In only 50 years, the world's consumption of raw materials has nearly quadrupled, to more than 100 billion tons. Less than $9 \%$ of this is reused. Batteries of old vehicles contain materials such as lithium, cobalt, manganese and nickel that are pricey and can be hard to obtain. Supply chains are long and complicated. Buyers' risks are being aggravated by their suppliers' poor environmental and labour standards. Reusing materials makes sense. Once batteries reach the ends of their lives, they should go back to a factory where their ingredients can be recovered and put into new batteries.

A set $(X)$ of 20 pipes can fill $70 \%$ of a tank in 14 minutes. Another set ( $\mathbf{Y}$ ) of 10 pipes fills 3/8th of the tank in $\mathbf{6}$ minutes. A third set (Z) of 16 pipes can empty half of the tank in 20 minutes. If half of the pipes of set $\mathbf{X}$ are closed and only half of the pipes of set $\mathbf{Y}$ are open, and all pipes of the set (Z) are open, then how long will it take to fill 50\% of the tank?

"A good statesman, like any other sensible human being, learns more from his opponents than from his fervent supporters. For his supporters will push him to disaster unless his opponents show him where the dangers are. So if he is wise he will often pray to be delivered from his friends, because they will ruin him. But, though it hurts, he ought also to pray never to be left without opponents; for they keep him on the path of reason and good sense. The national unity of free people depends upon a sufficiently even balance of political power to make it impracticable for the administration to be arbitrary and for opposition to be revolutionary and irreconcilable."

$\mathbf{X}$ can complete one-third of a certain work in $\mathbf{6}$ days, $\mathbf{Y}$ can complete one-third of the same work in $\mathbf{8}$ days and $\mathbf{Z}$ can complete three-fourth of the same work in 12 days. All of them work together for $n$ days and then $X$ and $Z$ quit and $Y$ alone finishes the remaining work in $8 \frac{2}{3}$ days. What is $n$ equal to?

Trust stands commonly defined as being vulnerable to others. Entrepreneurship implies trust in others and willingness to expose oneself to betrayal. Trust in expert systems is the essence of globalising behaviour; trust itself emerges as a supercommodity in the social market and defines the characteristics of goods and services in a global market. Trusting conduct also means holding others in good esteem, and an optimism that they are, or will be, competent in certain respects.

In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of number of runs scored by $\mathbf{X}$ to the number of runs scored by $\mathbf{Y}$ is equal to ratio of number of runs scored by $Y$ to number of runs scored by $\mathbf{Z}$.

$$ \begin{aligned} & \text { Value-I = Runs scored by X } \\ & \text { Value-II = Runs scored by Y } \end{aligned} $$

Value-III $=$ Runs scored by $\mathbf{Z}$

Which one of the following is correct?

Trust stands commonly defined as being vulnerable to others. Entrepreneurship implies trust in others and willingness to expose oneself to betrayal. Trust in expert systems is the essence of globalising behaviour; trust itself emerges as a supercommodity in the social market and defines the characteristics of goods and services in a global market. Trusting conduct also means holding others in good esteem, and an optimism that they are, or will be, competent in certain respects.

Consider a set of 11 numbers:

Value-I = Minimum value of the average of the numbers of the set when they are consecutive integers $\geq-5$.

Value-II = Minimum value of the product of the numbers of the set when they are consecutive non-negative integers.

Which one of the following is correct?