An electron, a doubly ionized helium ion (He⁺⁺) and a proton are having the same kinetic energy. The relation between their respective de-Broglie wavelengths $$\lambda $$_e, $$\lambda $$_He⁺⁺ and $$\lambda $$_p is :

A part of a complete circuit is shown in the figure. At some instant, the value of current I is 1A and it is decreasing at a rate
of 10² A s^–1. The value of the potential difference V_P – V_Q , (in volts) at that instant, is _________.

Initially a gas of diatomic molecules is contained in a cylinder of volume V₁ at a pressure P₁ and temperature 250 K. Assuming that 25% of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature 2000 K, when contained in a volume 2V₁ is given by P₂ . The ratio $${{{P_2}} \over {{P_1}}}$$ is ________.

The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is $$\left( {{x \over {100}}} \right)$$ %. If the relative errors in measuring the mass and the diameter are 6.0% and 1.5% respectively, the value of x is_______.