Data given for the following reaction is as follows :

FeO_(s) + C_(graphite) $$\to$$ Fe_(s) + CO_(g)

Substance	$$\Delta H^\circ $$ (kJ mol$$^{ - 1}$$)	$$\Delta S^\circ $$ (J mol$$^{ - 1}$$ K$$^{ - 1}$$)
$$Fe{O_{(s)}}$$	$$ - 266.3$$	57.49
$${C_{(graphite)}}$$	0	5.74
$$F{e_{(s)}}$$	0	27.28
$$C{O_{(g)}}$$	$$ - 110.5$$	197.6

The minimum temperature in K at which the reaction becomes spontaneous is ___________. (Integer answer)

The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m $$-$$ n = 0 and mn + nl + lm = 0, is :

Let $$A = \left( {\matrix{ {[x + 1]} & {[x + 2]} & {[x + 3]} \cr {[x]} & {[x + 3]} & {[x + 3]} \cr {[x]} & {[x + 2]} & {[x + 4]} \cr } } \right)$$, where [t] denotes the greatest integer less than or equal to t. If det(A) = 192, then the set of values of x is the interval :

Let M and m respectively be the maximum and minimum values of the function
f(x) = tan^$$-$$1 (sin x + cos x) in $$\left[ {0,{\pi \over 2}} \right]$$, then the value of tan(M $$-$$ m) is equal to :