The difference between an integer and its cube is divisible by
Write the first three terms in each of the following sequences defined by the following:
$a_{n}=2 n+5$
The sides of a right angled triangle are in arithmetic progression. If the triangle has area $24$ , then what is the length of its smallest side ?
The ratio of the sums of first $n$ even numbers and $n$ odd numbers will be
If $1, \log _{10}\left(4^{x}-2\right)$ and $\log _{10}\left(4^{x}+\frac{18}{5}\right)$ are in
arithmetic progression for a real number $x$ then the value of the determinant $\left|\begin{array}{ccc}2\left(x-\frac{1}{2}\right) & x-1 & x^{2} \\ 1 & 0 & x \\ x & 1 & 0\end{array}\right|$ is equal to ...... .