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)

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:

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

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is: