CAT (QA) PYQs

If $f_{1}(x)=x^{2}+11 x+n$ and $f_{2}(x)=x$, then the largest positive integer $n$ for which the equation $f_{1}(x)=f_{2}(x)$ has two distinct real roots, is

The equations $3x^2 - 5x + p = 0$ and $2x^2 - 2x + q = 0$ have one common root. The sum of the other roots of these two equations is

A quadratic equation $x^{2}+b x+c=0$ has two real roots. It the difference between the reciprocals of the roots is $1 / 3$ and the sum of the reciprocals of the squares of the roots is $5 / 9$, then the largest possible value of ( $b+c$ ) is