The money invested in a company is compounded continuously. If ₹ $200$ invested today becomes ₹ $400$ in $6$ years, then at the end of $33$ years it will become ₹ (in $\sqrt{2}$)

If $p, q, r$ are in one geometric progression and $a, b, c$ are in another geometric progression,then $cp, bq, ar$ are in

$A$ person has $2$ parents,$4$ grandparents,$8$ great-grandparents,and so on. Find the total number of his ancestors during the $10$ generations preceding his own.

If the sum of an infinite $GP$ $a, ar, ar^{2}, ar^{3}, \ldots$ is $15$ and the sum of the squares of its each term is $150$,then the sum of $ar^{2}, ar^{4}, ar^{6}, \ldots$ is:

If the roots of the equation $x^3-7x^2+14x-8=0$ are in geometric progression,then the difference between the largest and the smallest roots is

In an increasing geometric series,the sum of the second and the sixth term is $\frac{25}{2}$ and the product of the third and fifth term is $25$. Then,the sum of the $4^{\text{th}}$,$6^{\text{th}}$,and $8^{\text{th}}$ terms is equal to