If [Cu(H₂O)₄]²⁺ absorbs a light of wavelength 600 nm for d-d transition, then the value of octahedral crystal field splitting energy for [Cu(H₂O)₆]²⁺ will be ____________ $$\times$$ 10^$$-$$21 J. [Nearest Integer]

(Given : h = 6.63 $$\times$$ 10^$$-$$34 Js and c = 3.08 $$\times$$ 10⁸ ms^$$-$$1)

Number of grams of bromine that will completely react with 5.0 g of pent-1-ene is ___________ $$\times$$ 10^$$-$$2 g. (Atomic mass of Br = 80 g/mol) [Nearest Integer]

The value of $$\int\limits_0^\pi {{{{e^{\cos x}}\sin x} \over {(1 + {{\cos }^2}x)({e^{\cos x}} + {e^{ - \cos x}})}}dx} $$ is equal to:

Let f : N $$\to$$ R be a function such that $$f(x + y) = 2f(x)f(y)$$ for natural numbers x and y. If f(1) = 2, then the value of $$\alpha$$ for which

$$\sum\limits_{k = 1}^{10} {f(\alpha + k) = {{512} \over 3}({2^{20}} - 1)} $$

holds, is :