IPMAT Indore (SA) PYQs

The remainder when $7^{103} + 7^{101}$ is divided by $9$ is ___

A polynomial $P(x)$ leaves a remainder $2$ when divided by $(x - 1)$ and a remainder $1$ when divided by $(x - 2)$ The remainder when $P(x)$ is divided by $(x - 1)(x - 2)$ is

If $m$ is a positive integer then the values of $k$ for which $6m + k$ cannot be a perfect square are