The $$\mathop {Lim}\limits_{x \to 0} {{\sin \left( {{2 \over 3}x} \right)} \over x}\,\,\,$$ is

A parabolic cable is held between two supports at the same level. The horizontal span between the supports is $$L.$$ The sag at the mid-span is $$h.$$ The equation of the parabola is $$y = 4h{{{x^2}} \over {{L^2}}},\,\,$$ where $$x$$ is the horizontal coordinate and $$y$$ is the vertical coordinate with the origin at the centre of the cable. The expanssion for the total length of the cable is

The inverse of the matrix $$\left[ {\matrix{ {3 + 2i} & i \cr { - i} & {3 - 2i} \cr } } \right]$$ is

Ion concentrations obtained for a groundwater sample (having pH=8.1) are given below.

Ion	$$Ca^{2+}$$	$$Mg^{2+}$$	$$Na^+$$	$$HCO_3^-$$	$$SO_4^{2-}$$	$$Cl^{-}$$
Ionconcentration(mg/L)	100	6	15	250	45	39
Atomic Weight	Ca=40	Mg=24	Na=23	H=1,C=12,O=16	S=32,O=16	Cl=35.5

Total hardness (mg/L as $$CaCO_3$$) present in the above water sample is