In a harmonic oscillator, the total mechanical energy is the sum of kinetic and potential energy, which remains constant over time.

The first term is 1, the second term is 1/2, and the third term can be calculated as 1/(1 + 1/2) = 2/3. The sum is 1 + 1/2 + 2/3 = 2.

The reciprocals are 1 and 2, which are in arithmetic progression with a common difference of 1/2.

The reciprocals are 1 and 2, which are in arithmetic progression. The third term's reciprocal is 3, so the third term is 1/3.

In a harmonic progression, the reciprocals of the terms form an arithmetic progression. The reciprocals of 2 and 3 are 1/2 and 1/3. The common difference is 1/3 - 1/2 = -1/6. The third term's reciprocal will be 1/3 - 1/6 = 1/6, so the third term is 6.

In a harmonic progression, the reciprocals of the terms form an arithmetic progression. The reciprocals of 2 and 4 are 1/2 and 1/4. The common difference is -1/4. Therefore, the third term's reciprocal is 1/4 - 1/4 = 0, which means the third term is 1.

In a harmonic progression, the reciprocals of the terms form an arithmetic progression. The reciprocals of the first two terms are 1/2 and 3/4. The common difference is 1/4, so the reciprocal of the third term is 1/2 + 1/4 = 3/4. Therefore, the third term is 1/(3/4) = 4/3.

The reciprocals of 3 and 6 are 1/3 and 1/6, which are in arithmetic progression.

The reciprocals of the first two terms are 1/3 and 1/6. The common difference is 1/6 - 1/3 = -1/6, which is incorrect. The correct common difference is 1/3 - 1/6 = 1/6.

The reciprocals of the terms are 1/3 and 1/6. The common difference is (1/6 - 1/3) = -1/6. The third term's reciprocal will be 1/6 - 1/6 = 0, which means the third term is 1/12, thus the answer is 12.

The reciprocals of the terms are 1/4 and 1/2. The common difference is 1/2 - 1/4 = 1/4.

The reciprocals are 1/4 and 1/8. The common difference is 1/8 - 1/4 = -1/8, which means the common difference of the corresponding arithmetic progression is 1/8.

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.