Find the value(s) of $p$ for which the following pairs of linear equations have no solution:

$(3p+1)x+3y=2$

$\left(p^2+1\right)x+(p-2)y-5=0$

Find the value(s) of $k$ for which the following pairs of linear equations have infinite solutions:

$10x+5y-(k-5)=0$

$20x+10y-k=0$

Find the value(s) of $k$ for which the following pairs of linear equations have infinite solutions:

$kx+4y=k-4$

$16x+ky=k$

Find the value(s) of $k$ for which the following pairs of linear equations have infinite solutions:

$2x+3y=7$

$(k+1)x+(2k-1)y=4k+1$

Find the value(s) of $k$ for which the following pairs of linear equations have infinite solutions:

$2x+3y-7=0$

$(k-1)x+(k+1)y=3k-1$

For what value of $k$, the following pair of linear equations has a unique solution:
$2x+ky=1, 3x-5y=7$

For what value(s) of $k$, the following pair of linear equations has no solution:
$kx+3y=k-3, 12x+ky=k$

For what value(s) of $k$, the following pair of linear equations has infinitely many solutions:
$kx+3y=k-3, 12x+ky=k$