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 $\sqrt{2}$)

What will $Rs. 500$ amount to in $10$ years after its deposit in a bank which pays an annual interest rate of $10\%$ compounded annually?

In a certain test,there are $n$ questions. In this test,$2^{n-i}$ students gave wrong answers to at least $i$ questions,where $i = 1, 2, \ldots, n$. If the total number of wrong answers given is $2047$,then $n$ is equal to:

The sum of a $G.P.$ with common ratio $r = 3$ is $364$,and the last term is $243$. Find the number of terms $n$.

If the sum of the second,fourth and sixth terms of a $G.P.$ of positive terms is $21$ and the sum of its eighth,tenth and twelfth terms is $15309$,then the sum of its first nine terms is:

Let $S_1$ be the sum of areas of the squares whose sides are parallel to the coordinate axes. Let $S_2$ be the sum of areas of the slanted squares as shown in the figure. Then,$\frac{S_1}{S_2}$ is equal to