The reciprocals are 1/4 and 1/8. The common difference is 1/8 - 1/4 = -1/8. The third term's reciprocal will be 1/8 - 1/8 = 0, hence the third term is 16.

The first term is 5, and the second term in the harmonic progression corresponds to the reciprocal of the second term in the arithmetic progression, which is 5 + 2 = 7. Thus, the second term is 1/7.

The reciprocals are 1/5 and 1/10. The common difference is 1/10 - 1/5 = -1/10, which is the difference in the arithmetic progression.

The reciprocals are 1/5 and 1/10. The common difference is -1/10. The reciprocal of the third term is 1/10 - 1/10 = 1/15, so the third term is 15.

The nth term of a harmonic progression can be expressed as 1/(1/a + (n-1)d) where d is the common difference of the corresponding arithmetic progression.

Efficiency (η) = Work done / Input heat = 300 J / 500 J = 0.6 or 60%.

Efficiency = (Work output / Heat input) × 100 = (300 J / 800 J) × 100 = 37.5%.

Efficiency = (Work done / Heat absorbed) * 100 = (200 J / 500 J) * 100 = 40%.

Efficiency = (Work output / Heat input) × 100 = (200 J / 600 J) × 100 = 33.33%.

The work done by a heat engine is equal to the heat absorbed from the hot reservoir minus the heat rejected to the cold reservoir.

'1A' in hexadecimal is 1*16 + 10 = 26 in decimal.

In hexadecimal, 'A' represents 10 and '3' represents 3. Therefore, A3 = (10 * 16^1) + (3 * 16^0) = 160 + 3 = 163.

In a hexagonal close-packed (HCP) structure, there are 6 atoms per unit cell.

In a hexagonal close-packed (HCP) structure, the coordination number is 12, as each atom is in contact with 12 others.

If the intersection of sets A and B is empty, it indicates that A and B do not share any elements, making them disjoint sets.

Both elements x and y can be included in the hybrid set as they belong to their respective sets.

If both elements belong to their respective sets, they will also be included in the hybrid set.

If element X is found in both sets, it is classified as a common element, which is a key feature of hybrid sets.

The symmetric difference includes elements that are in either set C or set D but not in both, which are {a, d}.

Element 'a' is unique to set C as it does not appear in set D.

The symmetric difference includes elements that are in either set but not in both, which results in {a, d}.

The elements y and z are common to both sets C and D, but since the question asks for one, y is the first common element listed.

The maximum number of unique elements is calculated as (5 + 3 - 2) = 6.

The intersection of set P and set Q includes only the elements that are present in both sets, which are {b, c}.

Element 'a' is unique to set P, as it does not appear in set Q.

A hybrid set can include elements from both sets P and Q, thus {b, c, d, a} is a valid hybrid set.

If 'x' is present in both sets, it is part of the intersection, which is a key characteristic of hybrid sets.

The maximum number of unique elements is calculated as (5 + 3 - 2) = 6.

The union of set E and set F is {x, y, z, w}, which has a cardinality of 4.

The hybrid set formed by the intersection of R and S includes only the elements that are common to both sets, which are {y, z}.