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 the polynomial $ax^2 + bx + 5$ leaves a remainder $3$ when divided by $x - 1$, and a remainder $2$ when divided by $x + 1$, then $2b - 4a$ equals

The remainder when $1! + 2! + 3! + ... + 95!$ is divided by $15$ is

The remainder when $(29^{29})^{29}$ is divided by $9$ is

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

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

The remainder when $11^{1011} + 1011^{11}$ is divided by $9$ is