Which one of the following statements about the solstices, an event that occurs when the Sun appears to reach most northerly or southerly, is correct?

The correct answer is B, homolographic. A homolographic or equal-area projection keeps the ratio of areas on the map the same as on the globe, which is why world distribution maps of population, crops or forests are drawn on projections such as Mollweide's or the sinusoidal. Option A is wrong because orthomorphic, also called conformal, describes a projection that keeps shapes true locally, as Mercator's does; no projection can be both orthomorphic and homolographic over a large area. Option C is wrong because azimuthal or zenithal names the family of projections drawn on a plane touching the globe, not the property preserved. Option D is wrong because the gnomonic is one particular perspective zenithal projection on which a great circle plots as a straight line, useful in aviation.

The correct answer is A. A cadastral map is a very large-scale map of a village or a town drawn to register plots, fields, their boundaries and their owners, and it is the basis of land revenue records and of the registration of property. Option B is wrong because a rainfall map is a thematic or distribution map, drawn on a small scale with isohyets. Option C is wrong because air routes appear on small-scale route or atlas maps, where detail of the ground is deliberately left out. Option D is wrong because relief is shown on topographical maps with contours, and the words small scale make it doubly wrong, since cadastral maps are the largest-scale maps in regular use. The word cadastre itself means a register of property, which is the easiest way to remember it.

The correct answer is D, spatial resolution. It is usually expressed as the ground size of one pixel, so a sensor of one metre resolution can separate objects about a metre across, which is what makes high-resolution imagery useful for urban mapping. Option A is wrong because spectral resolution refers to the number of wavelength bands recorded and how narrow each is, which decides how finely different materials can be told apart. Option B is wrong because radiometric resolution is the sensitivity of the sensor to differences in the strength of the signal, expressed in the number of levels or bits. Option C is wrong because temporal resolution is the interval after which the same area is imaged again, which matters for watching a crop grow or a flood spread. All four together describe the quality of a data set.

The correct answer is B, Hyderabad. The National Remote Sensing Centre, a centre of the Indian Space Research Organisation, works from Hyderabad and operates the earth station at Shadnagar nearby, where data from Indian and foreign satellites is received. Option A is wrong because Bengaluru is the headquarters of ISRO itself and the location of the U. R. Rao Satellite Centre, where satellites are built. Option C is wrong because Ahmedabad is the home of the Space Applications Centre, which develops payloads and applications. Option D is wrong because Dehradun is the headquarters of the Survey of India, the topographical mapping agency, and also of the Indian Institute of Remote Sensing, which is a training and research institute rather than the data centre. Remember the three cities together: Bengaluru for ISRO headquarters, Ahmedabad for the Space Applications Centre and Hyderabad for the National Remote Sensing Centre, with Dehradun for the Survey of India.

The correct answer is C, about 36,000 km above the equator. At that height a satellite's orbital period equals the period of the earth's rotation, so it stays above the same point on the equator and appears fixed in the sky, which is what communication and weather satellites need. Option A is wrong because a few hundred kilometres is the range of the near-polar sun-synchronous orbits used by earth observation satellites, which cross the equator at the same local time on each pass. Option B is wrong because at ten thousand kilometres the period is far shorter than a day and the satellite would drift across the sky. Option D is wrong because one lakh kilometres is well beyond the geostationary belt and the satellite's period would be much longer than a day.