The sum of the integers from $1$ to $100$ which are not divisible by $3$ or $5$ is

If $x, y, z \in R^+$ such that $x + y + z = 4$,then the maximum possible value of $xyz^2$ is -

Three numbers are selected from the set ${3^1, 3^2, 3^3, \dots, 3^{20}}$. Find the number of ways these selected numbers can form an increasing Geometric Progression $(G.P.)$.

If $1 + \sin x + \sin^2 x + \dots \infty = 4 + 2\sqrt{3}$,where $0 < x < \pi$,then:

In a $G.P.$,the sum of three numbers is $14$. If $1$ is added to the first two numbers and subtracted from the third number,the series becomes an $A.P.$. Find the greatest number.

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of an arithmetic sequence are $a$,$b$,and $c$ respectively,then the value of $[a(q - r) + b(r - p) + c(p - q)]$ is: