1
JEE Advanced 2015 Paper 2 Offline
+4
-2
Consider a uniform spherical charge distribution of radius $${R_1}$$ centred at the origin $$O.$$ In this distribution, a spherical cavity of radius $${R_2},$$ centred at $$P$$ with distance $$OP=a$$ $$= {R_1} - {R_2}$$ (see figure) is made. If the electric field inside the cavity at position $$\overrightarrow r$$ is $$\overrightarrow E \overrightarrow {\left( r \right)} ,$$ then the correct statement(s) is (are)

A
$$\overrightarrow E$$ is uniform, its magnitude is independent of $${R_2}$$ but its direction depends on $$\overrightarrow r .$$
B
$$\overrightarrow E$$ is uniform, its magnitude depends on $${R_2}$$ and its direction depends on $$\overrightarrow r .$$
C
$$\overrightarrow E$$ is uniform, its magnitude is independent of a but its direction depends on $$\overrightarrow a$$
D
$$\overrightarrow E$$ is uniform and both its magnitude and direction depend on $$\overrightarrow a$$
2
JEE Advanced 2015 Paper 2 Offline
Numerical
+4
-0
Four harmonic waves of equal frequencies and equal intensities I0 have phase angles 0, $${\pi \over 3},{{2\pi } \over 3}$$ and $$\pi$$. When they are superposed, the intensity of the resulting wave is nI0. The value of n is
3
JEE Advanced 2015 Paper 2 Offline
Numerical
+4
-0
For a radioactive material, its activity A and rate of change of its activity R are defined as $$A = - {{dN} \over {dt}}$$ and $$R = - {{dA} \over {dt}}$$, where N(t) is the number of nuclei at time t. Two radioactive source P(mean life $$\tau$$) and Q (mean life 2$$\tau$$) have the same activity at t = 0. Their rate of change of activities at t = 2$$\tau$$ are RP and RQ, respectively. If $${{{R_P}} \over {{R_Q}}} = {n \over e}$$, then the value of n is
4
JEE Advanced 2015 Paper 2 Offline
Numerical
+4
-0
A monochromatic beam of light is incident at 60$$^\circ$$ on one face of an equilateral prism of refractive index n and emerges from the opposite face making an angle $$\theta$$(n) with the normal (see figure). For n = $$\sqrt 3$$ the value of $$\theta$$ is 60$$^\circ$$ and $${{d\theta } \over {dn}} = m$$. The value of m is