MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{{\sin (2 + x) - \sin (2 - x)}}{x} = $
- A$\sin 2$
- B$2\sin 2$
- ✓$2\cos 2$
- D$2$
$i.e.,$ $\mathop {\lim }\limits_{x \to 0} \frac{{\sin (2 + x) - \sin (2 - x)}}{x} = \mathop {\lim }\limits_{x \to 0} \frac{{2\cos 2.\sin x}}{x}$
$ = 2\cos 2.\mathop {\lim }\limits_{x \to 0} \frac{{\sin x}}{x} = 2\cos 2$
You may also apply $L-$ Hospital rule.
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$S _1=\{( i , j , k ): i , j , k \in\{1,2, \ldots, 10\}\}$
$S _2=\{( i , j ): 1 \leq i < j +2 \leq 10, i , j \in\{1,2, \ldots, 10\}\},$
$S _3=\{( i , j , k , l): 1 \leq i < j < k < l, i , j , k , l \in\{1,2, \ldots ., 10\}\}$
$S _4=\{( i , j , k , l): i , j , k$ and $l$ are distinct elements in $\{1,2, \ldots, 10\}\}$
and If the total number of elements in the set $S _t$ is $n _z, r =1,2,3,4$, then which of the following statements is (are) TRUE?
$(A)$ $n _1=1000$ $(B)$ $n _2=44$ $(C)$ $n _3=220$ $(D)$ $\frac{ n _4}{12}=420$