Two convex lenses of focal length $$20 \mathrm{~cm}$$ each are placed coaxially with a separation of $$60 \mathrm{~cm}$$ between them. The image of the distant object formed by the combination is at _____________ $$\mathrm{cm}$$ from the first lens.

For a certain organ pipe, the first three resonance frequencies are in the ratio of $$1:3:5$$ respectively. If the frequency of fifth harmonic is $$405 \mathrm{~Hz}$$ and the speed of sound in air is $$324 \mathrm{~ms}^{-1}$$ the length of the organ pipe is _________ $$\mathrm{m}$$.

A common example of alpha decay is $${ }_{92}^{238} \mathrm{U} \longrightarrow{ }_{90}^{234} \mathrm{Th}+{ }_{2} \mathrm{He}^{4}+\mathrm{Q}$$

Given :

$${ }_{92}^{238} \mathrm{U}=238.05060 ~\mathrm{u}$$,

$${ }_{90}^{234} \mathrm{Th}=234.04360 ~\mathrm{u}$$,

$${ }_{2}^{4} \mathrm{He}=4.00260 ~\mathrm{u}$$ and

$$1 \mathrm{u}=931.5 \frac{\mathrm{MeV}}{c^{2}}$$

The energy released $$(Q)$$ during the alpha decay of $${ }_{92}^{238} \mathrm{U}$$ is __________ MeV

A conducting circular loop is placed in a uniform magnetic field of $$0.4 \mathrm{~T}$$ with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of $$1 \mathrm{~mm} / \mathrm{s}$$. The magnitude of induced emf in the loop at an instant when the radius of the loop is $$2 \mathrm{~cm}$$ will be ___________ $$\mu \mathrm{V}$$.