At any instant the velocity of a particle of mass $$500 \mathrm{~g}$$ is $$\left(2 t \hat{i}+3 t^{2} \hat{j}\right) \mathrm{ms}^{-1}$$. If the force acting on the particle at $$t=1 \mathrm{~s}$$ is $$(\hat{i}+x \hat{j}) \mathrm{N}$$. Then the value of $$x$$ will be:

A cylindrical wire of mass $$(0.4 \pm 0.01) \mathrm{g}$$ has length $$(8 \pm 0.04) \mathrm{cm}$$ and radius $$(6 \pm 0.03) \mathrm{mm}$$. The maximum error in its density will be:

Two projectiles A and B are thrown with initial velocities of $$40 \mathrm{~m} / \mathrm{s}$$ and $$60 \mathrm{~m} / \mathrm{s}$$ at angles $$30^{\circ}$$ and $$60^{\circ}$$ with the horizontal respectively. The ratio of their ranges respectively is $$\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$$

For a nucleus $${ }_{\mathrm{A}}^{\mathrm{A}} \mathrm{X}$$ having mass number $$\mathrm{A}$$ and atomic number $$\mathrm{Z}$$

A. The surface energy per nucleon $$\left(b_{\mathrm{s}}\right)=-a_{1} A^{2 / 3}$$.

B. The Coulomb contribution to the binding energy $$\mathrm{b}_{\mathrm{c}}=-a_{2} \frac{Z(Z-1)}{A^{4 / 3}}$$

C. The volume energy $$\mathrm{b}_{\mathrm{v}}=a_{3} A$$

D. Decrease in the binding energy is proportional to surface area.

E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( $$a_{1}, a_{2}$$ and $$a_{3}$$ are constants)

Choose the most appropriate answer from the options given below: