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 pathdependent green investment without much disruption. A late, more chaotic transition is costlier.

The price (p) of a commodity is first increased by $\mathbf{k} \boldsymbol{\%}$; then decreased by $\mathrm{k} \%$; again increased by $\mathrm{k} \%$; and again decreased by $\mathrm{k} \%$. If the new price is q , then what is the relation between $p$ and $q$ ?

If the social inequality is the most acutely felt social problem in India, insecurity, more than poverty, is the most acutely felt economic problem. Besides those below the official poverty line, even those just over the poverty line are subject to multiple economic insecurities of various kinds (due to wealth and/or health risks, market fluctuations, job-related uncertainties). Many Government policies are actually intended towards mitigating these insecurities.

The petrol price shot up by $10 \%$ as a result of the hike in crude oil prices. The price of petrol before the hike was ₹$ 90$ per litre. A person travels 2200 km every month and his car gives a mileage of 16 km per litre. By how many km. should he reduce his travel if he wants to maintain his expenditure at the previous level?

If the social inequality is the most acutely felt social problem in India, insecurity, more than poverty, is the most acutely felt economic problem. Besides those below the official poverty line, even those just over the poverty line are subject to multiple economic insecurities of various kinds (due to wealth and/or health risks, market fluctuations, job-related uncertainties). Many Government policies are actually intended towards mitigating these insecurities.

A 4-digit number $N$ is such that when divided by $3,5,6$, 9 leaves a remainder $1,3,4,7$ respectively. What is the smallest value of $\mathbf{N}$ ?

If the social inequality is the most acutely felt social problem in India, insecurity, more than poverty, is the most acutely felt economic problem. Besides those below the official poverty line, even those just over the poverty line are subject to multiple economic insecurities of various kinds (due to wealth and/or health risks, market fluctuations, job-related uncertainties). Many Government policies are actually intended towards mitigating these insecurities.

What is the unit digit in the multiplication of $1 \times 3 \times 5 \times 7 \times 9 \times \ldots \times 999$ ?