My answer answers both this question, and https://gateoverflow.in/87037/gate2005-83b one.
It detects recursion and eliminates recursion
I don't think a grammar that derives an arbitrary length string can work without recursion in it. Removing recursion from a grammar is never the solution.
It detects reduce-reduce conflict, and resolves
No chance that $E + E.$ and $E * E.$ (notice the dot) can coexist in a state. The states would be split when one moves to a different state on + transition, and the other moves to a different state on * transition.
It detects shift-reduce conflict, and resolves the conflict in favor of a shift over a reduce action
It detects shift-reduce conflict, and resolves the conflict in favor of a reduce over a shift action
SR conflict is definitely a possibility.
A state can have $E+E.$ along with a terminal transition.
What's the action of YACC on detecting an SR conflict?
YACC isn't quick to reduce the string back to the Varibale, it lets the string shift so as to see more of the string.
Hence, Option C is correct.
PS: What does YACC do on an RR conflict?
It reduces the production that comes first textually.
Now, answering https://gateoverflow.in/87037/gate2005-83b
The SR conflict can be observed after the digit 2.
The compiler would be conflicted on whether to reduce $3*2$ into $6$, or to shift ahead and see more of the string.
It favours shift.
$3*2+1$ is entirely seen first.
Now, if you observe the grammar $+$ and $*$ have equal priority, and associativity isn't defined by the grammar properly.
The compiler is at the dot currently $3*2+1.$
This is as good as having an RR conflict. Whether to reduce $3*2$ first or $2+1$ first. As stated above, on an RR conflict, the compiler would reduce the production the comes first textually.
2+1 is closer to the dot, so do that first.
Now, do $3*3$, which results in 9.
If you notice, with equal precedence we treat symbols the same.
ie, $3<symbol> 2 <symbol> 1$
Still, we acted on the right symbol first, which means we implicitly assigned right asociativity.
Hence, Option B