Calculate the wavelength (in nanometer) associated with a proton moving at 1.0 x 10³ ms⁻¹ (Mass of proton = 1.67 $$\times$$ 10^-27 kg and h = 6.63 $$\times$$ 10^-34 Js) :

Statement - 1 : The variance of first n even natural numbers is $${{{n^2} - 1} \over 4}$$

Statement - 2 : The sum of first n natural numbers is $${{n\left( {n + 1} \right)} \over 2}$$ and the sum of squares of first n natural numbers is $${{n\left( {n + 1} \right)\left( {2n + 1} \right)} \over 6}$$

If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is equal to

For real x, let f(x) = x³ + 5x + 1, then