Statement-1 : `f(x) = 0` has a unique solution in `(0,pi)`. Statement-2: If `g(x)` is continuous in `(a,b) and g(a) g(b) <0`, then the equation `g(x)=0` has a root in `(a,b)`.

Let f(x)=ln(2+x)-(2x+2)/x Statement-1: The equation f(x)=0 has a unique solution in the domain of f(x) . Statement-2: If f(x) is continuous in [a , b] and is strictly monotonic in (a , b) then f has a unique root in (a , b)

Let f(x)=ln(2+x)-(2x+2)/(x) . Statement I The function f(x) =0 has a unique solution in the domain of f(x). Statement II f(x) is continuous in [a, b] and is strictly monotonic in (a, b), then f has a unique root in (a, b).

Let f(x)=ln(2+x)-(2x+2)/(x+3) . Statement I The function f(x) =0 has a unique solution in the domain of f(x). Statement II f(x) is continuous in [a, b] and is strictly monotonic in (a, b), then f has a unique root in (a, b).

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

Statement I f(x) = |cos x| is not derivable at x = (pi)/(2) . Statement II If g(x) is differentiable at x = a and g(a) = 0, then |g|(x)| is non-derivable at x = a.

Statement 1: The function f(x)=x In x is increasing in ((1)/(e),oo) Statement 2: If both f(x) and g(x) are increasing in (a,b), then f(x)g(x) must be increasing in (a,b).