MCQ
Which of the following is a finite set :
- A$\{x: x \in N\}$
- B$\{x: x>10 x \in N\}$
- ✓$\{x: x<10, x \in N\}$
- D$\{x: x=2 n, n \in N\}$
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$B=\left\{x \in R : 3^x\left(\sum_{x=1}^{\infty} \frac{3}{10^x}\right)^{x-3} < 3^{-3 x}\right\}$, where $[t]$denotes greatest integer function. Then,
$S _1=\{( i , j , k ): i , j , k \in\{1,2, \ldots, 10\}\}$
$S _2=\{( i , j ): 1 \leq i < j +2 \leq 10, i , j \in\{1,2, \ldots, 10\}\},$
$S _3=\{( i , j , k , l): 1 \leq i < j < k < l, i , j , k , l \in\{1,2, \ldots ., 10\}\}$
$S _4=\{( i , j , k , l): i , j , k$ 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?
$(A)$ $n _1=1000$ $(B)$ $n _2=44$ $(C)$ $n _3=220$ $(D)$ $\frac{ n _4}{12}=420$