SRCC GBO 2021 Question Paper

Option C: Correct. 

Understanding the tense here through the sentence is the key.

On the first glance the sentence is talking about an event that has happened in the past (criticisms...in recent years), and the impact of which is continuing to the present as well (critics arguing)

So we know that we have to use a combination of Present perfect and present continuous tense. 

The only option that uses the right combination of these tenses in the right sequence is option C.

Option C: Correct.

To answer the question we have to try making literal sense of the idiom used first and then understand its metaphorical sense through that.

To throw baby out with the bathwater, literally presents a picture of a baby being bathed and along with discarding the bathwater the baby is discarded in the process. 

This implies- while discarding something unimportant, something important is being discarded as well.

The option that fits this explanation is option C.

Option D: Correct.

We have to clearly understand the relationship between Tremble: Fear, first. 

This relationship indicates a physical action when a certain emotion is felt. 

A person "trembles with fear"

So with the action of frowning the most fitting emotion is "displeasure", hence option D is correct.

Option C: Correct.

In these questions we first scan through and see which phrase sounds incomplete or unfinished, usually that is the sentence that requires correction.

Here the last phrase sounds incomplete, so we scan for options that fix this issue.

"but the break is just as necessary" is the corrected usage for the fourth blank, as mentioned in the option C.

Option A: Correct.

Here we scan through the paragraph and see if there is a phrase that sounds grammatically incorrect.

We see that the entire sentence seems to be composed in present perfect tense.

Hence, the first phrase using future tense appears as an outlier. So we choose the option that fixes this issue and the only such option is A.

Option B: Correct.

Here there are exactly two words used to fill in the blanks to form a meaningful sentence. 

We have to first, know the precise meaning of the two words.

Then, understand what the sentence is trying to convey.

And, then place the words.

accept means to take something willingly

except means to exclude something

The sentence is trying to convey that people in question will not be taking any gifts but they will be taking donations.

So accept and except will be used. Hence, option B is correct.

Option A: Correct.

Understanding the meaning of the word and then the sentence is the key to the question.

Even if one of them is correctly understood, one may arrive to the right answer.

Irrefutable uses "ir" suffix which means "not", so irrefutable means something that can not be refuted.

So the sentence now means Ehlrich's argument can not be refuted or proven incorrect.

So option A, Indisputable is closest in the meaning.

Option B: Correct.

To answer the most appropriate fit for the sentence we have to first make sense of the sentence with blanks.

By reading the sentence we get an idea that- there is a certain quality about animal kingdom that the author envies and admires.

So we can get a sense through this conclusion that the quality being talked of should be a positive adjective.

The positive adjectives are only in option B- ease and grace.

Hence B is the right choice.

Option D: Correct.

The irrelevant sentence will be an outlier, although all the sentences seem to be centered around medicine. 

We can first form the clear pair- the first and the second sentence, the sentences are talking about some features of medicine and the connecting word- another feature, ties these sentences together. 

Now, we have to check the viability of the remaining two options and see which one fits with the above chosen pair of sentences.

Fourth sentence, speaks about breakthroughs in medicine and compares them with scientific revolutions. This feels out of place because the paired sentence talks about the features of medicine. Hence, sentence D is the odd one.

Option C: Correct.

We have to decipher the meaning of the word in the question first. The word decipher uses the suffix "dis" which means "not", "away" or "apart". Integrate means to put together or add together, so disintegrate means to pull apart.

The antonym of pull apart can be something that is together and thriving, so flourishing fits the bill here.

Option C: Correct.

In this sentence we have to place the correct prepositions in the blank.

Among the options given-

knowledge of/ about can be appropriate

woven into can be appropriate, since there is no weaving across the narratives- no sideways or overhead movement.

brought to life with will be appropriate

Hence option C, fits all the blanks.

Option C: Correct.

Understanding the relationship between Architect and drawing board is the key here, which will help us ascertain the approprite relationship of painter.

An architect works/creates his work on the drawing board, so drawing board is the surface of expression.

Similarly, for the painter the surface of expression is the canvas.

Option C: Correct.

The relationship between person and crowd is that a person is a singular unit of a crowd.

Similarly, a musician is a singular unit of an orchestra.

Option C: Correct.

Multiple forms of the same word are used, we have to figure out through the given sentence with blanks that where should the correct noun and the verb be placed. 

The verb will fit the second blank since it is describing an action.

Principal is the head of the school and principles are set of moral codes that one follows. The correct placement of these two nouns is dependent upon knowing the right spellings.  

Option A: Correct.

Correct use of prepositions has to be made.

Within/ after a few moments can be appropriate

among/ within/ in the trees can be appropriate

near/ by our house can be appropriate

only option A fits the right choice.

Option A: Correct.

We have to first skim through the paragraph and try to spot a phrase that may be grammatically or contextually unfit with its preceding or succeeding phrases/ words.

separated entangled by crowded slums, separated and entangled used without punctuation, simply put together, makes no sense. Hence this is the wrong phrase, which can be corrected by option A- separated by a tangle of.

Option A: Correct.

Relentless means repetitive, continuous, too pushy.

The sentence means continuous and pushy advertisements are supporting that coding shall help kids with their cognitive skills.

The word opposite of relentless is intermittent which means spaced, or discontinuous, as shown by the suffix "inter" which shows an interval.

Option D: Correct.

In this question, it will help us to form pairs and then arrange them appropriately.

Sentence A is a starting sentence expressing a positive opinion, and sentence D begins with the connecting phrase "this is because" and then goes on to explain the reasons behind a likely positive attitude, so A and D can be a likely pair.

Sentence D ends with expressing a challenge with "restrictions" and sentence B begins with a connecting word "while", elaborating on the restrictions and their impact. Hence, B will come after sentence D.

Remaining sentence C summarises and explains a reason for optimism in the initial sentence; hence, C is a fitting last sentence. 

Option C: Correct.

The sentence describes an action being performed in the present and to be completed in the future.

Hence, the future perfect tense will be used.

Option C uses the future perfect tense and is hence right. 

Option D: Correct.

Knowing the meaning of the phrases is the key to answering this question.

Hold to- to adhere to something

Hold up- delay/ withstand

Hold on- to wait

Hold fast- to grip tightly

Here, hold on is the most fitting choice, since the caller is asked to wait in the sentence. 

Option C: Correct.

To answer the question, we should first make literal sense of the idiom and then understand its metaphorical sense from that.

“ Missed the boat" literally means being late to catch the boat and thus missing out on an opportunity; this is the most probable meaning.  

Here, there are exactly two words used to fill in the blanks to form a meaningful sentence.

We must first understand the precise meaning of the two words. 

Then, understand what the sentence is trying to convey.

And then place the words.

Conscious means being aware of one's surroundings

Conscientious means the desire to do one's duty well

Hence, option D is correct.

Trying to make sense of the word through the sentence can help us ascertain its meaning even without knowing its vocabulary.

If a word denotes success in addressing poverty, then it will be removing or reducing poverty.

Hence, eradicate might mean removal or reduction.

According to this conclusion, the right antonym is "promote".

Hence, D is correct.

We first try to make sense of the passage as a whole from jumbled sentences, then arrange the sequence.

The passage introduces a fear of regulatory authorities about the lack of transparency in the antiquities trade; hence, a recent legislation was introduced to ensure transparency. It then discusses an additional scope of the law and what legal authorities think of its implications. 

So, the right sequence framework should be: Introduction of the topic -> immediate steps to address the topic -> comments/opinions on the topic -> an additional point related to the topic.

Option B fits this framework; hence, B is correct.

Knowing the meaning of epistolary is important here.

Epistolary means- in form of letters

Hence, option A is correct

All the options are prepositions.

Three of them will be used in the same context and one will have a different purpose.

Between, among and of, all three are used to describe position of an object or a person in a geographical or a group setting.

Whereas, and, is a connector conjunction.

Hence, option C is correct.

To answer the question, we should first make literal sense of the idiom and then understand its metaphorical sense from that.

An embarrassment of riches literally means that wealth is embarrassing in a certain context, possibly due to its abundance.

So option B fits closely. 

Understanding the paragraph's tone is key to answering this question. The paragraph refers to the negative opinions of critics on the medicine and the medical industry, expressing concerns on diseases and drugs. 

Option D should first be evaluated because it begins with a connecting phrase "still others", referring to another segment of critics and highlighting another criticism.

So this fits most perfectly as the follow-up sentence.

Hence, option D is correct.

The sentence is simply describing a past event.

Hence, the appropriate tense to be used here would be the simple past tense.

Therefore, option A is correct.

We should first identify if there is a pair in the passage by spotting connecting or referencing words. In sentence A, a program is being talked about, and sentence C begins with a referencing word- "It does" very little. Hence, A C is a pair.

As for B and D, B introduces the fact that China has lifted many farmers out of extreme poverty, and D explains the process of identifying poor households, so they naturally form a pair, with B as the first sentence.

Now, since B is introducing a fact and the rest of the sentences are explaining a fact, B is the first sentence.

So, the sequence becomes BDAC.

Hence, option A is correct.

We have to spot an outlier. We first make sense of what the extract is talking about- we can understand through at least three sentences that the extract is talking about how heritage buildings are an integral part of the culture and that they should be protected.

Here, sentence B is a clear outlier, as it's unrelated to the topic and discusses something entirely different, pertaining to Catalonian politics.

Hence, option B is correct.

Here, three words would belong to the same group, and one would be odd.

Hear, touch and smell are sensory activities, and hence are alike.

The mouth is a sensory organ; hence, it is odd.

Therefore, option C is correct.

Here, three words would belong to the same group, and one would be odd.

A knife, spoon, and fork are all utensils used for eating.

Shears are broad, scissor-like tools typically used in gardening or farming.

On the basis of usage, shears are the odd ones out.

Inferring the meaning of the sentence is important here; it states that fines will be imposed if someone trespasses or tries to stealthily occupy the tomb.

Word in place of stealthily is surreptitiously.

In options, secretly means the closest to wrongfully or illegally. 

We try to form pairs from the given parajumble, after making sense of what it is trying to convey.

The passage states about priority queuing and how different people have different opinions about it.

Looking at the likely pairs, "not everyone is enthused about....despite this, the concept is spreading worldwide is a likely pair, because of the presence of the right connecting word, "despite" , explaining that despite some people's disappointment with the concept of priority lines, the concept continues to grow worldwide. Hence, BD is a likely pair. 

A and C are a pair since sentence A talks about people and sentence C talks about the preferences of those people.

Option A fits this sequence and is therefore correct. 

The passage argues that the nomenclature of grouping countries into first, second, and third worlds is outdated and should be revised on a more accurate basis. It provides some facts to substantiate this claim.

Option A fits best in this explanation.

Option B is incorrect because the passage does not advise developed countries.

Option C is incorrect because the passage critiques the nomenclature, which was established by a French demographer and has been followed since then; it does not even mention any stance taken by developed nations on this issue.

Option D is incorrect because the passage is not about narrowing the gap between the first and third world but about the very fact that segregating countries based on this nomenclauture is irrelevant and inaccurate. 

The passage mentions many facts to support the claim that the 1-2-3 generalisation of the countries of the world is now out-of-date, insulting and confusing." It highlights how many parts of developed countries also have pockets of poverty, how countries described as third world are affluent, and how the Soviet Union, which was part of the first world, no longer exists.

It later concludes that a possible solution to address this nomenclature is to develop a data-based classification.

Hence, option B, which states that the classification is imprecise, is the best fit given the various anomalies in the basis of the 1-2-3 classification.

Spotting the right extract from the passage will help us answer this question.

"(However)… When you think about it, 'developing countries' are quite developed in some respects. In countries where government safety nets are practically nonexistent, people step forward to help out..."

This extract clearly shows that even the term "developing countries" can be misleading, as some can be quite advanced in certain areas due to their personal social welfare systems.

Hence, option C fits best.

When we review the reasons cited for the 1-2-3 classification being outdated, the reason that the second world is no longer a single bloc of countries is not mentioned.

The passage notes that the Soviet Union no longer exists, but this does not imply that the entire Second World Bloc no longer exists. 

Hence, option D is correct. 

Because many countries in the Third World were impoverished, the term came to be used to refer to the poor world. This extract proves that the author would agree with option A.

(However)… When you think about it, 'developing countries' are quite developed in some respects. This extract demonstrates that the author agrees with option B, that development and development are no longer reflective of today's context.

Second, the author does not agree with the need to re-classify just the second world; the crux of the passage is, in fact, to disband the nomenclature and classifications for all countries, not just a single bloc, and to make them data-driven. Hence, option C is correct.

The author agrees that the term "Third World" carries negative hierarchical connotations. 
So option D is also incorrect.

The number of cars produced by the company are as follows: 

Total number of Type B vehicles produced in 2013, 2014 and 2017 = (200000 + 280000 + 270000) = 750000

Total number of Type A vehicles produced in 2014, 2015 and 2018 = (250000 + 200000 + 450000) = 900000 

Total number of Type B vehicles as a percentage of total number of Type A vehicles = $$\ \dfrac{750000}{900000}\times100=83.33\%$$

Hence, total number of Type B vehicles is 83.33% of the total number of Type A vehicles. 

$$\therefore\ $$ The required answer is A.

The number of cars produced by the company are as follows:

Total number of Type B vehicles produced in 2015, 2016 and 2017 = (225000 + 255000 + 270000) = 750000

Average number of Type B vehicles produced in 2015, 2016 and 2017 = $$\ \dfrac{750000}{3}=250000$$

Number of vehicles of Type A produced in 2017 = 385000

Difference between the number of vehicles of Type A produced in 2017 and the average number of Type B vehicles produced = 385000 - 250000 = 135000

Percentage = $$\ \dfrac{135000}{385000}\times100=35.06\%$$

Hence, the average number of Type B vehicles produced in 2015, 2016 and 2017 is 35.06% less than the total number of Type A vehicles produced in 2017. 

$$\therefore\ $$ The required answer is C.

The number of cars produced by the company are as follows:

Total number of Type A vehicles produced in 2013, 2015 and 2016 = (185000 + 200000 + 315000) = 700000

90% of the total number of Type A vehicles produced = 700000 $$\times\ $$ 0.9 = 630000

Total number of Type B vehicles produced in 2014 and 2017 = (280000 + 270000) = 555000

Total number of Type B vehicles produced in 2015 and 2018 = (225000 + 350000) = 575000

Total number of Type B vehicles produced in 2015 and 2017 = (225000 + 270000) = 495000

Total number of Type B vehicles produced in 2014 and 2018 = (280000 + 350000) = 630000

Hence, Total number of Type A vehicles produced in 2013, 2015 and 2016 is equal to the total number of Type B vehicles produced in 2014 and 2018. 

$$\therefore\ $$ The required answer is D.

The number of cars produced by the company are as follows:

Total number of Type A vehicles produced in 2016 and 2017 = 315000 + 385000 = 700000

Total number of Type B vehicles produced in 2014 and 2018 = 280000 + 350000 = 630000

Required ratio = $$\ \dfrac{700000}{630000}=\ \dfrac{10}{9}$$

Hence, the total number of Type A vehicles produced in 2016 and 2017 is in the ratio of 10:9 with the total number of Type B vehicles produced in 2014 and 2018. 

$$\therefore\ $$ The required answer is D.

The number of cars produced by the company are as follows:

Number of Type A vehicles produced in 2015 = 200000

Number of Type A vehicles produced in 2016 = 315000

Percentage increase = $$\ \dfrac{\left(315000-200000\right)}{200000}\times100=\ \dfrac{115}{2}\%=57.5\%$$

Number of Type A vehicles produced in 2018 = 450000

Number of Type A vehicles produced in 2019 = $$450000\times\left(1+57.5\%\right)=450000\times1.575=708750$$

Total number of Type A vehicles produced in 2019 (in thousands) = 708.75

$$\therefore\ $$ The required answer is A. 

We will assume the incomes of companies A and B in 2013 to be 300 and 400 respectively.
Profit for Company A and B are 45% and 30% respectively.
Profit % = $$\frac{Income\ -\ Expenditures}{Expenditures}\times\ 100$$.
This gives the expenditures of Companies A and B as 206.8 and 307.6 respectively.
Percentage by which A's expenditure is less than B's expenditure = $$\frac{307.6-206.8}{307.6}\times\ 100\ =\ 32.79\%\approx\ 32.8\%$$.

Profit Percentage for A in 2016 = 75%.
Profit % = $$\frac{income\ -\ \exp enditure}{\exp enditure}\times\ 100$$ where expenditures = 65.
This gives the income = 113.75.

We are given that Profit is 65% for year 2014.
So, 65% of Expenditures = Profit = 59.28
So, Expenditures of 2014 = 91.2 and Income = Exp. + Profits = 150.48.

Profit % = $$\frac{Income\ -\ Expenditure}{Expenditure}\times\ 100$$
Income is given to us as 108.8 Cr. and Profit % of Company B in 2015 = 70%.
This gives the Expenditure = 64 Cr.

Income = Expenditure*(1+P%).
Let us assume the Expenditures of both companies A and B in 2018 = X.
Income of Company A = 1.35*X and Income of Company B = 1.4*X.
The required ratio = 1.35 : 1.4 = 27:28.

The average number of scooters sold by the dealer in January, March and April = $$\frac{245+300+325}{3}=290$$
The average number of motorcycles sold in February and May = $$\frac{210+250}{2}=230$$
The difference = 60.

The total number of motorcycles sold by the dealer in January, March and May are = 300 + 350 + 250 = 900 and,
the total number of scooters sold in January, March and June = 245 + 300 + 420 = 965.
The required percentage = $$\frac{965\ -\ 900}{965}\times\ 100\ \approx\ 6.7\%$$.

Percentage increase = $$\frac{Current\ sales\ -\ \Pr evious\ sales}{\Pr evious\ sales}\times\ 100$$.
Percentage increase in sales of scooters in the month of:
February = 14.28%
March = 7.14%
April = 8.33%
May = 7.69%
June = 20%.
The percentage increase is lower than 7.5% for the month of March.

Total Scooters sold in February and May = 280 + 350 = 630.
Total Motorcycles sold in April and June = 375 + 325 = 700.
The required ratio = 630 : 700 = 9:10.

The sale of scooters increased in June 2020 over the preceding month by $$\frac{420-350}{350}\times\ 100=20\%$$.
The production increased in July 2020 by the same percentage so the production in July 2020 = 1.2*420 = 504.

Total income in 2016 and 2018 = 350 +400 = 750 and,
total Expenditures in 2013 and 2015 = 200 + 350 = 550.
The required ratio = 750:550 = 15:11.

Percentage of Expenditures increased in 2018 over 2017 = $$\frac{280-250}{250}\times\ 100\ =\ 12\%$$.
Expenditures in 2019 = Increase of 12% over 2018 i.e. 1.12*280 = 313.6.

Percentage increase in Income = $$\frac{Current\ Income\ -\ \Pr evious\ income}{\Pr evious\ income}\times\ 100$$.
In 2018, the percentage increase in income = $$\frac{400-375}{400}\times\ 100=6.25\%$$ which is less than 7%.

We will assume the expenditures in 2015 and 2019 to be 7x and 9x.
Now, expenditure in 2015 = 350 = 7x. This gives x = 50.
So, expenditure in 2019 = 9x = 450 and the company earned a profit of 20% in 2019.
This means that the income will be 1.2*450 = 540.

Total Profits earned in 2013, 2014, 2015 and 2017 = Total Income - Total Expenditures.
==> (250+300+400+375) - (200+240+350+250) = 285.
The average profits = 285/4 = 71.25.

The number of students specializing in E = 75.6 degrees and in C = 54 degrees.
The percent by which the number of students specialising in E is more than the number of students specialising in C = $$\frac{75.6-54}{54}\times\ 100\ =\ 40\%$$.

Number of Male students specializing in B = $$\frac{13}{27}\times\ \frac{97.2}{360}\times\ 2400\ =\ 312$$,
Number of Male students specializing in C = $$\frac{7}{15}\times\ \frac{54}{360}\times\ 2400\ =\ 168$$.

Number of female students specializing in A = $$\frac{8}{17}\times\ \frac{61.2}{360}\times\ 2400\ =\ 192$$,
Number of female students specializing in D = $$\frac{3}{10}\times\ \frac{72}{360}\times\ 2400\ =\ 144$$ and,
Number of female students specializing in E = $$\frac{11}{21}\times\ \frac{75.6}{360}\times\ 2400\ =\ 264$$.

The ratio of total number of male students specialising in B and C to the total number of female students specialising in A, D and E is 480 : 600 = 4:5.

The total number of students specialising in A and B = $$\frac{158.4}{360}\times\ 2400\ =\ 1056$$.
And  the total number of students specialising in D and E = $$\frac{147.6}{360}\times\ 2400\ =\ 984$$.
The value of X = 1056 - 984 = 72 i.e. it lies between 70 and 75.

Total Students specializing in B = $$\frac{97.2}{360}\times\ 2400\ =\ 648$$ and female students = $$\frac{14}{27}\times\ 648=336$$.
Total Students specializing in C = $$\frac{54}{360}\times\ 2400\ =\ 360$$ and female students = $$\frac{8}{15}\times\ 360\ =\ 192$$.
Total female students = 336 + 192 = 528.

Total Students specializing in D = $$\frac{72}{360}\times\ 2400\ =\ 480$$. 
Total students specializing in C and D = 480 + 360 = 840.
Required percentage = $$\frac{528}{840}\times\ 100\ =\ 62.85\approx\ 62.9\%$$.

The number of female students specialising in D = $$\frac{3}{10}\times\ \frac{72}{360}\times\ 2400\ =\ 144$$ and,
the number of female students specialising in E = $$\frac{11}{21}\times\ \frac{75.6}{360}\times\ 2400\ =\ 264$$.
The percent by which the number of female students specialising in D is less than the number of female students specialising in E = $$\frac{264-144}{264}\times\ 100\ \approx\ 45.5\%$$.

Male employees in Office A = $$\frac{4}{7}\times\ 1680\ =\ 960$$
Male employees in Office D = $$\frac{6}{13}\times\ 2340=\ 1080$$.

Female employees in Office B = $$\frac{5}{12}\times\ 2160\ =\ 900$$
Female employees in Office E = $$\frac{9}{14}\times\ 2520\ =\ 1620$$.
Required Ratio = (960 + 1080) : (900 + 1620) = 2040 : 2520 = 17:21.

Number of female employees in D = $$\frac{7}{13}\times\ 2340\ =\ 1260$$,
in E = $$\frac{9}{14}\times\ 2520\ =\ 1620$$ and,
in F = $$\frac{15}{28}\times\ 2240\ =\ 1200$$.
The average number of female employees in offices D, E and F = Sum/3 = 1360.
The number of male employees in office B = $$\frac{7}{12}\times\ 2160\ =\ 1260$$.
The required difference = 1360 - 1260 = 100.

Male employees in C = $$\frac{12}{23}\times\ 2760\ =\ 1440$$ and Female employees = 1320.
Total Post graduate employees = 70% of 2760 = 1932 and 832 out of these are male. This gives the number of female post graduate employees = 1100.
Percentage of female employees who are post graduate = $$\frac{1100}{1320}\times\ 100\ =\ 83.33\%$$.

Female employees in,
A = $$\frac{3}{7}\times\ 1680\ =\ 720$$
C = $$\frac{11}{23}\times\ 2760\ =\ 1320$$
F = $$\frac{15}{28}\times\ 2240=1200$$.
Total Female employees in A,C and F = 3240.

Post graduate employees in,
B = 0.65*2160 = 1404
D = 0.55*2340 = 1287
E = 0.60*2520 = 1512.
Total Post Graduate employees in B, D and E = 4203 and Average = $$\frac{4203}{3}=1401$$.

Required percentage = $$\frac{1401}{3240}\times\ 100=43.24\%$$.

Ratio of male to female employees in Office A = 4:3.
From this, the percentage of female employees = $$\frac{3}{4+3}\times\ 100\ =\ 42.85\%$$.
Similarly, the percentage of female employees in:
Office B = 41.67%
Office C = 47.8%
Office D = 53.8%
Office E = 64.2% and,
Office F = 53.5%.
So, the correct option is Office C.

The total number of students enrolled in VC in institutes B, D and E in 2015 = 227 + 242 + 251 = 720 and,
the total number of students enrolled in institute C in 2016, 2017 and 2018 = 750.
The ratio of the total number of students enrolled in VC in institutes B, D and E in 2015 to the total number of students enrolled in institute C in 2016, 2017 and 2018 = 720 : 750 ==> 24:25

The total number of students enrolled in VC in institutes B and D in 2014 and 2016 = 222 + 232 + 228 + 258 = 940.
The total number of students enrolled in 2019 in all the five institutes = 256 + 292 + 280 + 310 + 252 = 1390.
The required percentage = $$\frac{940}{1390}\times\ 100\ \approx\ 67.6\%$$.

The total number of students enrolled in VC in institutes B and E in 2017 are 255 + 285 = 540 and, 
the total number of students enrolled in institute D in 2015 and 2016 are 242 + 258 = 500.

The percent by which the total number of students enrolled in VC in institutes B and E in 2017 more than the total number of students enrolled in institute D in 2015 and 2016 = $$\frac{540-500}{500}\times\ 100\ =8\%$$.

The total number of students enrolled in VC in institutes A, B and E in 2019 = 256 + 292 + 252 = 800. 
35% of this total = 280.
280 is 12% more than 250 i.e. the number of students enrolled in 2018 in the institute A.

The average number of students enrolled in VC in institute E in 2014, 2016 and 2017 = $$\frac{249\ +\ 246\ +285\ }{3}=260$$.
The average number of students enrolled in institute B in the years:
Option A = 241.5
Option B = 238.5
Option C = 260
Option D = 240.
The average is equal to the average in Option C.

Total number of students in School A = $$\frac{44}{360}\times\ 5400\ =\ 660$$ and number of boys are 220. 
thus the number of girls in School A = 440.

Similarly, number of girls in Schools C, D and E are 520, 360 and 558 respectively.
Total number of students in School B = 1395 and 40% of these students is 558.
This is equal to the number of girls in School E.

Number of Students in School A = 44/360 * 5400 = 660.
Girls in School A = 660 - 220 = 440.
Number of Students in School C = 960.
Girls in School C = 960 - 440 = 520.
Total girls in Schools A and C = 440 + 520 = 960.
Total Boys in Schools B and D = 830 + 450 = 1280.
Required Ratio = 1280 : 960 = 4 : 3.

Total number of students in D and E = $$\frac{105\ +\ 54}{360}\times\ 5400\ =\ 2385$$.
Total number of girls in D and E = 2385 - (450+1017) = 918.
The average number of girls in schools D and E = 918/2 = 459.
Number of students in C = $$\frac{64}{360}\times\ 5400\ =\ 960$$.
The required percentage = $$\frac{960-459}{960}\times\ 100\ \approx\ 52.2\%$$.

Marks of B in Maths = 0.64*150 = 96 and Marks of B in Hindi = 66.
Total marks of B in Maths and Hindi = 96 + 66 = 162.
Similarly, Total marks of E in English, Science, Hindi and Social Studies = 36+52+48+88 = 224.
Required percentage = $$\frac{162}{224}\times\ 100\ =\ 72.3\%$$.

The total marks obtained by A, C and D in mathematics = 80+70+90 = 240%.
Average marks = 240/3 = 80% of 150 = 120.
Total marks obtained by F in all the subjects = 0.84*50 + 0.92*150 + 0.90*80 + 0.84*75 + 0.73*100 = 388.
The required percentage = $$\frac{388\ -\ 120}{388}\times\ 100\ \approx\ 69.1\%\ $$.

This is a classic question from boats and streams, where you need to apply the equation of 'speed = distance/time'.

Given that the speed of the boat in still water is a kmph, and the speed of the current is b kmph.

In the instance where the boat goes against the stream (resultant speed is a-b): 0.5x = $$\ \frac{\ 3x}{(a-b)}$$

From this, (a-b) = 6    ........(1)

In the instance where the boat goes along with the stream (resultant speed is a+b): 0.3x= $$\frac{\ 2.4x}{(a+b)}$$

From this, (a+b)= 8    ............(2)

Using the two equations: a=7 and b=1

Hence, the value of $$(a^2 + b^2)$$ is 50.

The total number of possibilities the two dice can produce together is 36.

To have 9 as the sum on the two dice, the possible combinations are: (3,6)(6,3)(4,5)(5,4)

Hence, the probability is 4/36, which is 1/9.

To know the nature of roots, we need to find the discriminant of the equation.

The discriminant for this equation is $$(-7)^2$$-4(2)(2), which is 49-16= 35.

Now, the discriminant is greater than zero, which means that the roots will be real and distinct. However, $$\sqrt{35\ }$$ is an irrational number, and hence the roots shall be real, unique, and irrational. 

Here, we need to check the options and see which one has one element from A and the other from B in each pair, without having any pair with repetitions or elements from the same set. 

Option A has (1,1) contravenes the principle discussed above, as it has two elements from set A.

Option B is correct, as it has one element each from the two sets, and there is no repetition as such. 

Option C is incorrect, as the element '4' is repeated twice.

Option D is incorrect because of the same reason that was pointed out for Option A.  

The ratio of milk and water in A is 4:5, and in B is 3:1

Let us assume that in A, the volume of milk and water is 4x and 5x (total volume is 9x).

For B, the volume can be assumed as 3y and y (total volume is 4y).

After mixing A and B, we get the ratio of milk and water as 3:2

This means, $$\frac{\ (4x+3y)\ }{(5x+y)}$$ = $$\ \frac{\ 3}{2}$$

From the above equation, we get$$\ \frac{\ x}{y}$$as $$\ \frac{\ 3}{7}$$

Hence, the volume of A becomes 27, and that of B becomes 28. 

This makes the ratio of A and B as $$\ \frac{\ 27}{28}$$.

It is said that two opposite sides of the quadrilateral are parallel.

So, it can be Square, Rhombus, Parallelogram, or Rectangle.

It is not square and rhombus because two adjacent sides are unequal(given).

It is not rectangle, because if it is rectangle the diagonal length will be $$\sqrt{\ 3^2+4^2}=5^{ }$$

So, it is a parallelogram. 

We know that for a parallelogram $$d_1^2+d_2^2=2\left(a^2+b^2\right)$$.

$$d_1=1$$

a=3

b =4

$$1^2+d_2^2=2\left(3^2+4^2\right)$$.

$$1^2+d_2^2=2\left(3^2+4^2\right)$$.$$1+d_2^2=50\ \Rightarrow d_2^2=49\ \Rightarrow\ d_2=7$$.

The value of the expression $$(800 + 7n - n^2)$$ is $$(800 + 7*7- 7^2)$$=800+49-49=800

$$\sqrt{\ 16\ +\ 2\sqrt{\ 55}}$$ can be seen as the square root of 16 + $$2\sqrt{\ 55}$$

Now on observing 16 + $$2\sqrt{\ 55}$$, we can see it as an expansion of $$(a+b)^2$$: a being $$\sqrt{11\ }$$ and b being $$\sqrt{5\ }$$.

Hence, we can rewrite the equation as $$\left(\sqrt{\ 11}+\sqrt{\ 5}\right)^2$$ , whose square root is $$\sqrt{\ 11}$$+$$\sqrt{\ 5}$$.

Let the sides of the triangle be AB, BC, and AC.

Each of the sides is made of radii of two circles. Let us assume that the radius of the three circles are x, y, and z.

Hence, 

 x+y= 21 ..............(1)

 y+z= 22 ...............(2)

 z+x= 23 ................(3)

Now from equation 3, z= 23-x ........... (4)

Substituting equation 4 in equation 2, we get x-y= 1 ...............(5)

Using equation 1 and 5, we get x= 11, y= 10, and z= 12.

The smallest radius is 10 cm, and the area of that circle is $$\pi10^2\ $$, which is approximately 314$$cm^2\ $$

Let us take terms of GP as $$a,ar,ar^2$$

then the terms in AP will be $$ar,ar^2,a$$

In that case, $$ar^2=\frac{(a+ar)}{2}$$

$$2ar^2=a+ar$$

On simplifying the equation, we get r =  or r = -1/2

r can not be 1 as that will make each term of the GP same which will not make it an infinite GP, so we get r = -1/2

⇒ Also given that sum to infinite terms of the GP = 36

$$\frac{a}{1-r\ }=36$$

plugging r=-1/2 we get

a = 54.

For the common roots, the first approach shall be to find the common points of the two equations and see if it is the root for both of them. If not, then solve the equations independently and check for the common root. 

Using the first approach, $$x^2 + 10x + 24$$ = $$x^2 + 14x + 48$$, we get x as -6 for the common point. 

On substituting this in each of the equations, we find that it is a root to both the equations, and hence the answer. 

Cos(x) is an even function, because Cos(-x) has the same points that overlap with Cos(x).

Let's designate x  cm as the length of each side of rhombus ABCD. Its perimeter is  4x cm.

Thus, 4x = 40, which leads to x = $$x=\dfrac{40}{4}$$ = 10  cm.

In triangle ABC, L is the midpoint of side AB, and M is the midpoint of side BC, resulting in LM measuring 6 cm.

Applying the similarity criterion in triangles BLM and BAC, we get $$\dfrac{BL}{BA}=\frac{LM}{AC}$$

This simplifies to $$\dfrac{BA}{2BA}=\frac{LM}{AC}$$ , which further simplifies to 1/2 = 6/AC , leading to  AC = 12 cm.

Hence, in triangle ABC, the sides are a = 10cm,  b = 12cm, and  c = 10cm.

The semi-perimeter, s, is calculated as (10+12+10)/2 = 16

The area of triangle ABC is given by $$\sqrt{𝑠(𝑠−𝑎)(𝑠−𝑏)(𝑠−𝑐)\ }$$, which equals$$\sqrt{16\times(16−10)\times(16−12)\times(16−10)\ }$$​, which further simplifies to $$\sqrt{16\times6\times4\times6\ }=48cm^2$$

As the rhombus ABCD consists of two congruent triangles ABC, its area equals 2×area of triangle ABC=2×48 cm², resulting in 96cm².

Since the two persons are traveling toward each other, their relative speed will be (36+27)kmph, which is 63kmph. 

Now, they will meet at t= $$\ \frac{\ 84}{63}$$ hours, which is $$\ \frac{\ 4}{3}$$ hours.

Now, in $$\frac{CA\ }{(CA‒CB)\ }$$, CA is the distance traveled at a speed of 36 kmph in 't' hours and CB is (84-CA)

In 't' hours, CA= $$36\times\frac{\ 4}{3}$$, which is 48 km. 

Similarly, CB= 84-48= 36 km

Putting these values in (CA/(CA ‒ CB), we get the answer as 4.

Let us assume the unknown sum to be P.
Compound interest for 2 years = $$P\left(1+r\right)^2$$ and simple interest for 2 years = $$2\Pr$$.
The difference between them is equal to $$2401\times\ P$$.
This gives: $$P\left(1+r\right)^2-2\Pr=2401\times\ P$$ 
==> $$\left(1+r\right)^2-2r=2401$$. After opening the square, we get $$r^2=2401$$ or r = 49.
50(r+1) = 2500 and it's root will be 50 i.e. Option D.

This is a special property with respect to an equilateral triangle, where its orthocentre and centroid coincide with each other. 

Also, we know that the centroid divides the median in a ratio 2:1. Hence, the orthocentre shall divide the median in the same ratio. 

This is a direct relation: If the numbers are m and n, their product will equal the product of their LCM and HCF.

Applying the same in this question, m$$\times\ $$n = 196$$\times\ $$7

Putting this in the required expression, we get the answer as $$\sqrt{\ 196}$$, which is 14.

The direct method to solve the questions for non-negative integral solution is finding the value of

$$n+r-1_{C_{r-1}}$$

Here, n= 14 r=3

Substituting the values, we get $$\ 16_{C_2}$$which is 120.

Let us assume that the area under maize and barley in the larger plot is 8x and 9x. 

Similarly, the area under maize and barley in the smaller part is 13y and 15y. 

It is given that the total area under maize and barley (taking both the plots) is in the ratio 29:33.

By this, we get that $$\ \frac{\ 8x+13y}{9x+15y}$$= $$\ \frac{\ 29}{33}$$

This is, 264x+429y=261x+435y, making this as 3x=6y, or x=2y

For the ratio of area under maize (larger plot) to area under barley in smaller plot, we shall substitute the values in 8x:15y

The final ratio is 16y:15y, or 16:15.

The bigger circle is the incircle of the triangle ABC. We know that incenter of an equilateral triangle is also it's centroid. It means that OD = 1/3rd of AD.
It also implies that OE = OD = AE = 1/3rd of AD.
AE is the median for the smaller equilateral triangle and thus radius of the smaller circle = 1/3rd of AE ==> $$\frac{1}{3}\times\ \frac{1}{3}\times\ AD=\frac{1}{9}\times\ AD$$.
AD = $$\frac{\sqrt{\ 3}}{2}AB$$. This gives the smaller radius = $$\frac{1}{9}\times\ \frac{\sqrt{\ 3}}{2}AB=\frac{\sqrt{\ 3}}{18}\times\ AB$$ and Circumference = $$2\pi\ \times\ \frac{\sqrt{\ 3}}{18}\times\ AB\ =\ \frac{\sqrt{\ 3}\pi\ }{9}\times\ AB$$.
And the perimeter of the triangle = 3AB.
Thus, the required ratio = $$\frac{\sqrt{\ 3}\pi\ }{9}\times\ AB\ \ :\ 3\times\ AB=\ \pi\ :\ 9\sqrt{\ 3}$$.

Assume that the cost price of each of the articles as Rs.100. So, the total cost price is Rs.200.

The first article is sold at a profit of 30%, which makes its selling price as Rs.130.

The second article is sold at a loss of 20%, which makes its selling price as Rs.80. 

The total selling price is Rs.210, while the total cost price is Rs.200.

Hence, profit% = (10/200) * 100, which is 5%.

To solve such questions, it is always advisable to convert the number first into decimal (base 10) and then analyse the result. 

As per the question, we have 624 in base 7. To convert it into decimal, we do: 6$$\times\ $$ $$7^2$$ + 2$$\times\ $$ 7 + 4$$\times\ $$ 1, which is 312. 

This is exactly what we have in the question, which means that the number is 312 in base 10. 

Hence, $$10^2$$ = 100

To find $$\log_2(fog(64))$$, we shall first find the value of fog(64). 

The value of g(64): $$\sqrt[3]{f(64)}$$, where f(64) is $$8^9$$

The cube root of the following expression would be $$8^3$$, which is the value of g(64).

Now, fog(64) is f($$8^3$$), which is $$8^{13}$$.

For the final result, $$\log_2\left(8^{13}\right)$$, which is $$\log_2\left(2^{39}\right)$$ , or 39. 

We will assume the interest rate = 4r% pa and the time period to be t years.
$$X\ =\ Y\left(1+r\right)^{4t}$$.
And $$Y=\ 9X\left(1+r\right)^{4t}$$. 
Equating value of $$\left(1+r\right)^{4t}$$ from both the equations to get:
$$\frac{X}{Y}=\frac{Y}{9X}$$. 
$$Y^2\ =\ 9X^2$$ ==> Y = 3X.
After putting this into the equation, we get: $$750\times\ \left(\frac{9X^2+X^2}{3X^2}\right)=2500$$.

Observing the series shows that the difference between consecutive terms is in and AP. For instance: 3-1=2, 7-3=4, 13-7=6 and so on.

Hence, the general term (when the difference of terms is in an AP) is represented by a$$n^2$$+bn+c, where n is the number of that specific term in the series.

Putting n=1, we get a+b+c=1

Putting n=2, we get 4a+2b+c=3

Putting n=3, we get 9a+3b+c=7

On solving the three equations, a=1, b=(-1), and c=1

To find the $$12^{th}$$ term, we shall put n=12 and substituting  the values of a,b, and c in the equation a$$n^2$$+bn+c, we get it as 144-12+1= 133

Let us assume the total work as 10 units.

Now, Akbar alone takes 10 days to complete the work, making his efficiency as 1 unit/day.

Babar takes 5 days to complete the same work, which means his efficiency is 2 units/day.

It is also given that Akbar, Babar, and Changez together take 2 days to complete the work, which means their combined efficiency is 5 units/day.

Therefore, Changez's efficiency would be 2 units/day (excluding Akbar and Babar from the combined efficiency).

Now, the amount shall be distributed to the three in the ratio of their efficiencies, which is 1:2:2 (Akbar, Babar, and Changez).]

This makes Changez's earning as 40 dinars out of the total 100 dinars. 

Assume that the person traveled for 't' hours. 

As per the question (extra distance because of increased speed), 12t-10t = 20, which implies that t = 10 hours. 

Hence, the distance traveled by the person in 10 hours at the speed of 10 kmph shall be 100 km.  

Let us assume that Shyaam does 3x units of work per day, while Ram does x units per day. 

In 45 days of working together, they must have done work in the ratio of 3:1 as far as the units of work done are considered. Hence, the amount earned shall also be distributed in a similar ratio. 

So out of Rs.13,500, Shyaam would have received $$\left(\frac{\ 3}{4}\right)\times\ 13500$$ for 45 days of work, which is Rs.10,125 for 45 days or Rs.225 per day.

In 10 days, Shyaam would have earned Rs.2250.

In a 5 digit binary number set, there are five places _ _ _ _ _, which shall be filled with 2 numbers (0 or 1).

Hence, for every place, we have two choices. For 5 places, we will have a total of $$2^5$$ choices, making the total count as 32. 

This means n= 32. Therefore, 2n= 64.

$$8\left(1 + \frac{1}{2} + \frac{1}{4}.....\infty\right)$$ is an infinite GP (the expression under the brackets) with the first term being 1, and the common ratio being $$\frac{\ 1}{2}$$or 0.5.

For infinite GP with common ratio less than 1, the sum is $$\ \frac{\ a}{(1-r)}$$

Applying the same in this, we get the sum as $$\ \frac{\ 1}{(1-0.5)}$$, which is 2.

Hence, the value of the entire expression is $$8\times2$$, which is 16.

As per the question (assuming the proportionality quotient be 'k'): x = k($$y^2$$+4)

Substituting the given values, 39 = k(9+4), which makes k as 3. 

Now, the value of $$\sqrt{\ y}$$ when x is 60: 60 = 3($$y^2$$+4)

From the above equation, $$y^2$$ = 16, which makes y as 4 and the square root of y as 2. 

On cross-multiplying, we get the equation: $$x^2$$ = $$2^{\frac{7}{2}}$$*$$2^{\frac{1}{2}}$$*$$3^{\frac{4}{2}}$$ 

On solving the same, $$x^2$$ = $$2^4$$*$$3^2$$

This gives the value of x as $$4\times3$$ which is 12. 

Rearranging the inequation, we get 16y>-32, or y>-2

This means the solution set for this inequation is $$(-2, \infty)$$

Out of the ten books, we need to have a case where a specific pair of two books is always there. 

To solve this, the best way is to assume the two books as a single element. This leaves us with nine different elements, where one of them has two books in it. 

To arrange nine different elements, we have 9! ways.

Now, it is important to note that the two books considered as a single element can be arranged within themselves as XY or YX (2 ways). 

Therefore, we shall multiply the initial result by 2, which makes the total number of ways as 9!$$\times\ $$2.

The shortest method to solve this question is by finding the remainder when 315654 is divided by 11. 

By doing so, we find that the remainder is 9, and adding 2 would make it divisible by 11. 

Let us assume the lengths of the larger part of the bridge and the smaller part as mx and nx.

As per the question, $$\ \frac{mx+nx}{nx}$$ = 6$$\times\ $$ $$\ \frac{\ mx}{mx+nx}$$

This means, $$\left(m+n\right)^2$$ = 6mn

Or, $$m^2+n^2$$ = 4mn

Hence, the value of $$m^2+n^2$$ - 4mn = 0, thereby making the value of $$\sqrt{25 + mn(m^2 - 4mn + n^2)}$$ as 5.

Here, the height of the parallelogram and the triangle are the same, and also the base is the same. This is because the question states that the PE divided SR into half.

The area of triangle is 1/2*b*h=1/2*x*h=37 $$\Rightarrow$$ xh=74.

Area of the PQRE is b*h=x*h=74

The total area is 37+74=111 $$cm^2$$.

The line in question (slope 'a') is perpendicular to a straight line (slope 'b') joining (2, -3) and (4, 2). Hence, a$$\times\ $$b= -1

b= $$\ \frac{\ 5}{2}$$, which makes a= $$\ \frac{\ -2}{5}$$

Hence, the equation of line with slope $$\ \frac{\ -2}{5}$$ is y= $$\ \frac{\ -2}{5}$$x + 5

Let 'a' be the radius of the bigger circle where A is its center, while 'b' is the radius of the smaller circle and B is its center.

's' is the distance between their circumference, and D is the distance between the two centers.

Hence, D = a - (b+s)

Let us assume that the total is 8 units (LCM of 2,4,8).

This means Tom does 4 units/hour, Suresh does 2 units/hour, and Adil does 1 unit/hour.

Now, Suresh's efficiency is increased and becomes 2n units/hour.

Due to this, they all complete the 8 units of work in less than 1 hour. 

This means, $$\ \ \frac{\ 8}{5+2n}<1\ $$, or n>1.5

The nearest integer is 2, making the value of $$n^2 + 2$$ as 6

$$\log_x\left[\log_5(\sqrt{x + 5} + \sqrt{x})\right] = 0$$

Shifting the 'x' from the base of LHS to the RHS, we get,

$$\log_5(\sqrt{x+5}+\sqrt{x})=x^0\ =\ 1$$

Now, shifting the '5' from the base of LHS to the RHS, we get,

$$\sqrt{\ x\ +\ 5}+\sqrt{x}\ =\ 5^1\ =\ 5$$

$$\sqrt{\ x\ +\ 5}\ =\ 5\ -\ \sqrt{\ x}$$

Squaring on both sides, we get,

$$\ x\ +\ 5\ =\ 25\ +\ x\ -\ 10\sqrt{\ x}$$

$$\ 10\sqrt{\ x}\ =\ 20$$

$$\sqrt{\ x}\ =\ 2$$

$$x\ =\ 4$$

Hence, the correct answer is option C.

Case 1: P is wrong.
According to Q, it is night but according to R, it is neither night nor day which means that they both can't be true together. So, this case is not possible.

Case 2: Q is wrong.
Again, statements of P and R can not exist together, so this case is also not possible.

Case 3: R is wrong.
According to the statements of P and Q, it is night and this conclusion is supported by both the statements.
Thus, the answer is Option D.

Since it is given that ONLY creative and innovative people can score high on the test, it is clear that anyone who scores high shall be both creative and innovative. If Rahul has scored high, he shall be both creative and innovative.

1 2 3 are 3 consecutive numbers.
4 6 8 are alternate numbers.
9 10 11 are consecutive numbers.
12 14 16 are alternate numbers.
17 18 19 are consecutive numbers.
Considering the pattern, the next numbers should be alternate i.e. 20 22 24 and thus the answer is Option B - 202224.

A - B + C % D means that A is the mother of B and that B is also the daughter of C. It means that A and C are respectively the mother and father of B.
C % D implies that C is the brother of D and A is the wife of C. It means that A is the sister-in-law of D.
Thus, the correct answer is Option A.

The middle number represents the numerical position of the middle letter of the other 2 letters.
The terms start with capital letters alternatively. As the given last term is P17r, the next term shouldn't start with capital letter.
Considering these 2 conditions, only b3D could be the next term.

The letters follow a normal additive pattern
1st letter has a patter of +5, 2nd letter has a pattern for +7 and 3rd letter has a pattern of +9.
It means A+5 = F, p+5 = w and D+9 = M.
By following the same pattern in KdV, we get K+5 = P, d+7 = k and V+9 = E i.e. PkE.

J corresponds to the sum of 4 upper parts of the left wheel i.e. 1+2+3+4 = 10.
Z corresponds to the sum of 4 lower parts of the left wheel i.e. 5+6+7+8 = 26.
S corresponds to the sum of 4 lower parts of the right wheel i.e. 4+7+2+6 = 19.
So, the letter that should come at ? will be 9+1+3+5 = 18th letter i.e. R.

Both A and R are true, but A needs a reasoning that explains why doctoral fellows are hired as research assistants.  However, R merely talks about research training being imparted in doctoral fellows. 

s + 2d + 3t = 45 + 51 + 64 = 160 where "s" represents number of students who like only one of the three classes, "d" represents number of students who like only two of the three classes and "t" represents number of students who like all of the three classes.
s + d + t = 100 - 6 = 94.
By subtracting these equations, we get: d + 2t = 66. 
d = 29-X + 32-X + 25-X = 86 - 3X and t = X.
86-3X + 2X = 66 ==> X = 20.
t = 20 and d = 26. This gives s = 94 - 26 - 20 = 48.
So, the students who like only one of the three classes are 48% of the Total number of students i.e. 48% of 300 = 144.

From the given information, only Statement II is practical and can be inferred.

Only Conclusion 1 and 3 follow as conclusion 2 is only one of the possible cases and thus does not always follow.

$$G\ \times\ A\ -\ C\ +\ B$$ means that G is the father of A and A is the sister of C. 
Also, C + B implies that C is the brother of B. It means that G is father of C and C is a boy which implies that C is the son of G.
Thus, the answer is Option A.

Nether Conclusion 1 nor Conclusion 2 follows.

P # S $ Q @ R implies that P is the sister of S and S is the son of Q.
From this, we can infer that P is the daughter of Q and that's why the correct answer is Option B.

The formula is: $$\ \frac{\ 11}{2}$$ $$\ \times\ $$hour - 30$$\ \times\ $$minutes for the angle.

Keeping hours as 5 and minutes as 40, we get the expression as 220-150, which is 70 degrees.

The statement given is: "His mother is the wife of my father’s only son."

1. "My father’s only son" refers to the speaker himself because the speaker's father has only one son, which is the speaker.
2. "His mother" refers to the mother of the person in the photograph.

Putting it together, "His mother is the wife of my father’s only son" means "The mother of the person in the photograph is married to my father's only son ."

If the mother of the person in the photograph is married to the speaker, then the person in the photograph is the speaker's brother. Therefore, the speaker, being the brother's sister, is indeed the aunt of the person in the photograph.

Option C) is correct.

The circles are dotted in this pattern:

First, the dot just above the colored dot is filled.

Then, the dot just left of the colored dot is filled.

Then again, the dot just above the dot is filled, and this pattern continues.

So, in the final figure, a dot on the left side of the colored dot is filled.

Option A) is the correct answer.

The terms are AsT, cQv, EoX, ?, IkB

If you see the first term, that is AsT

First element is A, second element is s and third element is T.

If you see the second term, that is cQv

First element is c, second element is Q and third element is v.

We see that the first element of both terms follows a relation that is first term + 2

A+2 = c (Capital letter turns into the small letter and element is added by 2)

Similarly, for the second element, the relation is the first term - 2

s - 2 = Q (small letter turns into the capital letter and element is subtracted by 2)

Similarly, for the third element, the relation is first term + 2

T + 2 = v (Capital letter turns into small letter and element is added by 2)

So, the term after EoX will be

E + 2 = g

o -2 = M

X +2 = z

Thus, gMz is the correct answer. 

Pallavi beat Rashmi and Vijaya only which means that Pallavi got 4th rank and Rashmi and Vijaya got either 5th or 6th rank.
Urvashi was beaten by Teesta only which means that Teesta got 1st rank and Urvashi got the 2nd rank.
The only person left is Simran and the only rank left is 3rd. It means that Simran got the 3rd rank i.e. the Bronze medal.

Conclusion 1 is a restatement of the main statement, hence a valid conclusion.

Conclusion 2 introduced personal and professional details, which are not covered in the main statement. Hence, an invalid conclusion.

The final placement will be: 

People sitting between A and E are B and H i.e. Brad and Harriet.

The day of the week on 14 August 2010 was Saturday. You can find out by using this approach-

You must definitely know what today's date and day are.

Thus, by going backwards, you can find the day of the week on 14th August 2010.

Let's analyze the given information:

1. 20 air conditioners were sold in December 2020.

2. The number of washing machines sold was a quarter of the number of air conditioners sold, so it would be (1/4)*20 = 5 washing machines.

3. The number of televisions sold was the same as the number of air conditioners sold, which is 20 televisions.

We can find the ratio of the different electrical items sold:

- Air conditioners: 20

- Washing machines: 5

- Televisions: 20

Therefore, Statement A can be determined is correct.

We cannot determine the number of dishwashers sold based on the given information, Statement B can't be determined.

Thus, Option A) is the answer.

We will check each option and try to find any condition that makes it invalid; otherwise, that option can't be the answer.

The answer will be the option in which none of the conditions are invalid.

Option A) Chhavi, Dhairya, Eklavya, Gauri, Farah, Isha

We know from statement 2 that if Chhavi is selected, then Jayanti is definitely selected. But here, Jayanti is not selected, so this is incorrect.

Option B) Abhay, Bharti, Eklavya, Gauri, Isha, Keshav

We know from statement 3 that Himanshu and Keshav will always be selected together. But here, only Keshav is selected. Hence, this is incorrect.

Option C) Abhay, Bharti, Eklavya, Farah, Himanshu, Isha

We know from statement 3 that Himanshu and Keshav will always be selected together. But here, only Himanshu is selected. Hence, this is incorrect.

Option D) Bharti, Chhavi, Eklavya, Farah, Jayanti, Isha

All conditions are satisfied in this option.

Thus, Option D) is the correct answer.

Let us assume Lange is the Liar => The other two are truthful. But Pora's statement is a lie => Contradiction => Lange is not the Liar.

Let us assume Pora is the Liar => The other two are truthful.  But Lange's statement is a lie => Contradiction => Pora is not the Liar.

=> When Hiri is the liar, we don't find any contradictions in the statements of the 3 people=> Hiri is the Liar.

Using the given conditions we can get a grid like this.

We are told each girl plays two instruments => We know what Ankita and Litika will be playing.

=> Guitar is played by Ankita and Litika.

Let us denote people by the first letter of their names.

=> Let's say the height of T is 'x' => Height of R is 1.5x

=> Let's say height of K is 'y' => Height of S is 1.5y

Given that Pawan is half the height of Shyam and twice the height of Rakesh

=> 1.5y/2 = 3x => y = 4x

=> The heights of the people are R = 1.5x, T = x, S = 1.5y = 6x, K = 4x, P = 3x

=> S, i.e. Shyam is the tallest

=> Option-A

The hour hand moves through 7 hours.

If it covers 360 degrees in 12 hours, then in 7 hours, it will cover => 360/12 * 7 = 210 degrees.

=> Option-B

As given in the question, the trains take least expensive route between P and S.
The least expensive route between P and S is P - U - S and thus the answer is Option C.

As Hemang fulfills all the 4 criteria, he is to be directly appointed as the IT Head.

As Vandita fulfills only criteria 1 and 2 and has not worked as an IT administrator, she is not to be appointed a the IT Head.