Correct Option
Assertion (A) states that a jet aircraft moving at Mach Number equal to 1 travels faster at an altitude of 15 km than while moving at Mach Number equal to 1 near the sea level. The Mach number is defined as the ratio of the speed of an object to the speed of sound in the surrounding medium. The speed of sound in a gas is directly proportional to the square root of its absolute temperature (v ∝ √T). As altitude increases, the atmospheric temperature generally decreases. Therefore, the speed of sound is lower at an altitude of 15 km compared to sea level. Consequently, an aircraft flying at Mach 1 (which means its speed equals the local speed of sound) at 15 km altitude will have a lower actual velocity than an aircraft flying at Mach 1 at sea level. Thus, Assertion (A) is false.
Reason (R) states that the velocity of sound depends on the temperature of the surrounding medium. This statement is factually correct. As established, the speed of sound in a gas is primarily determined by the temperature of the medium, increasing with higher temperatures and decreasing with lower temperatures. Thus, Reason (R) is true.
Given that Assertion (A) is false and Reason (R) is true, option (d) is the correct choice.
Incorrect Options
Options (1) and (2) are incorrect because Assertion (A) is false. Option (3) is incorrect because Reason (R) is true, not false.