A radioactive nucleus emits $$4 \alpha$$-particles and $$7 \beta$$-particles in succession. The ratio of number of neutrons of that of protons, is [$$A=$$ mass number, $$Z=$$ atomic number]

A thin uniform rod has mass $$M$$ and length $$L$$ The moment of inertia about an axis perpendicular to it and passing through the point at a distance $$\frac{L}{3}$$ from one of its ends, will be

An obstacle is moving towards the source with velocity $$v$$. The sound is reflected from the obstacle. If $$c$$ is the speed of sound and $$\lambda$$ is the wavelength, then the wavelength of the reflected wave $$\lambda_r$$ is

If the angle of dip at places $$A$$ and $$B$$ are $$30^{\circ}$$ and $$45^{\circ}$$ respectively, then the ratio of horizontal component of earth's magnetic field at $$A$$ to that at $$B$$ will be $$\left[\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}, \sin \frac{\pi}{6}=\frac{1}{2}, \cos \frac{\pi}{6}=\frac{\sqrt{3}}{2}\right]$$