MCQ
If $y=\log \left(\sin e^x\right)$, then $\frac{d y}{d x}$ is
- A$\cot e^x$
- B$\operatorname{cosec} e^x$
- C$e^x \cot e^x$
- D$e^x \operatorname{cosec} e^x$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$\left| {\begin{array}{*{20}{c}}
{{{\log }_e}\,a_1^ra_2^k}&{{{\log }_e}\,a_2^ra_3^k}&{{{\log }_e}\,a_3^ra_4^k} \\
{{{\log }_e}\,a_4^ra_5^k}&{{{\log }_e}\,a_5^ra_6^k}&{{{\log }_e}\,a_6^ra_7^k} \\
{{{\log }_e}\,a_7^ra_8^k}&{{{\log }_e}\,a_8^ra_9^k}&{{{\log }_e}\,a_9^ra_{10}^k}
\end{array}} \right| = 0$
Then the number of elements in $S$, is