Let $${}^n{C_r}$$ denote the binomial coefficient of x^r in the expansion of (1 + x)ⁿ. If $$\sum\limits_{k = 0}^{10} {({2^2} + 3k)} {}^{10}{C_k} = \alpha {.3^{10}} + \beta {.2^{10}},\alpha ,\beta \in R$$, then $$\alpha$$ + $$\beta$$ is equal to ___________.

Let P(x) be a real polynomial of degree 3 which vanishes at x = $$-$$3. Let P(x) have local minima at x = 1, local maxima at x = $$-$$1 and $$\int\limits_{ - 1}^1 {P(x)dx} $$ = 18, then the sum of all the coefficients of the polynomial P(x) is equal to _________.

A plane electromagnetic wave propagating along y-direction can have the following pair of electric field $$\left( {\overrightarrow E } \right)$$ and magnetic field $$\left( {\overrightarrow B } \right)$$ components.

If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately : [Take g = 10 ms^$$-$$2, the radius of earth, R = 6400 $$\times$$ 10³ m, Take $$\pi$$ = 3.14]