If $\log _{10} 2, \log _{10} (2^x + 1), \log _{10} (2^x + 3)$ are in $A.P.,$ then :-
$x = 0$
$x = 1$
$x = \log _{10} 2$
$x = \frac{1}{2} \log _2 5$
The difference between any two consecutive interior angles of a polygon is $5^{\circ}$ If the smallest angle is $120^{\circ},$ find the number of the sides of the polygon.
The sum of the integers from $1$ to $100$ which are not divisible by $3$ or $5$ is
The number of terms of the $A.P. 3,7,11,15...$ to be taken so that the sum is $406$ is
If twice the $11^{th}$ term of an $A.P.$ is equal to $7$ times of its $21^{st}$ term, then its $25^{th}$ term is equal to
Let $a_1, a_2, a_3, \ldots, a_{100}$ be an arithmetic progression with $a_1=3$ and $S_p=\sum_{i=1}^p a_i, 1 \leq p \leq 100$. For any integer $n$ with $1 \leq n \leq 20$, let $m=5 n$. If $\frac{S_{m m}}{S_n}$ does not depend on $n$, then $a_2$ is