CAT 50 Day Streak Day 26

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CAT 50 Day Streak – Day 26

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

It’s impossible to forget just how much the sun affects life on our planet. It’s overwhelmingly the source of our light and heat, providing just enough to maintain the delicate climatic balance we enjoy. That’s not a coincidence; life on Earth evolved under the sun’s influence and, given time, adjusts to any changes. Adapting to the whims of a star is no small task, however. The sun may appear to be constant from day to day, but let time stretch out for millions or even billions of years, and things will change—a lot. And not always for the better.

For example, in its thermonuclear-driven core, the sun fuses about 700 million tons of hydrogen into 695 million tons of helium every second. The missing five million tons are converted into energy. This energy is enough, it turns out, to power a star. If you like mind-boggling numbers, the sun produces 4 × 10²⁶ watts of power—400 trillion trillion watts. In other words, the energy our star emits in a single second is sufficient to satisfy humanity’s total consumption for about 650,000 years.

It’s also enough to warm our planet to its current comfy clime. In fact, by using some basic physics principles, it’s possible to mathematically calculate how warm the Earth should be given the sun’s energy emission rate. Solar energy flows into space in all directions around the sun, and a tiny fraction (about half of one billionth) of it is intercepted by Earth, heating our planet. Just how much heating takes place is a bit complicated and depends on the actual radiant flux from the sun, Earth’s distance from it and reflectivity, and more. When we run the numbers, Earth’s average calculated temperature today is approximately –15 degrees Celsius, colder than the freezing point of water.

Actual measurements of Earth’s temperature, however, give a much warmer average: about 15 degrees C. The difference exists because greenhouse gases in the air essentially trap heat from the sun, warming Earth above the calculated temperature. This warming is mostly from natural greenhouse gases, mind you, but we’re adding approximately 40 billion tons of carbon dioxide into the atmosphere every year, significantly increasing the warming effect. Note that this increase has occurred over the past century or so, a timescale far too short for there to have been any change in the sun; Earth’s current climate change is all us.

But the sun’s production of energy does change noticeably—over hundreds of millions of years. That helium created in the core is inert; think of it as ash from the nuclear fusion. It settles in the center of the sun, building up over time at the rate of 695 million tons per second! As it gains mass, it also gets squeezed by the tremendous weight of the sun’s layers above it and becomes compressed. A basic law of physics is that compressing a gas heats it, so even though the fusion rate is mostly the same, the core of the sun is still slowly heating up over time—which means the sun itself is getting more luminous.

Q1MCQ

From the passage, it can be inferred that if greenhouse gases were suddenly removed from Earth’s atmosphere, then:

AEarth’s average temperature would likely drop below the freezing point of water.

BThe Sun would automatically increase its energy output to compensate.

CThe calculated and actual temperatures would become equal.

DEarth’s temperature would rise even further due to lack of reflection.

Solution Answer: A

Without the trapping effect, Earth would fall back toward its calculated temperature of about –15 °C. That is below the freezing point of water. The word “likely” matches the passage’s approximate figures.

B: the passage says the Sun changes only over hundreds of millions of years and does not react to Earth. C: the calculation is only approximate and depends on many factors, so “would become equal” claims more than the passage supports. D: this reverses the passage, since greenhouse gases warm Earth.

Q2MCQ

Which of the following, if true, would most weaken the author’s statement that “Earth’s current climate change is all us”?

AVolcanoes emit greenhouse gases comparable in quantity to human emissions.

BSatellite data reveal that solar energy output has risen sharply during the last century.

COcean currents redistribute heat and cause regional temperature variations.

DSome areas of the planet have cooled slightly in recent decades.

Solution Answer: B

The author rules out the Sun because a century is “far too short” for any solar change. If solar output had in fact risen sharply in that century, the Sun could share the blame, and the claim would collapse.

A: volcanoes have always emitted gases, so this does not explain a change over the past century. C: redistributing heat is not a cause of overall warming. D: regional cooling does not contradict global warming or its cause.

Q3MCQ

Suppose astronomers discover an Earth-sized planet orbiting a star that emits only half as much radiant energy as our Sun. According to the reasoning in the passage, which of the following outcomes would most likely occur?

AThe planet’s lower solar flux would have little impact on temperature, since stellar radiation is not the main factor determining climate.

BThe planet’s oceans and atmosphere would spontaneously generate extra heat to maintain thermal equilibrium similar to Earth’s.

CThe planet’s equilibrium temperature would remain identical to Earth’s because the distance from the star can fully compensate for reduced luminosity.

DThe planet’s surface temperature would be lower than Earth’s unless its atmosphere trapped significantly more heat through greenhouse gases.

Solution Answer: D

In the passage, temperature depends on the star’s radiant flux, raised further by greenhouse trapping. Less starlight means a colder planet, unless greenhouse gases make up the difference.

A: this contradicts the passage, where the Sun is “overwhelmingly” the source of heat. B: nothing in the passage supports spontaneous heat generation. C: the planet’s distance is never given, so “identical” is an unsupported assumption.

Q4MCQ

Which of the following assumptions is essential to the author’s conclusion that the Sun’s core heating makes the Sun gradually more luminous over time?

AThe compression of accumulated helium in the Sun’s core increases temperature even if the overall fusion rate remains nearly constant.

BThe helium produced by fusion remains in the core long enough to influence internal pressure and density.

CThe mass lost as energy through fusion is too small to offset the effects of increasing core compression.

DThe Sun’s layers adjust in a way that allows additional heat from the core to reach the surface instead of being reabsorbed internally.

Solution Answer: A

Detailed solution coming soon.

Q5TITA

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.

And like many emotional topics, a lot of people would rather avoid thinking about it.
Budgets ensure that we are not overspending, and that your money is going where you need it to go.
Money is emotional - it determines where we live, what we eat, the education and healthcare we can access, how we socialize, what hobbies we can take up and how much we can travel.
But avoiding a budget is often more of a headache than making one.
By reviewing your past spending, you can begin to reflect on whether your spending behaviours are aligned with your financial goals.

Solution Answer: 5

The coherent paragraph is 3 → 1 → 4 → 2:

3: Money is emotional.
1: “And like many emotional topics”, people avoid thinking about it.
4: “But” avoiding a budget is more of a headache than making one.
2: Budgets make sure money goes where it should, which explains why.

Sentence 5 is a specific how-to step (reviewing past spending). It belongs to a later discussion of budgeting methods, not to this argument for why a budget is worth making.

Q6TITA

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.

On rare occasions, some body parts—particularly hard ones such as shells, teeth, or bones—are preserved by being buried in mud or protected in some other way from predators and weather.
Eventually, they may become petrified and preserved indefinitely with the rocks in which they are embedded.
Methods such as radiometric dating—measuring the amounts of natural radioactive atoms that remain in certain minerals to determine the elapsed time since they were constituted—make it possible to estimate the time period when the rocks and the fossils associated with them were formed.
The earliest fossils resemble microorganisms such as bacteria and cyanobacteria (blue-green algae); the oldest of these fossils appear in rocks 3.5 billion years old.

Solution Answer: 1234

The order runs like this:

1: Hard body parts are sometimes preserved in mud.
2: “Eventually, they” (those parts) become petrified within rocks.
3: Radiometric dating estimates the age of “the rocks and the fossils associated with them”.
4: Using such dating, the oldest fossils appear in 3.5-billion-year-old rocks.

Q7TITA

Over the years, I started hoarding languages, perhaps to redeem myself after losing my first: Spanish, Italian and – in one half-hearted attempt – Catalan.
Consequently, many do not feel the need to learn the language, but I wanted to be a ‘good immigrant’ and assimilate.
I love their sounds, but they never quite fit in my mouth, so I kept trying to find a language other than English in which I’d make sense.
But I’ve only ever achieved a passable fluency that can support my survival for maybe five minutes.
Beyond that, the conversation is perforated by silences – much like the ones that pockmarked my last trip to Vietnam.

Solution Answer: 2

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

1: The writer hoards languages (Spanish, Italian, Catalan).
3: “I love their sounds”, but they never fit.
4: “But” only a passable fluency, good for about five minutes.
5: “Beyond that”, the conversation falls into silences.

Sentence 2 starts with “Consequently” with no cause in the paragraph, and “the language” has no referent. It is about immigrants assimilating, not the writer’s personal language-hoarding.

Q8TITA

It is characterized by intentional violence on the part of large bodies of individuals organized and trained for that purpose.
War, a state of conflict, generally armed, between two or more entities.
On the national level, some wars are fought internally between rival political factions (civil war); others are fought against an external enemy.
Wars have been fought in the name of religion, in self-defense, to acquire territory or resources, and to further the political aims of the aggressor state’s leadership.

Solution Answer: 2134

The order runs like this:

2: A definition of war, written as a dictionary-style opener.
1: “It” (war) is characterised by organised, intentional violence.
3: Types of war: internal (civil) or against an external enemy.
4: The reasons wars have been fought.

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 It’s only by building up our strength and endurance little by little that we may hope to get ourselves in the necessary shape.

Paragraph Growing moral fibre requires time and effort – what Epictetus calls our ‘winter training’, referring to the exercises Roman soldiers carried out during the winter to get ready for their military campaigns in the spring. ___(1)___. A bit less dramatically, we may draw an analogy with practising to prepare ourselves to run a marathon. ___(2)___. If we did nothing for months, then all of a sudden started running, we would not be able to complete the forty-two-kilometre challenge. ___(3)___. The same is true for our moral fortitude. Some of us may be naturally prone toward acts of heroism, but I’m guessing most are not. ___(4)___. Nevertheless, we can practice courage by nudging ourselves to speak out whenever we see injustice, even though it may be uncomfortable.

AOption 1

BOption 2

COption 3

DOption 4

Solution Answer: C (Option 3)

“If we did nothing for months… we would not be able to complete” the marathon states the problem. The missing sentence gives the remedy: build up strength “little by little”. Then “The same is true for our moral fortitude” applies the whole lesson to ethics. So it belongs at blank 3.

Blank 1 comes before the marathon analogy, where “the necessary shape” has nothing to refer to. At blank 2 it would give the conclusion before the illustration. At blank 4 the paragraph is about heroism and courage, not physical training.

Q10MCQ

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

Passage While most of what we consider to be “hi-tech” is closed off behind proprietary algorithms, the open-source technologies above all require community involvement. This can be immensely empowering, and can improve public trust: it’s hard (and unwise) to give yourself over to a technology that won’t tell you how it works, particularly when its predefined settings allow only for meagre approaches to “user privacy”. As I ask my students, if you could develop an AI at your own home, and programme it to reflect your values and prioritise your safety, wouldn’t you trust it more? Well, the idea isn’t so outlandish – it only feels impossible because big tech firms want us to think it is.

AOpen-source technologies, by encouraging transparency and community participation, can foster greater trust and empowerment than proprietary systems.

BProprietary technologies are safer than open-source technologies because they offer fixed privacy settings designed by experts.

CIt is impossible for individuals to create AI systems that align with their values because big tech monopolies control the market.

DOpen-source AI systems will eventually replace all proprietary technologies because users prefer transparency over privacy.

Solution Answer: A

A captures both parts of the passage: open-source tech requires community involvement, and that openness empowers people and builds trust, unlike opaque proprietary systems.

B reverses the author’s view; the passage criticises the “meagre” fixed privacy settings. C contradicts the passage, which says the idea “isn’t so outlandish” and only feels impossible. D makes an unsupported prediction (“replace all”) and sets transparency against privacy, which the passage does not do.

DILR · Data Interpretation & Logical Reasoning

Q11 – Q20 0/10

Set 1 · Q11 – Q15

The crossword below consists of numbers. No number starts with a zero.

Number crossword grid of 5 rows and 7 columns with black cells; clue numbers 1, 2, 3 in the top row, 4 and 5 in the second row, 6, 7 and 8 in the third row, and 9 and 10 in the bottom row

The hints are:

Across:

1: A two-digit number
2: Rearrange the digits of 6 across
6: Rearrange the digits of 1 across
8: 5 times 7 down
9: Ascending consecutive digits
10: 1 across plus 10

Down:

1: 1 across plus 5
3: Rearrange the digits of 8 across
4: Rearrange the digits of 6 across
5: 6 across plus 9
7: 11 times 4 down
8: 5 times 4 down

Q11MCQ

How many of the given numbers can be uniquely determined?

AAll

BAll but one

CAll but two

DAll but three

Solution Answer: B

1 across is in the 40s. 10 across (= 1 across + 10) starts with the last digit of 8 down (= 5 × 4 down), which is 0 or 5. It can’t be 0, so 10 across is in the 50s and 1 across is in the 40s. 1 down (= 1 across + 5) starts with the same digit, so 1 across is 40–44.
4 down is 41 or 43. 8 down must end in 5, so 4 down is odd. 4 down rearranges 6 across, which rearranges 1 across, so its digits are 4 and b. It must be ≥ 20 because 8 down has three digits. That leaves 41 or 43.
9 across fixes it. 7 down = 11 × 4 down = 451 or 473. Its last digit is the second digit of 9 across (consecutive ascending digits). 451 would make 9 across “01” ✗. So 4 down = 43, 7 down = 473 and 9 across = 23.
The rest follows. 6 across = 34 (it starts with 4 down’s last digit). Then 1 across = 43, 1 down = 48, 5 down = 43, 8 down = 215, 10 across = 53 and 8 across = 5 × 473 = 2365. Checks: 2365 starts with 2 (8 down) and its second digit 3 matches 5 down.
3 down is not fixed. 2 across is 34 or 43. 3 down rearranges 2365 and starts with the second digit of 2 across, so that digit must be 3 and 2 across = 43. 3 down has 5 in its third place (from 8 across), so it is 3256 or 3652.

Row	C1	C2	C3	C4	C5	C6	C7
1	■	■	4	3	■	4	3
2	4	■	8	■	4	■	2 / 6
3	3	4	■	2	3	6	5
4	■	7	■	1	■	■	6 / 2
5	2	3	■	5	3	■	■

Of the 12 numbers, only 3 down (3256 or 3652) is not unique: all but one.

Q12TITA

What is the second digit of 7 down?

Solution Answer: 7

From the table in Q11, 7 down = 11 × 43 = 473. Its second digit is 7.

Q13TITA

What is the sum of the digits of 8 across?

Solution Answer: 16

From the table in Q11, 8 across = 2365, so the digit sum is 2 + 3 + 6 + 5 = 16.

Q14MCQ

Which of the following statements is true about 3 down?

AIt is a multiple of 5

BIt is a multiple of 3

CIt is a multiple of 4

DNone of these

Solution Answer: C

3 down is 3256 or 3652. The last two digits are 56 or 52, both divisible by 4, so it is a multiple of 4 either way.

A: it ends in 6 or 2. B: the digit sum is 16, which is not divisible by 3.

Q15MCQ

Which of the pairs of numbers are equal?

A1 down and 4 down

B6 across and 10 across

C9 across and 6 across

D1 across and 5 down

Solution Answer: D

From the table in Q11: 1 across = 43 and 5 down = 34 + 9 = 43, so they are equal.

A: 48 vs 43. B: 34 vs 53. C: 23 vs 34.

Set 2 · Q16 – Q20

In a reality show called Whale Tank, five investors (called Whales), W1, W2, W3, W4, W5, invested a total of Rs. 50 Crores in 10 businesses – B1 through B10, such that each investor invested in exactly 3 businesses. All the amounts were integral multiples of 1 Cr.

Only B1, B6 and B7 had multiple investors. Each investor had an equal stake in a business that had multiple investors.
B1 received the highest investment of 12 Cr, while the highest investment by a single investor was 7 Cr in B3.
The biggest investment of W5 was 5 Cr in B4. He also invested in B2 and B10.
W3 did not invest in B3.
W2 made the highest investment of 12 Cr, while W1 was one of the two investors who invested the least, i.e. 8 Cr.
W1 and W4 invested in both B6 and B7.
Except for W5, each investor invested a distinct amount in all three businesses.
B5 received twice the money received by B8. W1 and W3 invested in these businesses, respectively.
A total of 6 Cr was invested in B6.

Q16MCQ

Who invested in B9?

AW1

BW2

CW3

DW4

Solution Answer: C

Investor totals. W1 = 8 and W2 = 12, so W3 + W4 + W5 = 30. Exactly two investors invested 8, and everyone else is between 8 and 12. So W3, W4 and W5 are 8, 11 and 11 in some order.
Who is where. W1 is in B5, B6 and B7, so W1 is full. W5 is in B2, B4 and B10. So B1’s investors come from W2, W3 and W4. B3 (7 Cr, single investor, not W3) belongs to W2 or W4.
B3 is not W4’s. If it were, W4 = 7 + B6 share + B7 share would force shares of 3 and 1. Then W1’s B5 = 4 and B8 = 2. B1 would have to be W2 and W3 at 6 each, and both would also enter B7 at 1 each. That makes W3 = 6 + 2 + 1 = 9 ✗.
So W2 holds B3 (7). W2’s other two investments total 5. A B1 share of 6 is impossible for W2, and if W2 skipped B1, then B1 = W3 + W4 at 6 each gives W1’s B5 = 3 and B8 = 1.5 ✗. So B1 has three investors (W2, W3, W4) at 4 each, and W2’s last investment is 1.
W4 and W1. W4 = 4 + B6 share + B7 share = 8 or 11. Shares of 3 + 1 give W4 = 8. The 2 + 5 option makes B5 = 1 and B8 = 0.5 ✗. So the B6 shares are 3 each (W1, W4 only), the B7 shares are 1 each, W1’s B5 = 4 and B8 = 2.
W3 and W5. W3 = 11 = 4 + 2 + 5, with the 5 in B9 (a B7 share would only be 1). W2’s 1 is in B7. Then W5 = 11, so B2 + B10 = 6.

Business	Investor(s)	Amount (Cr)
B1	W2, W3, W4 (4 each)	12
B2	W5	B2 + B10 = 6
B3	W2	7
B4	W5	5
B5	W1	4
B6	W1, W4 (3 each)	6
B7	W1, W2, W4 (1 each)	3
B8	W3	2
B9	W3	5
B10	W5	B2 + B10 = 6

Investor totals: W1 = 8, W2 = 12, W3 = 11, W4 = 8, W5 = 11. B9 was funded by W3.

Q17MCQ

What was the amount invested in B2?

ARs. 2 Cr

BRs. 3 Cr

CRs. 5 Cr

DRs. 6 Cr

Solution Answer: C

Detailed solution coming soon.

Q18TITA

How many investors invested in B1?

Solution Answer: 3

From the table in Q16, B1 was funded by W2, W3 and W4 at 4 Cr each: 3 investors.

Q19MCQ

What was the total amount invested by W3?

ARs. 11 Cr

BRs. 12 Cr

CRs. 8 Cr

DRs. 9 Cr

Solution Answer: A

From the table in Q16, W3 invested in B1 (4), B8 (2) and B9 (5), a total of Rs. 11 Cr.

Q20TITA

How many businesses received an investment of more than 5 Cr?

Solution Answer: 3

From the table in Q16: B1 (12), B3 (7) and B6 (6). B2 and B10 total 6 with each at least 1, so neither exceeds 5. The answer is 3 businesses.

QA · Quantitative Ability

Q21 – Q30 0/10

Q21MCQ

While working alone, Joy can complete a task in ‘x’ days; Imam can complete the same task in ‘y’ days. Hitesh alone can complete the task in (y – x) days. Joy and Imam together worked on the task and completed it in y4 days. Which of the following can be the ratio of the efficiencies of Hitesh, Imam, and Joy?

A2 : 3 : 5

B6 : 2 : 3

C3 : 2 : 5

D3 : 2 : 6

Solution Answer: D

1/x + 1/y = 4/y, so 1/x = 3/y and y = 3x. Hitesh takes y − x = 2x days.

Efficiencies H : I : J = 1/(2x) : 1/(3x) : 1/x = 3 : 2 : 6, so the answer is 3 : 2 : 6.

Q22MCQ

In the given figure, PQRST is a regular pentagon. QR and PT are tangents to the circle. RS extended meets the circle at U. Find angle STU.

Regular pentagon PQRST with a circle touching QR at R and PT at T; RS is extended to meet the circle at U, and T is joined to U

A36˚

B30˚

C27˚

D24˚

Solution Answer: A

In a regular pentagon, the diagonals split each 108° angle into three 36° parts, so ∠QRT = 72°.

QR is tangent at R, so by the alternate segment theorem ∠RUT = ∠QRT = 72°.

R, S, U are collinear, so ∠TSU = 180° − 108° = 72°. In triangle STU, ∠STU = 180° − 72° − 72° = 36°.

Q23TITA

If f(x + 2) + f(x²) = x² + x + 14, find f(4).

Solution Answer: 10

Put x = 2: f(4) + f(4) = 4 + 2 + 14 = 20.

So f(4) = 10.

Q24MCQ

The lengths of two trains are in the ratio 7 : 10. Their speeds are 72 km/h and 96 km/h, respectively. If the longer train crosses a person sitting in the shorter train in 90 seconds while moving in the same direction, then find the time taken by the shorter train to cross the person sitting in the longer train while moving in the opposite direction.

A7 seconds

B8 seconds

C9 seconds

D10 seconds

Solution Answer: C

Speeds: 72 km/h = 20 m/s (shorter train) and 96 km/h = 80/3 m/s (longer train).

Same direction: relative speed = 20/3 m/s, so the longer train’s length = 20/3 × 90 = 600 m. The shorter train is 600 × 7/10 = 420 m.

Opposite direction: relative speed = 20 + 80/3 = 140/3 m/s. Time = 420 ÷ 140/3 = 9 seconds.

Q25MCQ

Find the number of integral non-zero values of x that satisfy the inequality |x³ – 44| < 198.

A14

B13

C12

D11

Solution Answer: D

−198 < x³ − 44 < 198, so −154 < x³ < 242.

(−5)³ = −125 works but (−6)³ = −216 does not. 6³ = 216 works but 7³ = 343 does not. So x runs from −5 to 6: 12 integers, minus x = 0, gives 11.

Q26MCQ

There are ‘n’ rounds in a quiz. The average points scored by Amit is 45.45% more than the average points scored by Bimal. However, the total points scored by Bimal are 45.45% more than those by Amit. The number of rounds played by Bimal is what percentage of the number of rounds played by Amit?

A111%

B211%

C121%

D221%

Solution Answer: B

45.45% = 5/11, so “45.45% more” means × 16/11.

Rounds = total ÷ average. Bimal’s rounds ÷ Amit’s rounds = (Bimal’s total ÷ Amit’s total) × (Amit’s avg ÷ Bimal’s avg) = 16/11 × 16/11 = 256/121 ≈ 2.1157.

That is about 211%.

Q27MCQ

What is the length of the longest side of a cyclic trapezium if the angle between the longer parallel side and either oblique side is 60°, each oblique side measures 8 units, and the area of the trapezium is 96√3 square units?

A20 units

B24 units

C28 units

D32 units

Solution Answer: C

A cyclic trapezium is isosceles. Each oblique side of 8 at 60° gives height 8 sin 60° = 4√3 and a horizontal overhang of 8 cos 60° = 4 on each side.

If the shorter parallel side is a, the longer is a + 8. Area = (2a + 8)/2 × 4√3 = (a + 4) × 4√3 = 96√3, so a = 20.

Longest side = 20 + 8 = 28 units.

Q28TITA

If the product of three consecutive positive even numbers is 26880, then find the square of the largest number.

Solution Answer: 1024

The cube root of 26880 is about 30, so try 28 × 30 × 32 = 26880 ✓.

The largest number is 32, and 32² = 1024.

Q29TITA

Rajat had a certain amount with him. He could buy 12 pens or 28 pencils. He retained 15% of the amount for cab fare and bought 15 pencils and 3 pens. If he was left with Rs. 27, what is the price of a pen?

Solution Answer: 35

Let the amount be M. A pen costs M/12 and a pencil M/28.

Spent: 15M/28 + 3M/12 = 22M/28 = 11M/14. Cab fare: 3M/20. Together that is (110M + 21M)/140 = 131M/140.

Left: 9M/140 = 27, so M = 420. Price of a pen = 420/12 = Rs. 35.

Q30MCQ

In the following figure, a cone is cut parallel to the base and extracted into four segments having slant heights l₁, l₂, l₃, and l₄, and the radius of their bases are 1 cm, 2 cm, 3 cm, and 4 cm, respectively. Find the ratio of the curved surface area of the second largest segment to that of the smallest segment of the cone.