The centre of circle inscibed in square formed by the lines $${x^2} - 8x + 12 = 0\,\,and\,{y^2} - 14y + 45 = 0$$, is

Orthocentre of triangle with vertices $$\left( {0,0} \right),\left( {3,4} \right)$$ and $$\left( {4,0} \right)$$ is

The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices $$\left( {0,0} \right),\left( {0,21} \right)$$ and $$\left( {21,0} \right)$$, is

Coefficient of $${t^{24}}$$ in $${\left( {1 + {t^2}} \right)^{12}}\left( {1 + {t^{12}}} \right)\left( {1 + {t^{24}}} \right)$$ is