1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2:1:1.
2. The number of satellites serving all three of B, C, and S is 100.
3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B.
4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B.
What best can be said about the number of satellites serving C?
Must be between 450 and 725
- Cannot be more than 800
- Must be between 400 and 800
- Must be at least 100
The Correct Option is C
Solution and Explanation
The correct answer is (C):
The number of satellites serving region C is given by:
\[ \text{Satellites serving C} = z + 0.3x + 100 + y \]
Substitute the values from the equations:
\[ z = 550 - 5y,\quad x = 5y + 250 \] \[ \Rightarrow \text{Satellites serving C} = (550 - 5y) + 0.3(5y + 250) + 100 + y \]
Simplify:
\[ = 550 - 5y + 1.5y + 75 + 100 + y = 725 - 2.5y \]
This expression is maximum when \( y \) is minimum. Minimum value of \( y = 0 \), so:
\[ \text{Maximum satellites serving C} = 725 - 2.5 \times 0 = 725 \]
From equation (3):
\[ z = 550 - 5y \] Since the number of satellites cannot be negative, we must have: \[ z \geq 0 \Rightarrow 550 - 5y \geq 0 \Rightarrow y \leq 110 \]
Now, the maximum possible value of \( y \) is 110.
When \( y = 110 \):
\[ \text{Satellites serving C} = 725 - 2.5 \times 110 = 725 - 275 = 450 \]
Therefore, the number of satellites serving C lies between 450 and 725.
What is the minimum possible number of satellites serving B exclusively?
- 100
- 200
- 500
- 250
The Correct Option is D
Solution and Explanation
Given the problem, we need to determine the minimum number of satellites serving B exclusively. Let's break down the information:
Let B = 2x, C = x, and S = x based on the ratio 2:1:1.
The number of satellites serving all three (B ∩ C ∩ S) is 100.
Let Be, Ce, and Se be the satellites serving exclusively B, C, and S, respectively. Given Ce = Se = 0.3Be.
The number of satellites serving others (O) is the same as the number serving C and S but not B, let's denote this as C ∩ S - B.
Using these, we can set up equations based on the total number of satellites:
• Total satellites: B + C + S + O = 1600 (1)
• B = Be + C ∩ B - S + C ∩ B ∩ S + B ∩ S - C (2)
• C = Ce + C ∩ B - S + C ∩ B ∩ S + C ∩ S - B (3)
• S = Se + C ∩ S - B + C ∩ B ∩ S + B ∩ S - C (4)
• B ∩ C ∩ S = 100 (5)
• Ce = 0.3Be (6)
• Se = 0.3Be (7)
Based on equation 6 and 7, suppose Be = 1000, then Ce = Se = 0.3 × 1000 = 300.
Hence, equations (2), (3), (4) become:
B = 2x = Be + D
C = x = Ce + E
S = x = Se + F
Substituting the known values: B = 2x = 1000 + D, C = x = 300 + E, S = x = 300 + F, where D = E = F = H, which satisfy total 1600 condition.
If D + E + F + O = 1600 - (Be + Ce + Se + B ∩ C ∩ S = 1900), so D + 100 + O = 600.
Thus, O = C ∩ S - B = Ce + Se + 100.
If Be is minimised to 250, solving directly from equilibrated conditions where B: 2x, hence deductions confirm Be = 250 (since other conditions uphold a 4_ratio in disparity between C/S/B linked-exclusive constraints).
| Satellite | Count |
|---|---|
| Bexclusive | 250 |
| Ce = Se | 75 |
| B ∩ C ∩ S | 100 |
The minimum possible number of satellites serving B exclusively is confirmed as 250.
If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?
At most 475
- Exactly 475
- At least 475
- No conclusion is possible based on the given information
The Correct Option is A
Solution and Explanation
The correct answer is (A):
We are given that at least 100 satellites serve 0 regions. So, we take:
\[ y \geq 100 \]
From earlier equations, the number of satellites serving S is:
\[ \text{Satellites serving S} = 0.3x + z + 100 + y \]
Substitute the known expression: \[ = 725 - 2.5y \]
This value is minimum when \( y \) is maximum. From constraint (3), maximum possible \( y = 110 \).
So, minimum number of satellites serving S: \[ = 725 - 2.5 \times 110 = 725 - 275 = 450 \]
This value is maximum when \( y = 100 \).
So, maximum number of satellites serving S: \[ = 725 - 2.5 \times 100 = 725 - 250 = 475 \]
Therefore, the number of satellites serving S is at most 475.
If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE?
- The number of satellites serving C cannot be uniquely determined.
The number of satellites serving B is more than 1000 .
- All 1600 satellites serve B or C or S.
- The number of satellites serving B exclusively is exactly 250.
The Correct Option is A
Solution and Explanation
We are given relationships among the number of satellites serving regions B, C, and S. The goal is to find out the number of satellites serving at least two of B, C, or S.
Definitions:
- $x$: Number of satellites serving only one region
- $y$: Number of satellites serving all three regions (B, C, and S)
- $z$: Number of satellites serving exactly two of B, C, or S
- Total satellites serving at least two regions = $2z + y + 100$ (as given)
Also given:
- $z = 550 - 5y$
- $x = 5y + 250$
Step 1: Total satellites serving at least two of B, C, or S
Total = $z + z + y + 100 = 2z + y + 100$
Substitute $z = 550 - 5y$:
$2(550 - 5y) + y + 100 = 1200$
$1100 - 10y + y + 100 = 1200$
$1200 - 9y = 1200$
$\Rightarrow y = 0$
Step 2: Find values of $x$ and $z$
If $y = 0$:
- $x = 5y + 250 = 250$
- $z = 550 - 5y = 550$
Step 3: Satellites serving region C
Let number of satellites serving C be $k$.
Given:
$k = z + 0.3x + 100 + y$
Substitute the values:
$k = 550 + 0.3 \times 250 + 100 + 0 = 550 + 75 + 100 = 725$
Step 4: Satellites serving region B
Given: Satellites serving B = $2k = 2 \times 725 = 1450$
Conclusion:
- $y = 0$
- $x = 250$
- $z = 550$
- Satellites serving C = 725 (uniquely determined)
Hence, the statement "the number of satellites serving C cannot be uniquely determined" is false.
Correct Answer: (A)
Top Questions on Reading Comprehension
- The advent of social media has dramatically transformed the way individuals consume and share information. In earlier times, people largely depended on newspapers, radio, or television as their primary sources of knowledge about the world. These were institutions that followed established editorial practices and fact-checking processes. With the rise of digital platforms, however, the traditional ‘gatekeepers’ of information have been bypassed. Today, anyone with internet access can create content, express an opinion, or broadcast an idea to a global audience within seconds.
This shift has certainly democratized access and given voice to communities and individuals who were often ignored by mainstream media. Yet, this democratization comes with challenges. Alongside genuine voices, social media has also amplified misinformation, rumours, and half-truths. Unlike traditional journalism, where accountability and verification are built into the system, social media thrives on speed, virality, and emotion. A misleading headline, a misinterpreted statistic, or even a doctored image can travel across the world before fact-checkers have the chance to intervene.
The consequences of such unchecked information can be serious, ranging from the spread of fear and panic to the manipulation of public opinion. The impact of this transformation extends beyond individual users to institutions and democracies. Political campaigns, corporate branding, and even social movements are now shaped by algorithms that decide what people see and when they see it. These algorithms prioritize engagement, often promoting content that provokes stronger emotional reactions rather than balanced analysis.
As a result, echo chambers form, online spaces where people are repeatedly exposed to opinions that mirror their own, reinforcing biases and reducing openness to differing perspectives. This has contributed to increasing polarization in societies across the world. Moreover, the competition for attention has blurred the line between information and entertainment, leading to the rise of sensationalism even in serious public discourse. The credibility of expertise too has been undermined, as opinions from unverified sources are often placed on the same footing as evidence-based knowledge.
In response, several governments and technology companies are exploring ways to promote digital literacy, enhance transparency in algorithms, and strengthen fact-checking collaborations. Ultimately, the challenge lies in balancing the openness of digital spaces with mechanisms that ensure responsibility and trustworthiness in public communication.- AILET BALLB (Hons.) - 2026
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- I have still to be brother to a Prince, though I once came near to kinship with what might have been a veritable King, and was promised the reversion of a Kingdom, army, law-courts, revenue, and policy, all complete. But, today, I greatly fear that my King is dead, and if I want a crown I must go and hunt it for myself. The beginning of everything was in a railway train upon the road to Mhow from Ajmir. There had been a deficit in the Budget, which necessitated travelling, not Second class, which is only half as dear as First class, but by Intermediate, which is very awful indeed. There are no cushions in the Intermediate class, and the population is either Intermediate, which is Eurasian, or native, which for a long night journey is nasty; or Loafer, which is amusing though intoxicated. Intermediates do not patronize refreshment rooms. They carry their food in bundles and pots, and buy sweets from the native sweet meat sellers, and drink the roadside water. That is why in the hot weather Intermediates are taken out of the carriages dead, and in all weathers are most properly looked down upon.
My particular Intermediate happened to be empty till I reached Nasirabad, when a huge gentleman in shirt sleeves entered, and following the custom of Intermediates, passed the time of day. He was a wanderer and a vagabond like myself, but with an educated taste for alcohol. He told daring tales of things he had seen and done, of out-of-the-way corners of the Empire into which he had penetrated, and of adventures in which he risked his life for a few days’ food. “If India was filled with men like you and me, not knowing more than the crows where they’d get their next day’s rations, it isn’t seventy millions of revenue the land would be paying, it’s seven hundred millions,” said he; and as I looked at his mouth and chin I was disposed to agree with him.
We talked politics, the politics of Loaferdom that sees things from the underside where the lath and plaster is not smoothed off, and we talked postal arrangements because my friend wanted to send a telegram back from the next station to Ajmir, which is the turning off place from the Bombay to the Mhow line as you travel westward. He had the air of one who had seen strange countries and stranger men, yet bore himself without vanity. There was a restless light in his eyes, the sort that belongs to men who have lived too long without a fixed purpose. When he spoke of the Empire, it was not with loyalty nor with bitterness, but with the detached amusement of one who has played his part and lost interest in the game. His laughter came easily, though it seemed to echo from some remembered hardship. It struck me then that his stories were less of adventure than of survival.- AILET BALLB (Hons.) - 2026
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This balance ensures that while the majority has the power to make decisions through voting, the fundamental rights of minorities are not trampled upon. Such a system requires consistent vigilance and respect for the rule of law. Without these, democracies can devolve into majoritarian tyranny or authoritarianism. The practice of democracy is not merely limited to voting in elections. It encompasses freedom of speech, an independent judiciary, free press, and protection of individual rights. These elements together create a political environment where citizens can express dissent, hold leaders accountable, and participate actively in decision-making. When any component is weakened, the democratic process becomes vulnerable.
In recent times, democratic societies worldwide have grappled with new challenges. The rise of misinformation and fake news has eroded public trust in institutions and polarized societies. Social media platforms, meant to facilitate communication, have sometimes amplified divisive narratives and falsehoods. This has resulted in voter manipulation and a growing skepticism toward democratic processes. Literacy in media and critical thinking is increasingly vital to safeguard democracy from such threats. Economic inequality poses another significant challenge. While democracy promises equal rights politically, vast disparities in wealth and opportunity undermine this ideal.
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The Rule of Law
by Tom BinghamJustice: What’s the Right Thing to Do?
by Michael J. SandelLetters to a Law Student
by Nicholas J. McBrideIn The Rule of Law, former Lord Chief Justice Tom Bingham explores how the principle of legality underpins modern democratic life. He defines the rule of law as more than just adherence to formal rules; it is the assurance that power is exercised within clear, fair, and publicly known boundaries.
Bingham distills the concept into eight principles, including equality before the law, access to justice, and respect for fundamental human rights. Drawing on cases and historical examples, he warns that national security and administrative efficiency must never override the rights of individuals.
The book bridges legal philosophy and practice, arguing that law must be both predictable and humane. For Bingham, the rule of law represents a moral ideal, one that sustains public trust in justice and curbs arbitrary governance.Michael Sandel’s Justice: What’s the Right Thing to Do? examines moral reasoning in law and politics. Through examples like price gouging, affirmative action, and taxation, Sandel invites readers to explore competing notions of fairness.
He engages with philosophical traditions such as utilitarianism, libertarianism, and Rawlsian egalitarianism, showing that questions of justice cannot be separated from questions of virtue and the common good.
Sandel rejects the idea of a morally “neutral” legal system, arguing that public deliberation about values is essential to democracy. Ultimately, he argues that a just society is one that cultivates civic responsibility, not merely individual rights.Nicholas McBride’s Letters to a Law Student is a practical and reflective guide for aspiring lawyers. Written as a series of letters to a student beginning law school, it explores what legal study truly involves.
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- AILET BALLB (Hons.) - 2026
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\[ \begin{cases} x \geq y \geq 3 \\ x + y \leq 14 \end{cases} \]
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