Suppose four distinct positive integers are in GP. Let , , and
Statement I : The numbers are neither in AP nor in GP.
Statement II : The numbers are in HP.
Statement I is true; Statement II is false.
Explanation for the correct options:
Explanation for Statement-I : Finding if Statement I is true
Given are in GP.
Now
and
Thus, . Hence, are not in AP.
Again,
and
Thus . Hence, are not in GP.
Therefore are neither in AP nor in GP.
Hence, statement I is true.
Explanation for Statement-II : Finding if Statement II is true
Formula to be used : We know that are in HP if are in AP.
Now,
Again,
Thus, . So, are not in HP.
Thus statement II is false.
Hence, Statement I is true and statement II is false.
Therefore, option (C) is the correct answer.