1 gram of a carbonate (M₂CO₃) on treatment with excess HCl produces 0.01186 mole of CO₂. The molar mass of M₂CO₃ in g mol^–1 is:

The radius of the second Bohr orbit for hydrogen atom is:
(Planck’s Const. h = 6.6262 × 10^-34 Js; mass of electron = 9.1091 × 10^-31 kg; charge of electron (e) = 1.60210 × 10^-19 C; permittivity of vacuum ($${\varepsilon _0}$$) = 8.854185 × 10^-12 kg^-1 m^-3 A²)

Let $$a$$, b, c $$ \in R$$. If $$f$$(x) = ax² + bx + c is such that
$$a$$ + b + c = 3 and $$f$$(x + y) = $$f$$(x) + $$f$$(y) + xy, $$\forall x,y \in R,$$

then $$\sum\limits_{n = 1}^{10} {f(n)} $$ is equal to

The function $$f:R \to \left[ { - {1 \over 2},{1 \over 2}} \right]$$ defined as

$$f\left( x \right) = {x \over {1 + {x^2}}}$$, is