The energy required to break one mole of Cl–Cl bonds in Cl₂ is 242 kJ mol^–1. The longest wavelength of light capable of breaking a single Cl – Cl bond is
(c = 3 x 10⁸ ms^–1 and N_A = 6.02 x 10²³ mol^–1)

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

Let $$f:R \to R$$ be a positive increasing function with

$$\mathop {\lim }\limits_{x \to \infty } {{f(3x)} \over {f(x)}} = 1$$. Then $$\mathop {\lim }\limits_{x \to \infty } {{f(2x)} \over {f(x)}} = $$

If $$\alpha $$ and $$\beta $$ are the roots of the equation $${x^2} - x + 1 = 0,$$ then $${\alpha ^{2009}} + {\beta ^{2009}} = $$