1
JEE Advanced 2015 Paper 2 Offline
Numerical
+4
-0
The energy of a system as a function of time t is given as E(t) = $${A^2}\exp \left( { - \alpha t} \right)$$, where $$\alpha = 0.2\,{s^{ - 1}}$$. The measurement of A has an error of 1.25 %. If the error in the measurement of time is 1.50 %, the percentage error in the value of E(t) at t = 5 s is
2
JEE Advanced 2015 Paper 2 Offline
Numerical
+4
-0
The densities of two solid spheres A and B of the same radii R vary with radial distance r as $${\rho _A}(r) = k\left( {{r \over R}} \right)$$ and $${\rho _B}(r) = k{\left( {{r \over R}} \right)^5}$$, , respectively, where k is a constant. The moments of inertia of the individual spheres about axes passing through their centres are $${I_A}$$ and $${I_B}$$, respectively. If, $${{{I_B}} \over {{I_A}}} = {n \over {10}}$$, the value of n is
3
JEE Advanced 2015 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r) is the pressure at r (r < R), then the correct option(s) is(are)
A
$$P(r = 0) = 0$$
B
$${{P(r = 3R/4)} \over {P(r = 2R/3)}} = {{63} \over {80}}$$
C
$${{P(r = 3R/5)} \over {P(r = 2R/5)}} = {{16} \over {21}}$$
D
$${{P(r = R/2)} \over {P(r = R/3)}} = {{20} \over {27}}$$
4
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 $$\overrightarrow a$$
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