Q. Passage-2
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.6) 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)?
Answer: A
Notes:
Exp) Option a is the correct answer
Given that there are three prime numbers p, q and r each less than 20 such that p-q = q-r.
Consider p-q = q-r
Rearranging we get
2q = p+r
q = (p+r)/2
Therefore, we need to find triplets of prime numbers less than 20 such that one of the numbers is the average of other two.
Below is the list of prime numbers less than 20:
2, 3, 5, 7, 11, 13, 17, 19
By introspection we find the following triplets satisfying the above conditions:
- 3, 5, 7
- 3, 7, 11
- 5, 11, 17
- 7, 13, 19
In each of the above triplets, the middle number is the average of the other two.
Distinct possible value for “p+q+r” are given by:
- 3+5+7 = 15
- 3+7+11 = 21
- 5+11+17 = 33
- 7+13+19 = 39
Thus, there are four distinct possible values.
Hence Option (a) is the correct answer.
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