$${N_2}{O_{5(g)}} \to 2N{O_{2(g)}} + {1 \over 2}{O_{2(g)}}$$

In the above first order reaction the initial concentration of N₂O₅ is 2.40 $$\times$$ 10^$$-$$2 mol L^$$-$$1 at 318 K. The concentration of N₂O₅ after 1 hour was 1.60 $$\times$$ 10^$$-$$2 mol L^$$-$$1. The rate constant of the reaction at 318 K is ______________ $$\times$$ 10^$$-$$3 min^$$-$$1. (Nearest integer)

[Given : log 3 = 0.477, log 5 = 0.699]

If the concentration of glucose (C₆H₁₂O₆) in blood is 0.72 g L^$$-$$1, the molarity of glucose in blood is ____________ $$\times$$ 10^$$-$$3 M. (Nearest integer)

[Given : Atomic mass of C = 12, H = 1, O = 16 u]

Let S_n denote the sum of first n-terms of an arithmetic progression. If S₁₀ = 530, S₅ = 140, then S₂₀ $$-$$ S₆ is equal to:

Let f : R $$\to$$ R be defined as

$$f(x) = \left\{ {\matrix{ { - {4 \over 3}{x^3} + 2{x^2} + 3x,} & {x > 0} \cr {3x{e^x},} & {x \le 0} \cr } } \right.$$. Then f is increasing function in the interval