Y products are B.

12% of 3000 = 360. Company Y produces 360 products of type B.

company X produces 30% more units of B than Y.

Company X produces 468 products of type B.

iii) The ratio of the units of product A produced by companies X and Y is 5: 6, and the total number of units of A is 990.

Let's say the constant proportionality of the given ratio is k. 5k+6k = 11k = 990.

$$\Rightarrow$$ k = 90

Company X produces 450 products of type A, and Company Y produces 540 products of type A.

iv) The number of units of product D produced by company X is 650, and company Y produces 40% more of it.

The number of units of product D produced by company X is 650.

Company Y produces 40% more than company X. That will be 910.

v) company X produces 550 units of C, and Company Y produces 55 more.

Company X produces 550 units of C. And Company Y produces 605(55 more).

vi) The units of the products left with companies X and Y are of product E.

The product left for company X is 382, and that for company Y is 585.

The average number of units of products A, B and E produced by company Y is $$\frac{(540+360+585)}{3}$$ = 495

The average number of units of products C and D produced by company X is $$\frac{(550+650)}{2}$$ = 600

The average number of units of products A, B and E produced by company Y is 105 less than the average number of units of products C and D produced by company X.

That is $$\frac{105}{600}$$*100 = 17.5%

Profit earned by the company in 2015 and 2017 together = (560 + 655) - (440 + 600) = 175 and,
loss incurred in 2016 and 2019 together = (560 + 500) - (400 + 450) = 210.
The required ratio = 175:210 = 5:6.

Income for 2016 and 2019 together = 400 + 450 = 850.
Expenditures for 2016 and 2019 together = 560 + 500 = 1060.
Loss incurred = 1060 - 850 = 210.
Loss% = $$\frac{210}{1060}\times\ 100=\frac{2100}{106}=\frac{1050}{53}=19.81\%$$.

Profit = Income - Expenditures.
This gives the profit as 120, 55, 175 and 125 for years 2015, 2017, 2018 and 2020 respectively.
The average profits = $$\frac{120+55+175+125}{4}=118.75$$.

Let us assume the expenditures in 2021 = X.
Now, 525 : X = 7:11. This gives X = 825.
Profit Percentage in 2021 = 18%.
The income for 2021 will be 1.18*825 = 973.5.

It is given in the question that Profit percent = $$\frac{Income - Expenditure}{Expenditure} \times 100$$.

That means profit is calculated as a percent of expenditure.

Income = Expenditure + $$\frac{profit percent * Expenditure}{100}$$

Let 'e' be the expenditure company A in 2019. 

The profit percentage of company A is 55, and B's is 40.

The income of company A in 2019 = Expenditure + $$\frac{profit percent * Expenditure}{100}$$ = e+$$\frac{55 * e}{100}$$=1.55e

The income of company B in 2019 = Expenditure + $$\frac{profit percent * Expenditure}{100}$$ = e+$$\frac{40 * e}{100}$$=1.4e

The total income of companies A and B in 2019 is 1.55e+1.4e = 2.95e.

Given that the total income of both companies was ₹354 crores.

So, 2.95e = 354

$$\Rightarrow$$ e = 120.

Then the total expenditure (in ₹ crores) of A and B in 2019 is 2e = 2*120=240

It is given in the question that Profit percent = $$\frac{Income - Expenditure}{Expenditure} \times 100$$.

That means profit is calculated as a percent of expenditure.

Income = Expenditure + $$\frac{profit percent * Expenditure}{100}$$

The question shows that the expenditure for company B in 2016 was ₹240 cr.

From the graph, the profit percent for company B in 2016 is 45.

Income for company B in 2016 = expenditure +  $$\frac{profit percent * Expenditure}{100}$$ = 240+ $$\frac{45 * 240}{100}$$ = ₹348 cr.

The income for company B in 2020 is also equal to ₹348 cr.

From the graph, the profit percent for company B in 2020 is 60.

Let's assume the expenditure of company B in 2020 is e. 

Income for company B in 2020 = expenditure + $$\frac{profit percent * Expenditure}$${100} 

348 = e+$$\frac{60 * e}{100}$$ = 1.6e

e = $$\frac{348}{1.6}$$ = 217.5

Profit % = $$\frac{Income\ -\ Expenditures}{Expenditures}\times\ 100$$.
Profit % of A for 2018 and 2020 is 40 and 35 respectively.
We will assume the expenditure to be 1 and calculate Income for both years using the stated formula.
Incomes for 2018 and 2020 will be $$\frac{100}{140}\ and\ \frac{100}{135}$$ respectively.
Their ratio will be 28:27.

Profit percent for B in 2017 = 55% and Income = 446.6 crores.
55 = $$\frac{446.6-Expenditure}{Expenditure}\times\ 100$$.
This gives Expenditure $$\approx\ $$ 288 crores.

A total of 225 students passed from School Y in the year 2017. 
We are given that among these students, the boys and girls are in the ratio of 7:8
This would give us the girls passing from school Y in 2017 to be $$\frac{225}{15}\times\ 8=120$$, and the boys passing from school Y in 2017 to be $$\frac{225}{15}\times\ 7=105$$

Next, we are given the ratio of boys and girls that passed from school X in the year 2019 as 12:13
The total number of students that passed from X in 2019 is 280; this would give us the number of boys and girls passing in that year to be $$\frac{275}{25}\times\ 12=132$$ and $$\frac{275}{25}\times\ 13=143$$ respectively.

The total number of girls passing from X and Y would be: 120+143 = 263

We are given that in 2020, 80% of the students who appeared were girls, giving us this value to be $$\frac{80}{100}\times\ 400=320$$

We are asked how many percentages is 263 less than 320; this value would be $$\frac{320-263}{320}\times\ 100=17.81\%$$

Therefore, Option C is the correct answer.  

for this question, we only have to consider the data from School Z
We need to subtract the number of students who passed from the number of students who appeared for each year and see in which year is that value at the second lowest rank.

2016: 300-285 = 15

2017: 320-304 = 16

2018: 380-362 = 18

2019: 352-325 = 27

2020: 400-381 = 19

If we rank the years in the increasing order of their differences:
2016(15), 2017 (16), 2018 (18), 2020(19), 2019 (27)

We see that the year with the second-lowest difference is 2017

Therefore, Option A is the correct answer. 

For this question, we would have to find the total number of students that passed from school Y

The number of students that passed from school Y: 175+225+254+280+276 = 1210

The average number of students that passed from Y would be 1210/5 = 242

The average number of students that passed from all three schools combined in 2018 would be $$\frac{242+254+362}{3}=\frac{858}{3} = 286$$

Giving us the ratio to be $$242:286$$
$$11:13$$

Therefore, Option A is the correct answer. 

The total number of students that appeared from school X in 2016, 2017 and 2019 are 250+275+300 = 825

The number of students that passed from School Y in 2018 and 2020 is 254+276= 530

The difference between the two is 825-530 = 295

We need to find the percentage of this value compared to the total number of students who passed from school Y in 2018 and 2020, giving the answer to be $$\frac{295}{530}\times\ 100\approx\ 55.66\%$$

This is closest to option D, which shows a value of 55.7%

Therefore, Option D is the correct answer. 

Since $$\left(x^2 + \frac{1}{x^2}\right) = 8.25$$, we can rewrite the same as $$\left(x-\ \frac{\ 1}{x}\right)^2\ +\ 2x\times\ \ \frac{\ 1}{x}$$ = 8.25

This gives us $$\left(x-\ \frac{\ 1}{x}\right)^2$$ = 6.25

Or, $$\left(x-\ \frac{\ 1}{x}\right)$$ = 2.5

Now, $$\left(x\right)^3-\ \left(\frac{\ 1}{x}\right)^3$$ = 

On substituting the values, we get the answer as 30.625

Since x is inversely proportional to  $$(2y^2 - 5)$$, we get the equation as x= $$\frac{k\ }{2y^2-5}$$ where k is the proportionality constant.

Now, x= 25 when y=15. Putting this in the above equation, we get the value of k as 11,125.

When y= 10, x = $$\frac{11125\ }{200-5}$$, which is approximately equal to 57.

g(x) = $$x^4$$

Now, fog(x) is $$x^4$$ + 7, which is Option C.

The summation of 10 steps, 11 steps, and 20 steps is 41 steps. 

The section formula to find the point dividing the line is $$\ \frac{\ na+mb}{n+m}$$ where the ratio is n:m and the coordinates (x or y axis) are a and b.

Applying the same for x-coordinate:  $$\ \frac{\ 44}{8}$$, which is equal 5.5

For y-coordinate: $$\ \frac{\ 56}{8}$$ which is 7.

Hence, the point is (5.5 , 7)

Since the different combinations (both selection and placement) would produce different signals, we need to consider each case.

Case 1: When only 1 light is used

Here, we need to select and arrange 1 light out of seven. It can be done in 7 ways. However, two produce signals, we need at least two lights. Hence, we shall discard this case. 

Case 2: When 2 lights are used

This can be done by selecting two lights out of seven and then arranging them, which is $$7c_2\times\ 2!$$, which is 49 ways

Case 3: When 3 lights are used

This can be done by selecting three lights out of seven and then arranging them, which is $$7c_3\times\ 3!$$, which is 210 ways

Case 4: When 4 lights are used

This can be done by selecting four lights out of seven and then arranging them, which is $$7c_4\times\ 4!$$, which is 840 ways

Case 5: When 5 lights are used

This can be done by selecting five lights out of seven and then arranging them, which is $$7c_5\times\ 5!$$, which is 2520 ways

Case 6: When 6 lights are used

This can be done by selecting 6 lights out of seven and then arranging them, which is $$7c_6\times\ 6!$$, which is 5040 ways

Case 7: When 7 lights are used

This can be done by selecting 7 lights out of seven and then arranging them, which is $$7c_7\times\ 7!$$, which is 5040 ways

Adding Case 2 till Case 7, we get the answer as 13,699

Let the ratio in which the two varieties are mixed be a:b

Hence, $$\ \frac{40a+50b}{a+b}$$ = 43

$$\ 40a+50b=43a+43b$$

This gives us 7b = 3a or a:b = 7:3

The option has an error; this happened in the actual exam paper, so we can't change it.

Since the reduction is ₹250, which is 5% of the total bill amount.

Hence, the total due amount is x, whose 5% is ₹250.

This gives us: 5% of x is ₹250, which makes x as 5% is ₹5,000

In 8 litres of A, the quantity of petrol (40% of the total quantity) is 3.2 litres and that of kerosene is 4.8 litres. 

In 12 litres of B, the quantity of petrol (60% of the total quantity) is 7.2 litres and that of kersone 4.8 litres. 

In the final mixture, the quantity of petrol becomes 10.4 litres and that of kerosene becomes 9.6 litres, making the ratio as 13:12.

$$6^{15} + 6^{16} + 6^{17} + 6^{18}$$

Let's take $$6^{15}$$ common from the whole.

We get $$6^{15}$$(1+$$6^{1}$$+$$6^{2}$$+$$6^{3}$$).

$$6^{15}$$ can be written as $$2^{15}$$*$$3^{15}$$.

24 can be written as $$2^{3}*3$$.

So, $$6^{15}$$ is divisible by 24. Hence, the remainder is zero.

All options are wrong in this P.Y.Q.

The volume of a cube is $$s^3$$, where s is the edge measure. 

Hence, the volume of the three cubes is: 125 cub.cm, 343 cub.cm, and 729 cub.cm

When melted, the total volume is 1,197 cub.cm.

To find the cube's edge with the volume of 1,197 cub.cm, we shall find the cube root of this number, which happens to be 10.62 cm (approximately).

Since $$\beta\ =\ 5\alpha\ \ $$, we can say that the product of roots ($$5\alpha\ ^2\ \ $$) = $$\ \frac{\ c}{a}$$ ............ (1)

and sum of roots ($$6\alpha\ $$) = $$\ \frac{\ -b}{a}$$ ................. (2)

Hence, $$\alpha\ $$ = $$\ \frac{\ -b}{6a}$$    ............. (3)

Substituting (3) in (1), we get $$5\times\ \ \frac{\ b^2}{a^2}$$ = $$\ \frac{\ c}{a}$$

or, $$5b^2 = 36 ac$$

Probability of at least 3 bottles being safe = Probability of at least 3 bottles being safe + Probability of all 4 bottles being safe

To find Probability of all 4 bottles being safe, we also need to multiply the result with 4, since any of the four bottles can be damaged.

Also, probability of a bottle being damaged is $$\ \frac{\ 9}{10}$$

Hence, Probability of at least 3 bottles being safe = $$\ \ \left(\frac{\ 8}{9}\right)^4$$ + 4$$\ \times\ $$ $$\ \left(\frac{\ 8}{9}\right)^3\times\ \left(\ \frac{\ 1}{9}\right)$$

On solving this, we get the answer as $$\frac{\ 2048}{2187}$$

The common difference of $$[p_n]$$ is 2, while that of $$[qn]$$ is 3. 

The last term for $$[p_n]$$ will be 4 + 49$$\times\ $$2, which is 102

Similarly, the last term for $$[qn]$$ will be 2 + 49$$\times\ $$3, which is 149

Now, the first common term for these two series is 8. Further, the common difference for the series of common terms shall be the LCM (2,3), which is 6.

Hence, 8 + 6K < 102

Or, K < 15.666.... 

This means K can take the maximum value of 15 and minimum of 0. Hence, 16 terms are common to the two series. 

In this question, we need to assume two cases for the sign of the denominator because of the inequality.

Case 1: 2x-1 > 0, or x> $$\frac{\ 1}{2}$$

This makes x+1 > 2x-1, or x<2

Hence, the range is $$\frac{\ 1}{2}$$ < x < 2

Case 2: 2x-1 < 0, or x < $$\frac{\ 1}{2}$$

This makes x+1 < 2x-1, or x > $$\frac{\ 1}{2}$$

This case is inconsistent in nature. Hence, the answer is $$\frac{\ 1}{2}$$ < x < 2

$$\angle A$$+$$\angle B$$+$$\angle C$$ = 180

Or, $$\angle B$$+$$\angle C$$ = 126

Now, the angle bisectors divide $$\angle B$$ and $$\angle C$$ into half, hence their sum is 63

Now, in $$\triangle BOC$$, we 63+$$\angle BOC$$ = 180, or $$\angle BOC$$ = $$117^\circ$$

=> Avinash invested ₹6,400 in three business at 3%, 5% and 7% per year with simple interest.

Simple interest formula is $$SI\ =\ \frac{PRT}{100}$$

Where P is principal, R is rate of interest and T is time duration in years

Here, Let us assume the amount invested in three businesses is P1, P2 and P3.

Therefore, the interest after 1 year because of simple interest will be 3P1/100 , 5P2/100 and 7P3/100

These are equal, Hence

=> 3P1 = 5P2 = 7P3

It is also known that total investment done in three business is equal to 6400

P1 + P2 + P3 = 6400

Substituting values of P2 and P3 in terms of P1

P1+3P1/5 + 3P1/7 = 6400

We need to calculate the value of P1

(35+21+15)P1/35 = 6400

=> 71P1/35 =6400

=> P1 is approximately 3200 (Option B is correct answer)

To divide $$(21^{13} + 29^{13})$$ by 25, we shall divide 21 and 29 individually by 25. 

 By doing so, we get the remainder as $$(4^{13} + (-4)^{13})$$, which is 0. 

First, we shall consider the series as a summation if two infinite series: 

S1: $$\ \ \frac{\ 1}{5}\ +\ \ \frac{\ 1}{25}+\ ......$$

S2: $$\ \ \frac{\ 3}{25}\ +\ \ \frac{\ 3}{625}+\ ......$$

Taking S1: The sum of series shall be $$\ \ \frac{\ a}{1-r}\ $$, hence $$\ \ \frac{\ \ \frac{\ 1}{5}}{1-\ \frac{\ 1}{25}}\ $$, which is $$\ \frac{\ 25}{120}$$

Taking S2: The sum of series shall be $$\ \ \frac{\ a}{1-r}\ $$, hence $$\ \frac{\ \ \frac{\ 3}{25}}{1-\ \frac{\ 1}{25}}$$, which is $$\ \frac{\ 1}{8}$$

Adding S1 and S2, we get the answer as $$\ \frac{\ 1}{3}$$

Let the number subtracted be x. Hence, the terms are 8-x, 10-x, and 14-x.

10-x = $$\ \frac{\ 2\left(8-x\right)\left(14-x\right)}{8-x+14-x}$$

On cross multiplying, we get x as -2. 

The population after 3 years will be: 10,000 $$\times\ 1.1\times\ 1.15\times\ 0.95$$, which is equal to 12,018 (approximately).

The above expression can be simplified as $$\log\ \ \frac{\ 27}{125}\times\ \ \frac{\ 21}{x}\times\ \ \frac{\ 625}{81}$$ = 0

On solving the same, we get $$\log\ \ \frac{\ 35}{x}=\ 0$$, for which x shall be 35, making $$\log1=\ 0$$

Let the total number of people be X. 

1) When X is divided by 15, we get a remainder of 10. Hence, X = 15a + 10

2) When X is divided by 20, we get a remainder of 15. Hence, X = 20b + 15

3) When X is divided by 24, we get a remainder of 19. Hence, X = 24c + 19

4) When X is divided by 28, we get a remainder of 23. Hence, X = 28d + 23

This is a classic case when the difference between the divisor and remainder is the same, which is 5 in this case. In such instances, the number is expressed as (LCM of the divisors)$$\times$$K - (difference between the divisors and remainders).

Hence, the number of people shall be 840k - 5.

The minimum number is when k=1, hence the minimum number shall be 835.

Let the sides of the polygons be 2x and 3x. 

Hence, the ratio of the sum of interior angles for the two polygons is: $$\ \frac{\ \left(2x-2\right)\times\ 180}{\left(3x-2\right)\times\ 180}$$ = $$\ \frac{\ 5}{8}$$

On solving this, x=6

This increases the number of sides in the first polygon to 12 and 18 for the second one.

To find the measure of each interior angle of the second polygon, we get $$\ \frac{\ \left(18-2\right)\times\ 180}{18}$$, which is 160 degrees.

Revenue is the product of spending and consumption. Hence, this is a case of successive percentage change.

The multiplying factor of reduction of 20% is 0.8, while that of increase by 15% is 1.15.

Assuming the initial revenue be X, we get the new revenue as X$$\times\ 1.15\times\ 0.80$$, which 0.92X.

This means there is a reduction of 8% in the revenue.

The radius of the bigger circle is 5 cm while of the smaller circle is r cm.

Since the two sides of the wall are tangential to the circles, we get a square formed by the radius of the bigger circle and the two sides wall, each with the length of 5 cm. 

Now, the diagonal of this square (s1) shall be $$5\sqrt{\ 2}$$.

Focusing on the smaller circle, on which the wall is tangential again. We get a square here as well, the diagonal of which is  $$r\sqrt{\ 2}$$.

Hence, the diagonal of s1: $$5\sqrt{\ 2}$$ = r +  $$r\sqrt{\ 2}$$ + 5

On solving this, we get r = $$15 - 10sqrt{\ 2}$$

Let us assume the number be 'x'.

Also, let us assume that the divisor is 'n'

Hence, x = n(a) + 20, where 'a' is the quotient ............ (1)

Also, 3x = n(b) + 7, where 'b' is the quotient ................(2)

Dividing (2) by (1), we get n (b-3a) = 53

Now, 53 is a prime number, and it can be broken into 53$$\times$$1.

Further, it is clear that the divisor cannot be 1, hence n = 53

In this scenario, the ant has three options: 

1) Go to C directly from A, for which it has 3 paths. 

2) Use the path A-B-C, for which it has 5$$\times\ $$4, which is 20 paths. 

3) Use the path A-E-D-C, for which it has 3$$\times\ $$5$$\times\ $$6, or 90 paths.

Adding the above numbers, we get 113 as the total number of ways in which the ant can reach C from A.

Let the number be 5x. 

As per the question, 2x = x+5, or x = 5. 

Hence, 5x = 25

The total sum of heights of 30 students was 30 $$\times$$ 165, which is 4950 cm. 

Now, 5 students with an average height of 172 cm joined the class, which makes the total height as 860+4950= 5810 cm.

The average height of the 35 students now will be $$\ \frac{\ 5810}{35}$$ = 166 cm. 

In any star-shaped figure, the sum of vertex angles is 180$$\times\ $$(n-4), where n is the number of vertices. 

Hence, in this case, it has to be 180$$\times\ $$(5), which is 900$$^\circ$$

The multiplying factor for a decrease of 25% is 0.75

Hence, the value of the ATM machine after two years shall be 55,000$$\times0.75\times\ 0.75$$, which is 30,937.5

In this question, we shall find the HCF of the three numbers 780, 690, and 950, which shall match with the options. 

It is clear that 10 shall be the answer, which can used to measure all the three different volumes. 

When f(x) is shifted 2 units to left, it becomes f(x+2). Now, 12 units downwards would mean f(x+2) - 12

Hence, the new equations h(x) is $$\left(x+2\right)^2-5\left(x+2\right)\ +\ 6\ -12$$, which is $$x^2 - x - 12$$

For $$f(x) = \log_{5}(x-4)-4, x > 0$$ to be valid, (x-4) has to be greater than 0. Hence, x > 4

Now, the VA is a line that guides the graph (above which the graph is valid and below which it becomes invalid). Hence, it has to be the line x=4, as x>4 for the graph to be valid.

The sum of two co-interior angles in the same side shall add up to 180$$^\circ$$.

Hence, $$\frac{3x}{4}$$+$$\left(\frac{5x}{4} - 20 \right)$$ = 180

Or 8x = 800, making x = 100

Hence, $$\frac{3x}{4}$$ = 75 and $$\left(\frac{5x}{4} - 20 \right)$$ = 105

Area of ellipse is: $$\pi\ ab$$, where a and b are the half of the length of major and minor axis. 

Substituting a with 6 and b with 1.4 ($$\pi$$ being 3.14), we get the area as 26.4 approximately.  

$$(x^2 - x - 6)$$ is a factor of the fourth degree equation. Hence, the roots of $$(x^2 - x - 6)$$ (3 and -2) will satisfy the fourth degree equation.

Putting x=3 in $$x^4 + ax^3 - x^2 - bx - 12 = 0$$, we get 81+27a-9-3b-12=0, or 27a-3b= -60..............(1)

Putting x= -2 in the equation, we get 16-8a-4+2b-12=0, or 8a-2b=0............ (2)

Solving the two, we get a as -4 and b as -16

Let the speed of the train be x km/h.

The resultant speed of the train with respect to the first person shall be (x-4) km/h, and that for the second person is (x-6) km/h.

In 4.2 seconds, the train overtakes the first person. Hence, the distance between them is $$\frac{\ 4.2}{3600}\times\ \left(x-4\right)$$

In 4.8 seconds, the train overtakes the first person. Hence, the distance between them is $$\frac{\ 4.8}{3600}\times\ \left(x-6\right)$$

These two values are equal. From this, we get x= 20 km/h.

The passage discusses how the presence of wealth in a country does not necessarily mean the country is out of poverty. The author's argument is that having a strong economy is meaningless if a significant portion of the population is struggling to survive.

Therefore, Option A is the correct answer. 

Converting the speed of the train from km/hr into m/s, we get $$72\times\ \frac{5}{18}=20$$ m/s

To completely cross the bridge, the train end would have entered from one end, and the end of the train would have to come out, which, we are given, makes 30 seconds. 
The total distance covered by the engine of the train int his distance would be the train's length and bridge's length. 

$$20\times\ 30=250+$$ Bridge length
Bridge length $$=600-250=350$$ m

Therefore, option B is the correct answer. 

In such questions, instead of writing down all the possible team combinations, we should consider each option individually and see which option does not break any rule and is a valid team composition. 

looking at the options, 
We can eliminate option B on the basis of rule 1 itself. 
Rule 1 says that Ruby and Yash will always be selected together. In option B, we have Yash but not Ruby, so this configuration would not be possible. 

We can eliminate option C on the basis of breaking rule 2.
Rule 2 says that if Sonal is selected, neither Manish nor Bhuvan can be selected, yet in option C, we have Sonal and Bhuvan on the same team. 

We can eliminate option A on the basis of breaking rule 3. 
Rule 3 states that if Raveena is selected, Bhuvan is definitely selected, but in option A, Raveena is selected, and Bhuvan is not selected. 

That leaves us with only option D, which would be our answer. 

The main statement talks about ban/tax on plastic bags and measures not being implemented properly. 

Hence, we can safely say that plastic bags are illegal to use at certain places as they are banned in some countries. This makes 1 a valid conclusion.

Further, the lack of implementation of measures show that authorities are not strict enough. This makes 2 a valid conclusion.

The information in the statements can be represent as follows:

Coming to conclusions:
(1) As we can see, there might be some vultures that are not parrots. Therefore, conclusion 1 is not necessarily true. 

(2) "Some parrots are eagles." Although in the diagram, there is an overlapping region between Parrots and Eagles, the region can be empty as well. Therefore, we cannot conclusively say that some parrots are eagles. 

(3) This conclusion directly goes against statement c which said that all vultures are sparrows, therefore, this too can be concluded. 

None of the conclusions can be reached from the statements. 

Therefore, option A is the correct answer. 

Multiplying the opposite numbers in the first diagram we get $$5\times\ 2=10\ \&\ 6\times\ 3=18$$
Adding them, we get the number in between, which is 28

Multiplying the opposite numbers in the second figure, we get $$4\times\ 4=16\ \&\ 3\times\ 8=24$$
Adding them, we get the number in between, which is 40

Similarly, for the third figure, by multiplying the opposite numbers, we get $$6\times\ 4\ =24\ \&\ 6\times\ 5=30$$
Addin them, we should get the number which should come in between, which is 54

Therefore, Option A is the correct answer. 

The difference between the first two numbers is 117-113 = 4
The difference between the third and the second number is 126-117=9
The difference between the fourth and the third number is 151-126=25
The difference between the fifth and the fourth number is 200-151=49

We can see that all the differences are squares of the prime numbers. 
The next difference would be the square of the next prime number, $$11^2=121$$
making the sixth number of the series to be 200+121 = 321

Therefore, Option C is the correct answer. 

Ishan was initially facing east, so when he turned right, he faced south. 
Then he walked 30 m south. 
The then turned left, facing east, walked 10 m east. 
He then finally turned left again, facing north and walked 15m 

In essence, he walked 30 m south and 15 m not, making him move 15 m southwards. 
And he moved 10 m eastwards. 

Givng his net distance from his starting position to be $$\sqrt{\ 225-100}=\sqrt{\ 125}$$, which is slightly more than 11m 

From statement III in the question, if Raveena is selected, then Bhuvan has to be definitely selected. Given that Raveena is selected, we can say that Bhuvan is also selected. 

From statement II, we can see that Sonal can be selected only when none of Manish and Bhuvan are chosen.

We know that Bhuvan is selected. So, Sonal can't be chosen.

The number of days in between 1 January 2011 and 1 January 2007 is 1461.

1461%7 = 5. So, if 1 January 2007 is Wednesday then 1 January 2011 is Monday(5 days after Wednesday).

Vishi's statement contradicts Shruti's and Vihan's statements, so only Vishi's statement can be false.

This means Vihan's statement, "She is wearing red," is true. So, Anu's dress is red.

A talks about a stable atom having zero net charge. R talks about the ionization of atoms. Both statements are true, but A needs an explanation as to why a stable atom has a net charge of zero, which R doesn't.

Paper is green.

Plastic is cut in a square but not pink. Only color left is red.

So. Plastic is cut in a square and colored red.

So, cloth is pink. The questions says that pink colored material is circle shaped.

So, cloth is pink and circled shaped. And paper is triamgle.

There was an error in the question, even in the actual exam. We can't resolve it.

Roma was ranked $$8^{th}$$ from the top, and Arjun was ranked $$9^{th}$$ from the bottom. In the next exam, their rankings were interchanged. This means Arjun is ranked $$8^{th}$$ from the top and is also given as $$28^{th}$$ from the bottom. So, there are seven people ahead of Arjun and 27 below Arjun. The total number of students is 7+27+1(Arjun) = 35.

A states that hard work and doing the same smartly are important for achieving the desired goals. R elaborates upon the same and substantiates that only hard work is not sufficient to reach the goals. Hence, A and R are true with R being the correct explanation of A. 

Let us take the LCM of 12 and 24, which is 24 (total work). 

Hence, we can say that Becca does 2 units of work per day while Jason does 1 unit of work per day. 

Together, they shall do 3 units of work per day. 

To complete 24 units, they shall take 8 days.

Statements:
(a) All curtains are sheets.
(b) Some sheets are shawls.
(c) Some covers are sheets.

The venn diagram of the information from above statements looks as 

Conclusions I. Some curtains are covers.

From the diagram the statement some curtains are covers is not true.

Conclusions II. Some shawls are covers.

We can see in the diagram, that there is no intersection in the shawls and covers. So, conclusion II is also false.

Let us use the initials of names to denote them.

We know:  

1. It can be SMP or PMS

2. A_ _ _ _ 

3. A_ _ P_ 

Now, for 3 to be valid, we can have SMP from 1 as the second combination will make this invalid. 

Hence, ASMP_, which means Monisha is in middle. 

Statement a) All cities are villages.

Statement b) Some states are cities.

Since all cities are villages and some states are cities, some states are villages.

Conclusion i)All states are villages.

We know only some states are villages. So, all states cannot be villages.

Conclusion II. Some villages are states.

We know only some states are villages. So, some villages will definitely be states.

Conclusion III. Some villages are cities.

We know all cities are villages. So, some villages are cities is true.

Conclusion II and III follows but not I.

The path he travelled will look as below.

From start the final position is in north-east direction.

The oviparous animal or bird reproduces by laying eggs. Ostrich is oviparous. Some types of sharks are oviparous. So, the diagram looks as follows.

So, option 2 is the answer.

Statement A discusses how small industries often lead to development and urbanization in rural areas. Statement B provides an example of this concept in action.

Conclusion A exaggerates in two ways: first, by using the word "definitely," which implies certainty, whereas the statements indicate that this process often occurs but is not guaranteed; second, by suggesting that people are encouraged to seek a better life. The statements focus on development and urbanization, not on people's motivations or aspirations.

Conclusion B states that big corporations help facilitate development in some way. This logically follows from the statements, as even if big corporations are not directly serving the rural areas where they set up industries, they contribute to development through infrastructure improvements.

Therefore, option D is the correct answer.

We are given that Tara is Lakshay's granddaughter. 
And we are also given that Lakshay only had one child. 
Along with the information that Lakshay is Ruchi's father-in-law, we can deduce that Lakshay had a son who was married to Ruchi, and they had a daughter named Tara

We are given that Ani is Tara's sister. 
We are also given that Indar is Ani's father, making Indar Ruchi's husband and Lakshay's son. 

Finally, we are given that Arohi is Indar's paternal grandmother. 
Making Arohi Lakshay's mother. 

We can finally get Ani to be Arohi's great-granddaughter. 

Therefore, option C is the correct answer. 

The main statement concerns the high number of road accidents. Hence, the course of action shall be aimed at reducing the same and shall be reasonable at the same time.

This makes 1 correct. 2 is incorrect, as it is an unreasonable step to stop people from using the roads.