An astronomical refracting telescope will have large angular magnification and high angular resolution, when it has an objective lens of

An electron of mass m with an initial velocity $$\overrightarrow v = {v_0}\widehat i$$ (v₀ > 0) enters an electric field $$\overrightarrow E = - {\overrightarrow E _0}\widehat i$$ (E₀ = constant > 0) at t = 0. If $$\lambda $$₀ is its de-Broglie wavelength initially, then its de- Broglie wavelength at time t is

When the light of frequency 2$${\upsilon _0}$$ (where $${\upsilon _0}$$ is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v₁ . When the frequency of the incident radiation is increased to 5$${\upsilon _0}$$ , the maximum velocity of electrons emitted from the same plate is v₂ . The ratio of v₁ to v₂ is

In the combination of the following gates the output Y can be written in terms of inputs A and B as