MCQ
If $\sin \theta + {\rm{cosec}}\theta = 2,$ the value of ${\sin ^{10}}\theta + {\rm{cose}}{{\rm{c}}^{10}}\theta $ is
- A$10$
- B${2^{10}}$
- C${2^9}$
- ✓$2$
$ \Rightarrow $${\sin ^2}\theta + 1 = 2\sin \theta $
$ \Rightarrow $${\sin ^2}\theta - 2\sin \theta + 1 = 0$
$ \Rightarrow $${(\sin \theta - 1)^2} = 0$
$\Rightarrow \sin \theta = 1$ Required value of
${\sin ^{10}}\theta + {\rm{cose}}{{\rm{c}}^{10}}\theta = {(1)^{10}} + \frac{1}{{{{(1)}^{10}}}} = 2$.
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$(A)$ $\left|z+\frac{1}{2}\right| \leq \frac{1}{2}$ for all $z \in S$ $(B)$ $|z| \leq 2$ for all $z \in S$
$(C)$ $\left|z+\frac{1}{2}\right| \geq \frac{1}{2}$ for all $z \in S$ $(D)$ The set $S$ has exactly four elements
$1.$ The numbers $\left|A_1\right|,\left|A_2\right|, \ldots,\left|A_m\right|$ are distinct.
$2.$ $A_1, A_2, \ldots, A_m$ are pairwise disjoint.(Here $|A|$ donotes the number of elements in the set $A$ )Then, the maximum possible value of $m$ is