1.Set Theory
medium

The number of elements in the set $\left\{ n \in N : 10 \leq n \leq 100\right.$ and $3^{ n }-3$ is a multiple of $7\}$ is $........$.

A

$15$

B

$14$

C

$13$

D

$12$

(JEE MAIN-2023)

Solution

$n \in[10,100]$

$3^{ n }-3 \text { is multiple of } 7$

$3^{ n }=7 \lambda+3$

$n =1,7,13,20, \ldots .97$

Number of possible values of $n=15$

Standard 11
Mathematics

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