CAT 50 Day Streak Day 28

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CAT 50 Day Streak – Day 28

30 questions across VARC, DILR & QA · +3 for a correct answer · −1 for a wrong MCQ · no negative marking for TITA

0/30Attempted

0Correct

0Wrong

0Score / 90

VARC · Verbal Ability & Reading Comprehension

Q1 – Q10 0/10

Passage · Q1 – Q4

Every now and then, life asks us a question we aren’t quite sure how to answer. Which career should we pursue? Should we have children? Should we move to the coast, or closer to our friends? We gather information, read testimony, and place our exhaustively researched options on either side of the scales, but the scales never settle. One option seems better in some ways, the other seems better in others, and we find ourselves stuck between them. The ‘best’ answer eludes us. This is what the philosopher Ruth Chang calls a ‘hard choice’. Chang proposes that what makes these kinds of choices hard is not so much their content but their structure: they don’t fit into our standard trichotomy of value in decision making.

Usually, we compare two options using ‘better’, ‘worse’, or ‘equal to’. If there are better reasons to do X than Y, then the rational thing is to pick X; meanwhile, if X and Y are equal, then it doesn’t matter which one we pick. But hard choices defy this evaluative framework. They involve cases where choices are no better or worse than each other. Our dilemma surely exists, we might think, because the options are equally good and we can’t decide between them. But Chang suggests this is a mistake. One option is no better or worse than the other, but they lead to different — often mutually exclusive — kinds of futures, and we cannot decide which kind of future to have. When it comes to hard choices, Chang thus argues, the standard trichotomy of ‘better’, ‘worse’, and ‘equal to’ is insufficient. To aid our thinking, she introduces a fourth dimension: parity. We should think of the options not as equal but as on par.

Thinking in terms of parity can help us clarify what’s at stake in hard choices. Suppose a young person is stuck between pursuing a career in forestry or law. They see the former as better in some ways, and law as better in others. They’ve researched the decision as much as they possibly can. They’ve garnered testimony from foresters and lawyers. But still they can’t decide. The young person might think, “if only I could see how my life would go in forestry, and then in law, so I could compare the two and make a more informed choice about which is better or worse…” But Chang argues that even if the young person could do this, it wouldn’t help them decide. They would simply bear witness to two different kinds of life, both with their own rewards and hardships, and watch themselves become a different version of themselves in each.

This is the crux of a hard choice: when options are on a par, we hunt for a definitive reason, given to us by the world, for picking one over the other. The way isn’t signposted. External reasons have ‘run out’. But rather than feel mired in gloom or anxiety by this, Chang notes, we might actually see it as quite powerfully liberating. If external reasons have run out, then perhaps we can choose to be guided by internal ones.

Q1MCQ

According to the passage, all of the following are true about ‘hard choices’ EXCEPT:

AThey cannot be resolved by comparing options as better, worse, or equal.

BThey often involve decisions that can shape fundamentally different futures.

CThey arise because individuals lack sufficient information about their options.

DThey resist resolution even when both options seem to offer unique advantages.

Solution Answer: C

The passage says the opposite of C. The young person has “researched the decision as much as they possibly can”, and Chang argues that even seeing both lives “wouldn’t help them decide”. Hard choices come from their structure, not from missing information.

A matches the claim that the trichotomy “is insufficient”. B matches “different — often mutually exclusive — kinds of futures”. D matches “better in some ways… better in others” while the scales “never settle”.

Q2MCQ

According to the author’s discussion of Ruth Chang’s ideas, all of the following are implied EXCEPT:

AHard choices expose the limitations of traditional evaluative categories.

B‘Parity’ represents a distinct way of comparing options that are neither better nor worse.

CWhen external reasons fail, personal values and commitments can guide the decision.

DThe existence of parity implies that rational decision-making is impossible.

Solution Answer: D

Chang never says rational choice becomes impossible. When external reasons run out, we can still be guided by internal ones, and she calls that “liberating”. So D is not implied.

A follows from “hard choices defy this evaluative framework”. B is the definition of parity as a fourth dimension. C is the passage’s final line.

Q3MCQ

Which of the following, if true, would most seriously weaken Chang’s claim that additional empirical information would not help in resolving cases of parity?

AControlled studies indicate that participants who vividly simulate both possible futures—through immersive scenarios and reflective journaling—tend to report greater decisional clarity and reduced indecision over time.

BLongitudinal data reveal that even individuals facing difficult life choices typically experience eventual satisfaction, regardless of the method used to make their decisions.

CExperimental findings suggest that people who deliberate with close friends and family before making major choices are more likely to express post-decision regret than those who decide independently.

DStatistical comparisons demonstrate that while career options such as law and medicine differ substantially in average income and stability, subjective well-being across these fields remains broadly similar.

Solution Answer: A

Chang says that even seeing how life would go down each path wouldn’t help. A shows that simulating both futures, which is close to that exact thought experiment, does produce clarity. That directly undercuts her claim.

B is about eventual satisfaction, not about resolving the choice. C concerns advice from family, not extra information about the options. D, if anything, supports parity (different options, similar well-being).

Q4MCQ

Which implicit assumption underlies Chang’s argument as described in the passage?

AAll significant life choices can be ranked by a single measurable metric.

BDistinct lives produced by different choices can each be valuable in different ways.

CPeople prefer external guidance to internal deliberation in difficult situations.

DParity implies that choices are meaningless and arbitrary.

Solution Answer: B

Parity only makes sense if two different lives can each be valuable in their own way, “both with their own rewards and hardships”, without one being better overall. That is the unstated premise.

A contradicts the argument, since a single metric would allow ranking. C isn’t needed; Chang actually suggests internal reasons can be liberating. D contradicts her view that the choice is meaningful and can be guided by our own values.

Q5MCQ

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.

Sentence The thought of their kids traveling solo might get some parents wringing their hands, and for good reason.

Paragraph ___(1)___. Biking can be risky, and finding an appropriate place to practice can be tricky in the city or in the suburbs. ___(2)___. But if parents can find safe environments for teaching their children to navigate streets confidently on their own, the amount of freedom those kids will gain is invaluable. ___(3)___. On a bike, a child gets to choose where to go and how to get there without having to check in with a parent, which lets them practice making decisions. ___(4)___. As they ride more, the activity can even start to rewire their brain, helping them form spatial maps of their neighbourhood.

AOption 1

BOption 2

COption 3

DOption 4

Solution Answer: A (Option 1)

The sentence introduces parents’ worry “for good reason”. The next sentence supplies those reasons: biking is risky and safe practice spaces are hard to find. Then “But if parents can find safe environments…” answers the worry. So it opens the paragraph at blank 1.

At blanks 2–4 the paragraph has already moved past the worry to the benefits of freedom, decision-making and spatial maps, so a fresh worry would break the flow.

Q6TITA

Five jumbled-up sentences (labelled 1, 2, 3, 4 and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence and key in the number of that sentence as your answer.

The good news is, lots of other people want to be more sociable too.
I study not just what choices people make during their social interactions, but also how they might make better ones.
These puzzles guide my research into conversation.
Some people take conversations for granted because the best ones feel easy and natural.
And yet I’m often surprised by the opportunities people miss to enjoy one another’s company, to learn from each other, and to start building new, meaningful connections.

Solution Answer: 4

The coherent paragraph is 1 → 5 → 3 → 2:

1: Many people want to be more sociable (“the good news”).
5: “And yet” they miss chances to connect, which contrasts with that wish.
3: “These puzzles” (the missed opportunities) guide the author’s research.
2: What that research studies: the choices people make and how to make better ones.

Sentence 4 offers a reason why people take conversation for granted. Nothing else in the chain picks up that idea, so it is the odd one out.

Q7TITA

The four sentences (labelled 1, 2, 3 and 4) given below, when properly sequenced, would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer.

Because A.I. can generate abridgments, summaries, and other condensed editions on demand, we may even switch between versions as circumstances dictate.
We may routinely start with alternative texts and only later decide to seek out originals, in roughly the same way that we now download samples of new books to our Kindles before committing to them.
But over the next decade or so, that polarity may well reverse.
In our current reading regime, summarized or altered texts are the exception, not the rule.

Solution Answer: 4321

The order runs like this:

4: Today, altered texts are the exception, not the rule.
3: “But… that polarity may well reverse” refers back to exception vs. rule.
2: What the reversal looks like: we start with alternative texts and seek originals later.
1: “We may even switch between versions” takes the idea one step further.

Q8MCQ

The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.

Passage Before Flores entered her 60s, her name was almost entirely unknown outside her own community. Her work is steeped in the ancient Shipibo-Conibo tradition of patternmaking known as kené. The art form is communal and typically anonymous. Historically, few practitioners signed their work. Kené’s unwritten rules and symmetrical designs have been passed down matrilineally for generations. Most Shipibo-Conibo art was long dismissed as folkloric by the cultural establishment. But in 2011, an Italian-born artist, Matteo Norzi, discovered Flores’ work in Peru and later helped her showcase it internationally for the first time in 2018.

AMatteo Norzi’s discovery and promotion of Flores shows that a single intermediary can be decisive in turning a previously anonymous traditional artist into an internationally exhibited figure.

BFlores’s belated international recognition illustrates how Shipibo-Conibo kené—a communal, matrilineal art long dismissed as folkloric—has begun to gain appreciation beyond its local context.

CThe passage argues that kené remained completely unknown outside its community until large cultural institutions began systematically showcasing it abroad.

DFlores achieved fame by signing and commercializing her kené designs, thereby breaking with local tradition and attracting international attention.

Solution Answer: B

B captures all three elements: Flores’s late recognition, the nature of kené (communal, matrilineal, dismissed as folkloric), and its move onto the international stage.

A turns Norzi into the main point and draws a general lesson the passage doesn’t make. C invents “large cultural institutions”; it was one artist. D invents signing and commercialisation.

Q9MCQ

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.

Sentence NASA’s share of the mission cost $1.2 billion, and ISRO’s contribution was comparable, NASA officials said.

Paragraph ___(1)___. The idea for a mission like NISAR dates back to a recommendation that appeared in a once-a-decade report by earth scientists that lays out the field’s top priorities for observing Earth from space. ___(2)___. NASA looked for an international partner to share the work and cost and finally found one in India in 2014. ___(3)___. Collaboration with India in space has increased in recent years. An Indian astronaut, Shubhanshu Shukla, flew on the private Axiom-4 mission to the International Space Station last month, spending 18 days there. ___(4)___.

AOption 1

BOption 2

COption 3

DOption 4

Solution Answer: C (Option 3)

The sentence splits the cost between NASA and ISRO. It must come right after NASA finds a partner “to share the work and cost” in India, which puts it at blank 3.

At blanks 1 and 2, India hasn’t been introduced yet, so “ISRO’s contribution” would have nothing to refer to. Blank 4 follows the Shukla astronaut example, which is a different topic.

Q10TITA

One way I might describe it is to say that I study symmetries of mathematical objects.
But when I went to college at Harvard, I took a course in topology, which is the study of spaces.
There are a lot of other ways symmetries come up, and they can get really, really complicated.
This comes about when you’re interested in things like our universe, where the Earth is rotating, and it’s also rotating around the sun, and the sun is in a larger system that is rotating.
All those rotations are symmetries.

Solution Answer: 2

The coherent paragraph is 1 → 4 → 5 → 3:

1: The author studies symmetries of mathematical objects.
4: “This comes about” with the example of a rotating universe.
5: “All those rotations are symmetries.”
3: “A lot of other ways” symmetries come up, beyond rotations.

Sentence 2 is a biographical aside about a college topology course. Its “But” has nothing to contrast with, and it breaks the explanation of symmetry.

DILR · Data Interpretation & Logical Reasoning

Q11 – Q20 0/10

Set 1 · Q11 – Q15

Each of the four professors - Anwar, Badal, Casper, and Daljeet - taught for an integral number of years in each of the three colleges - IIT X, IIT Y, and IIT Z. The total time spent in the three colleges together was distinct for the four professors. The total time spent by the four professors together in IIT X, IIT Y, and IIT Z was 12, 13, and 14 years respectively. No professor spent an equal number of years in any two colleges. No two professors spent an equal number of years in any college. Each professor taught for at least one year in each college. It is also known that:

Among the three colleges, Daljeet spent the least time in IIT Y and the maximum time in IIT Z.
The number of years spent by Anwar and Casper in IIT Z was 4 and 2 respectively.
The total time spent in the three colleges together by Casper was more than that by Anwar.
The total time spent by Badal in the three colleges together was 16 years.
The difference between the number of years spent by Anwar in IIT X and the number of years spent by Casper in IIT Y was 2.

Q11TITA

How many years did Badal spend at IIT Z?

Solution Answer: 5

Possible column values. Each college has four distinct values, each at least 1. For IIT X (sum 12), the sets are {1,2,3,6} or {1,2,4,5}. For IIT Y (sum 13), they are {1,2,3,7}, {1,2,4,6} or {1,3,4,5}. So X ≤ 6 and Y ≤ 7.
IIT Z. Anwar and Casper have 4 + 2, so Badal + Daljeet = 8 with values other than 2 and 4. Daljeet’s Z is his maximum, so Daljeet’s Z ≥ 3. That leaves (Badal, Daljeet) = (1, 7), (3, 5) or (5, 3).
Badal = 16. If Badal’s Z were 1, he’d need 15 from X + Y, which is above the maximum 6 + 7 = 13 ✗. If it were 3, he’d need X = 6 and Y = 7, which leaves Casper only {1, 3} in X and Y. Then |Anwar’s X − Casper’s Y| = 2 can’t be met ✗. So Badal’s Z = 5 and Daljeet’s Z = 3.
Daljeet. His Z = 3 is his maximum and Y is his minimum, so Y = 1, X = 2, total 6.
Badal. He needs X + Y = 11 with no value repeating his 5, which forces X = 4 and Y = 7. So X = {1,2,4,5} and Y = {1,2,3,7}.
Anwar and Casper. They share X {1, 5} and Y {2, 3}. Casper’s Z is 2, so Casper’s Y = 3 and Anwar’s Y = 2. |Anwar’s X − 3| = 2 gives Anwar’s X = 1 or 5. If it were 5, Casper would total 6, less than Anwar ✗. So Anwar’s X = 1 and Casper’s X = 5.

Professor	IIT X	IIT Y	IIT Z	Total
Anwar	1	2	4	7
Badal	4	7	5	16
Casper	5	3	2	10
Daljeet	2	1	3	6
Total	12	13	14	39

Badal spent 5 years at IIT Z.

Q12TITA

What was the highest number of years spent by any professor in any of these colleges?

Solution Answer: 7

From the table in Q11, the highest single value is Badal’s 7 years at IIT Y.

Q13MCQ

What was the total time spent (in years) by Casper in the three colleges altogether?

B10

C11

D12

Solution Answer: B

From the table in Q11, Casper: 5 + 3 + 2 = 10 years.

Q14MCQ

Who spent the least time in IIT X?

AAnwar

BBadal

CCasper

DDaljeet

Solution Answer: A

From the table in Q11, the IIT X values are Anwar 1, Badal 4, Casper 5 and Daljeet 2. The least is Anwar.

Q15MCQ

Which of the following is not the time spent by any of the professors in any of the colleges?

A4 years

B5 years

C6 years

D7 years

Solution Answer: C

From the table in Q11, the values used are 1, 2, 3, 4, 5 and 7. No professor spent 6 years in any college.

Set 2 · Q16 – Q20

Eight customers - Pushkar, Quinton, Rehman, Sandeep, Tilak, Uday, Veer, and Wahab ordered one food item each from Chicken, Burger, Pizza, Biryani, Noodles, Pasta, Idli, and Fries using different coupon codes - Happy Hours, Desi, Stay Home, Match Day and BOGO from a food delivery app.

Four delivery boys, Ahmad, Bhanu, Charanjeet, and David, delivered orders to these customers. No more than two people order food using the same code. Each delivery boy delivered two customer orders. Quinton ordered the food using the code Desi, but the order was not delivered by Bhanu. Sandeep ordered Noodles, and the order was delivered by Ahmad. Veer used the code Happy Hour, and his order was delivered by Charanjeet. Biryani was ordered using the code Happy Hour and was delivered by Charanjeet. Rehman is the only person who used the BOGO code, and he ordered a Burger. Pushkar ordered Fries, and the order was delivered by Bhanu. Both Sandeep and Tilak used the same code. The same was the case with Pushkar and Uday. Idli was ordered using the Match Day code. Wahab did not order Pizza. Pizza was ordered using the Happy Hour code. Chicken and the food ordered using the code BOGO were delivered by David. Ahmad did not deliver the order to Quinton or Tilak. Ahmad did not deliver the Pasta.

Q16MCQ

Who ordered Pasta?

ATilak

BUday

CQuinton

DWahab

Solution Answer: A

Happy Hours. Pizza and Biryani both used Happy Hours, and so did Veer. The code allows only two people, so Veer and one other person ordered Pizza and Biryani.
The second Happy Hours customer. It can’t be Sandeep/Tilak or Pushkar/Uday, because each pair shares a code and that would make three. It can’t be Quinton (Desi) or Rehman (BOGO). So it is Wahab. Wahab didn’t order Pizza, so Wahab has Biryani and Veer has Pizza. Charanjeet delivered both.
Other codes. Desi can’t take either pair (that would be 3 with Quinton), so Desi is used only by Quinton. The two pairs take Stay Home and Match Day.
Deliveries. David has Rehman plus the Chicken order. Quinton, Tilak and Uday fill the remaining slots with Ahmad, Bhanu and David. Ahmad can’t take Quinton or Tilak, so Ahmad delivers Uday. Quinton isn’t Bhanu’s, so David delivers Quinton, who therefore has Chicken. Bhanu delivers Tilak.
Foods and codes. Ahmad didn’t deliver Pasta, so Uday has Idli and Tilak has Pasta. Idli used Match Day, so Pushkar and Uday used Match Day, and Sandeep and Tilak used Stay Home.

Customer	Food	Code	Delivered by
Pushkar	Fries	Match Day	Bhanu
Quinton	Chicken	Desi	David
Rehman	Burger	BOGO	David
Sandeep	Noodles	Stay Home	Ahmad
Tilak	Pasta	Stay Home	Bhanu
Uday	Idli	Match Day	Ahmad
Veer	Pizza	Happy Hours	Charanjeet
Wahab	Biryani	Happy Hours	Charanjeet

Tilak ordered Pasta.

Q17MCQ

What code was used by Sandeep?

AMatch Day

BStay Home

CDesi

DHappy Hours

Solution Answer: B

From the table in Q16, Pushkar and Uday took Match Day (Uday ordered Idli), so Sandeep and Tilak used Stay Home.

Q18MCQ

Which of these codes was used only once?

AMatch Day

BStay Home

CDesi

DHappy Hours

Solution Answer: C

From the table in Q16, Match Day, Stay Home and Happy Hours were each used twice. Desi was used only by Quinton. BOGO was also used once, but it isn’t among the options.

Q19MCQ

Who delivered the order to Tilak?

AAhmad

BBhanu

CCharanjeet

DDavid

Solution Answer: B

From the table in Q16, Tilak’s Pasta was delivered by Bhanu.

Q20MCQ

What food item did Uday order?

AChicken

BPasta

CBiryani

DIdli

Solution Answer: D

From the table in Q16, Uday was delivered by Ahmad, who didn’t deliver Pasta. So Uday ordered Idli.

QA · Quantitative Ability

Q21 – Q30 0/10

Q21TITA

A tank is filled by three pipes with different uniform flow rates. While the first two pipes are operating simultaneously, they fill the tank in the same duration that the third pipe takes to fill it alone. The second pipe can fill the tank 5 hours quicker than the first pipe, yet 4 hours slower than the third pipe. What is the time (in hours) needed for the first pipe to fill the tank?

Solution Answer: 15

Let the first pipe take a hours. Then the second takes a − 5 and the third takes a − 9.

1a + 1a − 5 = 1a − 9, so (2a − 5)(a − 9) = a(a − 5).

This gives a² − 18a + 45 = 0, i.e. (a − 15)(a − 3) = 0. Here a = 3 would make the other times negative, so a = 15 hours.

Q22MCQ

A company needs to manufacture a closed rectangular tank with a square base. The required volume of the tank is 72 cubic meters. The material for the top and bottom of the tank costs Rs. 800 per square meter, while the material for the four vertical sides costs Rs. 300 per square meter. What is the minimum possible cost to build such a tank?

A36000

B40800

C43200

D39600

Solution Answer: C

Let the base side be x and the height h, with x²h = 72.

Cost = 800 × 2x² + 300 × 4xh = 1600x² + 1200 × 72x = 1600x² + 86400x.

Setting the derivative to zero: 3200x = 86400x², so x³ = 27 and x = 3 (h = 8).

Minimum cost = 1600 × 9 + 86400/3 = 14400 + 28800 = Rs. 43,200.

Q23MCQ

If f(x) = log 1 + x1 − x, then f(x) + f(y) is:

Af(x + y)

Bf(x + y1 + xy)

C(x + y) f(11 + xy)

Df(x) + f(y)1 + xy

Solution Answer: B

f(x) + f(y) = log (1 + x)(1 + y)(1 − x)(1 − y) = log 1 + xy + x + y1 + xy − x − y.

Divide the numerator and denominator by (1 + xy) and let t = x + y1 + xy. The expression becomes log 1 + t1 − t = f(t).

So f(x) + f(y) = f((x + y)/(1 + xy)).

Q24MCQ

Rahul and Sajal start simultaneously from opposite ends of a 1 km-long walkway. Rahul is on the walkway, moving from end X to end Y, while Sajal is on the stationary ground parallel to it, moving from end Y to end X. The walkway moves at a constant speed from X to Y. They cross each other after 18 seconds. After crossing, Sajal takes 27 more seconds to reach his destination (end X) than Rahul takes to reach his (end Y). The speed of the walkway is half of Sajal’s walking speed. What is the ratio of Rahul’s walking speed to Sajal’s walking speed?

A2:1

B5:4

C4:3

D3:2

Solution Answer: D

Let Sajal’s speed be s and the walkway’s speed w = s/2. Rahul’s effective speed is R = r + w.

In 18 s, Rahul covers 18R and Sajal covers 18s. After crossing, each covers the other’s distance:

Sajal’s time − Rahul’s time = 18Rs − 18sR = 27.

With k = R/s: k − 1/k = 1.5, so 2k² − 3k − 2 = 0 and k = 2. So R = 2s.

Rahul’s walking speed r = 2s − 0.5s = 1.5s. Ratio r : s = 3 : 2.

Q25MCQ

How many integers from 1 to 1000000, both inclusive, are either perfect squares or perfect cubes or perfect fourth powers?

A1090

B1115

C1121

D1131

Solution Answer: A

Every fourth power is also a perfect square, so we only need squares or cubes.

There are 1000 squares (1² to 1000²) and 100 cubes (1³ to 100³). Numbers that are both are sixth powers: 1⁶ to 10⁶, which is 10.

Total = 1000 + 100 − 10 = 1090.

Q26TITA

If x, y, z are positive integers such that xy + z = 2020 and x + yz = 2021, find the largest value among x, y, and z.

Solution Answer: 674

Subtracting the two equations: x + yz − xy − z = 1, so (x − z)(1 − y) = 1.

Since y ≥ 1, the factor 1 − y ≤ 0. So both factors must be −1: y = 2 and z = x + 1.

Then 2x + x + 1 = 2020, so x = 673 and z = 674. Check: 673 + 2 × 674 = 2021 ✓.

The largest value is 674.

Q27MCQ

A coin is tossed 10 times. Find the probability of getting at most six heads.

A343/512

B53/64

C105/128

D201/256

Solution Answer: B

P(7 or more heads) = (¹⁰C₇ + ¹⁰C₈ + ¹⁰C₉ + ¹⁰C₁₀)/2¹⁰ = (120 + 45 + 10 + 1)/1024 = 176/1024.

P(at most 6) = 1 − 176/1024 = 848/1024 = 53/64.

Q28MCQ

A right circular cylinder whose diameter is equal to its height is inscribed in a right circular cone of base diameter 16 cm and height 48 cm. The axes of both solids coincide. What is the volume of the solid inside the cone but outside the cylinder?

A512π cm³

B540π cm³

C592π cm³

D616π cm³

Solution Answer: C

The cone has radius 8 and height 48. Let the cylinder have radius r and height 2r.

By similar triangles, r/8 = (48 − 2r)/48, so 48r = 384 − 16r and r = 6. The cylinder’s height is 12.

Cone = ⅓π × 64 × 48 = 1024π. Cylinder = π × 36 × 12 = 432π.

Required volume = 1024π − 432π = 592π cm³.

Q29TITA

In the given figure, EBCD is a rectangle and ABC is a right-angled triangle. Also, BE = AB < AC. If the area of ABC = 54 sq cm, find the area of EBCD (in sq cm)

Rectangle EBCD with ED = 15 cm; right-angled triangle ABC sits on side BC with the right angle at A, area 54 sq cm; AB and BE are marked equal

Solution Answer: 135

BC = ED = 15, and the right angle is at A. So AB² + AC² = 225 and ½ × AB × AC = 54, i.e. AB × AC = 108.

(AB + AC)² = 225 + 216 = 441, so AB + AC = 21. (AC − AB)² = 225 − 216 = 9, so AC − AB = 3. That gives AB = 9 and AC = 12.

BE = AB = 9, so the area of EBCD = 15 × 9 = 135 sq cm.

Q30MCQ

A drum contains 200 L of milk. From the drum, 40 L of milk is removed and replaced with water. This process is repeated one more time. Subsequently, 50 L of the resulting mixture is taken out and replaced with pure milk. This process is repeated one more time. What is the final quantity of milk in the drum?

A159.5 L

B155 L

C162.5 L

D164 L

Solution Answer: A

After the two water replacements: milk = 200 × (4/5)² = 128 L.

First milk replacement: 128 × ¾ + 50 = 96 + 50 = 146 L.

Second milk replacement: 146 × ¾ + 50 = 109.5 + 50 = 159.5 L.

Day 28 complete! 🔥

0 / 90

Correct: 0 · Wrong: 0 · Accuracy: 0%

Keep the streak alive. See you tomorrow for Day 29.