Glycerin of density $$1.25 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$$ is flowing through the conical section of pipe The area of cross-section of the pipe at its ends are $$10 \mathrm{~cm}^{2}$$ and $$5 \mathrm{~cm}^{2}$$ and pressure drop across its length is $$3 ~\mathrm{Nm}^{-2}$$. The rate of flow of glycerin through the pipe is $$x \times 10^{-5} \mathrm{~m}^{3} \mathrm{~s}^{-1}$$. The value of $$x$$ is ___________.

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