A particle is moving along $$x$$-axis with its position (x) varying with time $$(t)$$ as $$x=\alpha t^4+\beta t^2+\gamma t+\delta$$. The ratio of its initial velocity to its initial acceleration, respectively, is:

The radius of gyration of a solid sphere of mass $$5 \mathrm{~kg}$$ about $$X Y$$ is $$5 \mathrm{~m}$$ as shown in figure. The radius of the sphere is $$\frac{5 x}{\sqrt{7}} \mathrm{~m}$$, then the value of $x$ is:

The I-V characteristics shown above are exhibited by a

The magnetic moment and moment of inertia of a magnetic needle as shown are, respectively, $$1.0 \times 10^{-2} \mathrm{~A} \mathrm{~m}^2$$ and $$\frac{10^{-6}}{\pi^2} \mathrm{~kg} \mathrm{~m}^2$$. If it completes 10 oscillations in $$10 \mathrm{~s}$$, the magnitude of the magnetic field is