What is the number of moves required in the Tower of Hanoi problem for $k$ disks?

Split $207$ into three parts such that these are in $\mathrm{A}.\mathrm{P}.$ and the product of two smaller parts is $4623$.

State whether the following statement is true or false.

The number of moves required in the Tower of Hanoi problem for $k$ disks can be expressed as $2^k-1$.

Neha spends $₹5$ on first day, $₹10$ on second day, $₹20$ on third day and so on. Find how much $\left(\mathrm{in} ₹\right)$, in all, will she spend in $10$ days?

Find a rational number which will have as its expansion:

$.\overline{68}$

Sirish started work in $2001$ at an annual salary of $₹2000$ and received an increment of $₹100$ each year. In which year did his income reach $3500$?

Write a general formula to calculate the amount remaining of the substance. If you start with a $60-\mathrm{gram}$ sample of the isotope, how much will remain  in $7.2$ years.

Half-life is the time required for a substance to decay to half of its original amount. A radioactive isotope has a half-life of $1.23$ years. Explain what this means.

Jasmine saves $₹20$ during the first month, and $₹15$ more every month. If she continues to save in this manner, in how many months will she save $₹3250$.

Half-life is the time required for a substance to decay to half of its original amount. A radioactive isotope has a half-life of $1.23$ years. Explain what this means.

Write a general formula to calculate the amount remaining of the substance. If you start with a $52-\mathrm{gram}$ sample of the isotope, how much will remain  in 7.2 years.

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

$55$ logs are to be stacked in the following manner: $10$ logs in the bottom, $9$ in the next row, then $8$ and so on, in how many rows can there $55$ logs be stacked?

Write a general formula to calculate the amount remaining of the substance. If you start with a $52-\mathrm{gram}$ sample of the isotope, how much will remain  in $7.2$ years.

Half-life is the time required for a substance to decay to half of its original amount. A radioactive isotope has a half-life of $1.23$ years. Explain what this means.