The random variable $X$ has a probability density function given by:

The value $E(X^2)$(rounded off to one decimal place) is ______.

Match the following based on the equipment usage in a comminution circuit:

An air receiver of a compressor, having volume 0.5 m³, supplies air for charging ANFO in drill holes. During the charging process the absolute pressure of the air receiver falls from 900 kPa to 700 kPa. Assuming the entire process is isothermal, the volume of air supplied by the receiver at 100 kPa ambient pressure, in m³ is

A random sample has five observations as shown below.

The coefficient of variation of the sample is ______ (round off to 3 decimal places).

For $w = \frac{e^{t} - t}{e^{t} + t}$, the value of $\frac{dw}{dt}$ is

For the differential equation $y\sqrt{1-x^2} \, dy + x\sqrt{1-y^2} \, dx = 0$, assuming the constant of integration to be $C$, the general solution is

The equation for peak particle velocity (PPV) from blast induced ground vibration is given by

where k and B are site constants.

In a field study, the following readings are recorded.

The value of $B$ is ______ (round off to 3 decimal places).

If '—' denotes increasing order of intensity, then the meaning of the words [drizzle → rain → downpour] is analogous to [_____ → quarrel → feud]. Which one of the given options is appropriate to fill the blank?

Statements:

1. All heroes are winners.
2. All winners are lucky people. Inferences: I. All lucky people are heroes. II. Some lucky people are heroes. III. Some winners are heroes. Which of the above inferences can be logically deduced from statements 1 and 2?

Out of the support categories given for an underground coal mine, identify the ‘active support’.