MCQ
If $\alpha ,\;\beta ,\;\gamma $ are the geometric means between $ca,\;ab;\;ab,\;bc;\;bc,\;ca$ respectively where $a,\;b,\;c$ are in A.P., then ${\alpha ^2},\;{\beta ^2},\;{\gamma ^2}$ are in
- ✓$A.P.$
- B$H.P.$
- C$G.P.$
- DNone of the above
.Hence ${2^{n - 1}} > 100$ are in A.P.
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$f(x)=\sin \left(\frac{\pi x}{12}\right) \text { and } g(x)=\frac{2 \log _{ e }(\sqrt{x}-\sqrt{\alpha})}{\log _{ e }\left( e ^{\sqrt{x}}- e ^{\sqrt{\alpha}}\right)} \text {. }$
Then the value of $\lim _{ x \rightarrow \alpha^{+}} f( g ( x ))$ is