UPSC - CSAT 2025
Q1–10 of 80(COMMON INFORMATION FOR QUESTIONS 1 TO 2)
Maintaining an ecosystem just to conserve biodiversity will affect its commercial potential as well as the livelihoods dependent on the ecosystem. There is also a conflict between using an ecosystem only for livelihoods, for commercial exploitation, or strictly for conservation. Deforestation caused due to commercial exploitation will lead to indirect harm like floods, siltation problems and microclimatic instability, apart from adversely affecting livelihoods dependent on forests. These conflicts are particularly acute in developing countries where the dependence of people on the ecosystem is significant, and commercial exploitation has the potential to boost national income.
Q. Which one of the following statements best
reflects the critical message conveyed by the
author of the passage ?
The author emphasizes that ecosystems face conflicting pressures from conservation, livelihood dependence, and commercial exploitation. When livelihoods rely heavily on ecosystems, unchecked commercial use degrades them, indirectly harming both the environment and people. This mutual reinforcement of livelihood stress and ecological degradation creates imbalance, leading to environmental problems like floods and climate instability, especially in developing countries where dependence on natural resources is high.
(COMMON INFORMATION FOR QUESTIONS 1 TO 2)
Maintaining an ecosystem just to conserve biodiversity will affect its commercial potential as well as the livelihoods dependent on the ecosystem. There is also a conflict between using an ecosystem only for livelihoods, for commercial exploitation, or strictly for conservation. Deforestation caused due to commercial exploitation will lead to indirect harm like floods, siltation problems and microclimatic instability, apart from adversely affecting livelihoods dependent on forests. These conflicts are particularly acute in developing countries where the dependence of people on the ecosystem is significant, and commercial exploitation has the potential to boost national income.
Q. With reference to above passage, the following assumptions have been made:
I. No country needs to depend on ecosystems to boost national income.
II. Resource-rich countries need to share their resources with those of scant resources so as to prevent the degradation of ecosystems.
Which of the above assumptions is/are valid?
The passage clearly states that commercial exploitation of ecosystems can boost national income, especially in developing countries, so Assumption I is invalid. Assumption II about resource-rich countries sharing resources is not discussed or implied anywhere in the passage. The author focuses on conflicts between conservation, livelihoods, and commercial use within countries, not on international resource sharing. Hence, neither assumption logically follows from the passage.
(COMMON INFORMATION FOR QUESTIONS 3 TO 4)
The history of renewable energy suggests there is a steep learning curve, meaning that, as more is produced, costs fall rapidly because of economies of scale and learning by doing. The firms’ green innovation is path-dependent: the more a firm does, the more it is likely to do in the future. The strongest evidence for this is the collapse in the price of solar energy, which became about 90% cheaper during the 2010s, repeatedly beating forecasts. Moving early and gradually gives economies more time to adjust, allowing them to reap the benefits of path-dependent green investment without much disruption. A late, more chaotic transition is costlier.
Q. Which one of the following statements best
reflects the central idea of the passage ?
• Green technology follows a learning curve — more production means lower costs.
• Innovation is path-dependent — early efforts encourage future progress.
• Solar energy prices dropped nearly 90% due to early, steady investment.
• Early and gradual transition allows smooth economic adjustment.
• Late transition is chaotic and more expensive.
Hence, timing is the key factor in green technology development.
(COMMON INFORMATION FOR QUESTION 3 TO 4)
The history of renewable energy suggests there is a steep learning curve, meaning that, as more is produced, costs fall rapidly because of economies of scale and learning by doing. The firms’ green innovation is path-dependent: the more a firm does, the more it is likely to do in the future. The strongest evidence for this is the collapse in the price of solar energy, which became about 90% cheaper during the 2010s, repeatedly beating forecasts. Moving early and gradually gives economies more time to adjust, allowing them to reap the benefits of path-dependent green investment without much disruption. A late, more chaotic transition is costlier.
Q. With reference to the above passage, the following assumptions have been made:
I. Path-dependent green investments will eventually most likely benefit growth as well as public finances in a country like India.
II. If other green technologies follow the same pattern as that of solar energy, there will most likely be an easy green transition.
Which of the above assumptions is/are valid?
The passage says that renewable energy becomes cheaper as production increases. It also says that starting the green transition early makes it smoother and less costly. Solar energy is given as an example of this process.
Assumption I
This assumption says that green investments will benefit economic growth and public finances in a country like India. The passage does not talk about economic growth, public finances, or India. It only talks about cost reduction and adjustment. So this assumption adds new ideas that are not required for the author’s argument. Hence, it is not a valid assumption.
Assumption II
This assumption says that if other green technologies behave like solar energy, the green transition will be easy. The author’s argument about an easier and less costly transition depends on the idea that other green technologies can also show similar cost reductions. This idea is taken for granted in the passage. So this assumption is valid.
Correct Answer
(b) II only
NOTE: This answer may be logically correct, but it is not correct as per the UPSC assumption question framework
A natural number N is such that it can be expressed as N = p + q + r, where p, q and r are distinct factors of N. How many numbers below 50 have this property ?
We can have the following numbers:
6 = 1 + 2 + 3
12 = 2 + 4 + 6
18 = 3 + 6 + 9
24 = 4 + 8 + 12
30 = 5 + 10 + 15
36 = 6 + 12 + 18
42 = 6 + 14 + 21
48 = 8 + 16 + 24
So, the required numbers below 50 are 6, 12, 18, 24, 30, 36, 42 and 48, i.e., 8 numbers. Hence, option (c) is correct.
NOTE: This answer may be logically correct, but it is not correct as per the UPSC assumption question framework.
Three prime numbers p, q and r, each less
than 20, are such that p – q = q – r. How
many distinct possible values can we get for
(p + q + r) ?
Given:
Three prime numbers p,q,rp, q, rp,q,r, each less than 20, satisfy
p − q = q − r
Step 1: Use the condition
From
p − q = q − r
we get
p + r = 2q
So, p, q, r are in arithmetic progression, with q as the middle term.
Step 2: List primes less than 20
2, 3, 5, 7, 11, 13, 17, 19
Step 3: Find valid prime arithmetic progressions
-
(5, 3, 2) → sum = 10
-
(7, 5, 3) → sum = 15
-
(11, 7, 3) → sum = 21
-
(17, 11, 5) → sum = 33
All other cases fail because at least one number is not prime or exceeds 20.
Step 4: Count distinct sums
10, 15, 21, 33
Final Answer: 4
How many possible values of \(p+q+r\) are there satisfying \(\frac{1}{p}+\frac{1}{q}+\frac{1}{r}=1\), where \(p,q\) and \(r\) are natural numbers (not necessarily distinct)?
Given:
Natural numbers p, q, r (not necessarily distinct) satisfy
1/p + 1/q + 1/r = 1
We are asked for the number of possible values of p + q + r.
Step 1: Use symmetry
Since the equation is symmetric in p, q, r, we can assume
p ≤ q ≤ r without loss of generality.
Step 2: Try small natural numbers
-
p = 2
Then
1/2 + 1/q + 1/r = 1
⇒ 1/q + 1/r = 1/2
Possible solutions:
-
q = 3, r = 6
-
q = 4, r = 4
So we get:
-
(2,3,6) → sum = 11
-
(2,4,4) → sum = 10
-
p = 3
Then
1/3 + 1/q + 1/r = 1
⇒ 1/q + 1/r = 2/3
Only possible solution:
-
q = 3, r = 3
So:
-
(3,3,3) → sum = 9
-
p ≥ 4
Then
1/p ≤ 1/4, so
1/p + 1/q + 1/r ≤ 3/4 < 1
No solutions possible.
Step 3: List distinct sums
The valid sums are:
-
9
-
10
-
11
Final Answer: 3
Team X scored a total of N runs in 20 overs.
Team Y tied the score in 10% less overs. Had
team Y’s average run rate (runs per over)
been 50% higher, the scores would have been
tied in 12 overs. How many runs were scored
by team X ?
Given that Team \(X\) scored \(N\) runs in \(20\) overs.
Team \(Y\) tied the score in \(10\%\) fewer overs, that is, in \(18\) overs.
If Team \(Y\)’s average run rate were increased by \(50\%\), the same score would be tied in \(12\) overs.
We are required to find the value of \(N\).
Step 1: Express the run rates
The original run rate of Team \(Y\) is \( \dfrac{N}{18} \).
If the run rate is increased by \(50\%\), the new run rate becomes
\( 1.5\times\dfrac{N}{18} \).
Step 2: Use the second condition
With the increased run rate, Team \(Y\) ties the score in \(12\) overs. Hence,
\( 12\times1.5\times\dfrac{N}{18}=N \).
Simplifying,
\( \dfrac{12\times1.5}{18}N=N \).
Since \( \dfrac{12\times1.5}{18}=1 \),
we get \( N=N \).
Step 3: Interpretation
The equation reduces to an identity, which is true for all values of \(N\).
Hence, no unique value of \(N\) can be determined from the given information.
Final Answer:
The value of \(N\) cannot be determined.
The price \(p\) of a commodity is first increased by \(k\%\), then decreased by \(k\%\), again increased by \(k\%\), and again decreased by \(k\%\). If the new price is \(q\), then what is the relation between \(p\) and \(q\)?
A. \( p(10^4-k^2)^2=q\times10^8 \),
B. \( p(10^4-k^2)^2=q\times10^4 \),
C. \( p(10^4-k^2)=q\times10^4 \),
D. \( p(10^4-k^2)=q\times10^8 \)
Given that the price \(p\) of a commodity is changed four times as follows:
increased by \(k\%\),
decreased by \(k\%\),
again increased by \(k\%\),
again decreased by \(k\%\).
The final price obtained is \(q\).
Step 1: Effect of one increase and one decrease
An increase by \(k\%\) multiplies the price by \( \left(1+\dfrac{k}{100}\right) \).
A decrease by \(k\%\) multiplies the price by \( \left(1-\dfrac{k}{100}\right) \).
So, one increase followed by one decrease gives the net factor
\( \left(1+\dfrac{k}{100}\right)\left(1-\dfrac{k}{100}\right) =1-\dfrac{k^2}{10000} \).
Step 2: Apply the same process twice
Since this increase–decrease process occurs twice, the overall multiplying factor becomes
\( \left(1-\dfrac{k^2}{10000}\right)^2 \).
Hence, the final price is
\( q=p\left(1-\dfrac{k^2}{10000}\right)^2 \).
Step 3: Remove the fraction
Rewrite the expression as
\( q=p\left(\dfrac{10000-k^2}{10000}\right)^2 \).
Multiplying both sides by \(10000^2=10^8\), we get
\( q\times10^8=p(10000-k^2)^2 \).
Final Relation:
\( \boxed{p(10^4-k^2)^2=q\times10^8} \).
What comes at X and Y respectively in the following sequence ?
January, January, December, October, X, March, October, Y, September.
Sequence given:
January, January, December, October, X, March, October, Y, September
Step 1: Convert months to numbers
-
January = 1
-
December = 12
-
October = 10
-
March = 3
-
September = 9
So the sequence becomes:
1, 1, 12, 10, X, 3, 10, Y, 9
Step 2: Observe the pattern
The sequence is made of two interleaved sequences.
Odd positions:
1st, 3rd, 5th, 7th, 9th
→ 1, 12, X, 10, 9
This decreases as:
1 → 12 (−1 mod 12), 12 → 10 (−2), 10 → 9 (−1)
So X = 7, which is July.
Even positions:
2nd, 4th, 6th, 8th
→ 1, 10, 3, Y
This follows:
1 → 10 (−3 mod 12), 10 → 3 (−7), 3 → 4 (+1)
So Y = 4, which is April.
Final Answer:
X = July, Y = April
Correct option: B