Sir please help me to solve this question. What is the concept behind it or is it a trick question?

this is a wrong ques. you can also check on wolfram alpha and the limit does not exist as it is negative infinity. the reason is that as x tends to infinity, x^2 tends to infinity and cot-1x tends to zero so that ln(arccotx) tends to – infinity. hence the product tends to – infinity so the lim does not exist.