Explanation: The longitudinal extent of a region refers to the range of longitudes that the region covers from west to east. In the case of Tamil Nadu, a state located in the southern part of India, its longitudinal extent is from 76$^circ$18 E to 80$^circ$20 E. This means that the state spans from 76 degrees 18 minutes east to 80 degrees 20 minutes east of the Prime Meridian, which is the reference line of 0$^\circ$ longitude that runs through Greenwich, England.
Understanding the concept of longitudinal extent is crucial for geographical studies and for understanding the spatial distribution of various features within a region. The Prime Meridian divides the Earth into the eastern and western hemispheres, and longitudes are measured in degrees east or west from this line. In the case of Tamil Nadu, it is located entirely in the eastern hemisphere, which is why the correct longitudinal extent is given in terms of east longitudes.
The coordinates provided in the correct answer, 76$^circ$18 E to 80$^circ$20 E, accurately represent the geographical boundaries of Tamil Nadu. The westernmost point of the state is at 76$^circ$18 E, and the easternmost point is at 80$^circ$20 E. This range reflects the east-west span of the state and is consistent with its location in the eastern part of India.
It is important to note that the other options provided in the question are incorrect due to either incorrect hemisphere designation (west instead of east) or incorrect degree and minute values. The misconception of choosing the wrong hemisphere (west instead of east) can arise from a lack of understanding of the Prime Meridian and the division of the Earth into eastern and western hemispheres. Similarly, the incorrect degree and minute values can result from a misremembering of the exact coordinates of Tamil Nadu's boundaries.
In summary, the longitudinal extent of Tamil Nadu is a fundamental geographical fact that helps in understanding the spatial distribution and location of the state within the broader context of India and the world. The correct answer, 76$^circ$18 E to 80$^circ$20 E, accurately represents the east-west span of the state and is essential for geographical studies and examinations.