Problem

Problem

Match the statements of Column I with values of Column II.
Column IColumn II
(A) Number of the values of xx lying in (0,π2)\left(0, \frac{\pi}{2}\right) at which f(x)=ln⁡(sin⁡x)f(x) = \ln(\sin x) is not monotonic, is(p)0
(B) If the greatest interval of decrease of the function f(x)=x3−3x+2f(x) = x^3 - 3x + 2 is [a,b][a, b] , then a+ba + b equals(q)2
(C) Let f(x)=x2+2[x]f(x) = \frac{x^2 + 2}{[x]} , 1≤x≤31 \le x \le 3 where [.][. ] greatest integer function, then least value of f(x)f(x) is(r)-3
(D) Set of all possible values of aa such that f(x)=e2x−(a+1)ex+2xf(x) = e^{2x} - (a+1)e^x + 2x is MI for all x∈Rx \in R is (−∞,a](-\infty, a] , then aa equals(s)3

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