#  JEE (Advanced) 2015 Paper-2 

Instructions   


For the following questions answer them individually

Question 11   


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 $$\overrightarrow{E} (\overrightarrow{r})$$ , then the correct statement(s) is(are)  


A

$$\overrightarrow{E}$$ is uniform, its magnitude is independentof $$R_2$$ 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 independentof a but its direction depends on $$\overrightarrow{a}$$

D

$$\overrightarrow{E}$$ is uniform and both its magnitude and direction depend on $$\overrightarrow{a}$$

Question 12   


In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in the figure. Then the correct statement(s) is(are)  


A

P has more tensile strength than Q

B

P is more ductile than Q

C

P is more brittle than Q

D

The Young’s modulus of P is more than that of Q

Question 13   


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

$$\frac{P \left(r = \frac{3R}{4}\right)}{P \left(r = \frac{2R}{3}\right)} = \frac{63}{80}$$

C

$$\frac{P \left(r = \frac{3R}{5}\right)}{P \left(r = \frac{2R}{5}\right)} = \frac{16}{21}$$

D

$$\frac{P \left(r = \frac{R}{2}\right)}{P \left(r = \frac{R}{3}\right)} = \frac{20}{27}$$

Question 14   


A parallel plate capacitor having plates of area S and plate separation d, has capacitance $$C_1$$ in air. When two dielectrics of different relative permittivities $$(\epsilon_1 = 2$$ and $$\epsilon_2 = 4)$$ are introduced between the two plates as shown in thefigure, the capacitance becomes $$C_2$$. The ratio $$\frac{C_2}{C_1}$$ is

A

$$\frac{6}{5}$$

B

$$\frac{5}{3}$$

C

$$\frac{7}{5}$$

D

$$\frac{7}{3}$$

Question 15   


An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature $$T_1$$, pressure $$P_1$$ and volume $$V_1$$ and the spring is in its relaxed state. The gas is then heated very slowly to temperature $$T_2$$, pressure $$P_2$$ and volume $$V_2$$. During this process the piston moves out by a distance x. Ignoring the friction between the piston and the cylinder, the correct statement(s) is(are)  


A

If $$V_2 = 2V_1$$ and $$T_2 = 3T_1$$, then the energy stored in the spring is $$\frac{1}{4}P_1 V_1$$

B

If $$V_2 = 2V_1$$ and $$T_2 = 3T_1$$, then the change in internal energy is $$3 P_1 V_1$$

C

If $$V_2 = 3V_1$$ and $$T_2 = 4T_1$$, then the work done by the gas is $$\frac{7}{3}P_1 V_1$$

D

If $$V_2 = 3V_1$$ and $$T_2 = 4T_1$$, then the heat supplied to the gas is $$\frac{17}{6}P_1 V_1$$

Question 16   


A fission reaction is given by $$_{92}^{236}U \rightarrow _{54}^{140}Xe + _{38}^{94}Sr + x + y$$ where x and y are two particles. Considering $$_{92}^{236}U$$ to be at rest, the kinetic energies of the products are denoted by $$K_{Xe}, K_{Sr}, K_x (2 MeV)$$ and $$K_y (2 MeV),$$ respectively. Let the binding energies per nucleon of $$_{92}^{236}U, _{54}^{140}Xe$$ and $$_{38}^{94}Sr$$ be 7.5 MeV, 8.5 MeV and 8.5 MeV,respectively. Considering different conservation laws, the correct option(s) is(are)

A

$$x = n, y = n, K_{Sr} = 129 MeV, K_{Xe} = 86 MeV$$

B

$$x = p, y = e^-, K_{Sr} = 129 MeV, K_{Xe} = 86 MeV$$

C

$$x = p, y = n, K_{Sr} = 129 MeV, K_{Xe} = 86 MeV$$

D

$$x = n, y = n, K_{Sr} = 86 MeV, K_{Xe} = 129 MeV$$

Instructions   


In a thin rectangular metallic strip a constant current I flows along the positive x-direction, as shown in the figure. The length, width and thickness of the strip are l, w and d, respectively.   
A uniform magnetic field $$\overrightarrow{B}$$ is applied on the strip along the positive y-direction. Due to this, the charge carriers experience a net deflection along the z-direction. This results in accumulation of charge carriers on the surface PQRS and appearance of equal and opposite charges on the face opposite to PQRS. A potential difference along the z-direction is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.  


Question 17   


Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are $$w_1$$ and $$w_2$$ and thicknesses are $$d_1$$ and $$d_2$$, respectively. Two points K and M are symmetrically located on the opposite faces parallel to the x-y plane (see figure). $$V_1$$ and $$V_2$$ are the potential differences between K and M instrips 1 and 2, respectively. Then,for a given current I flowing through them in a given magnetic field strength B, the correct statement(s) is(are)

A

If $$w_1 = w_2$$ and $$d_1 = 2d_2$$, then $$V_2 = 2V_1$$

B

If $$w_1 = w_2$$ and $$d_1 = 2d_2$$, then $$V_2 = V_1$$

C

If $$w_1 = 2w_2$$ and $$d_1 = d_2$$, then $$V_2 = 2V_1$$

D

If $$w_1 = 2w_2$$ and $$d_1 = d_2$$, then $$V_2 = V_1$$

Question 18   


Consider two different metallic strips (1 and 2) of same dimensions (length l, width w and thickness d) with carrier densities $$n_1$$ and $$n_2$$, respectively. Strip 1 is placed in magnetic field $$B_1$$ and strip 2 is placed in magnetic field $$B_2,$$ both along positive y-directions. Then $$V_1$$ and $$V_2$$ are the potential differences developed between K and M in strips 1 and 2, respectively. Assuming that the current I is the same for both the strips, the correct option(s) is(are)

A

If $$B_1 = B_2$$ and $$n_1 = 2n_2$$, then $$V_2 = 2V_1$$

B

If $$B_1 = B_2$$ and $$n_1 = 2n_2$$, then $$V_2 = V_1$$

C

If $$B_1 = 2B_2$$ and $$n_1 = n_2$$, then $$V_2 = 0.5V_1$$

D

If $$B_1 = 2B_2$$ and $$n_1 = n_2$$, then $$V_2 = V_1$$

Instructions   


Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index $$n_1$$ surrounded by a medium of lower refractive index $$n_2$$. The light guidance in the structure takes place due to successive total internal reflections at the  
interface of the media $$n_1$$ and $$n_2$$ as shown in the figure. All rays with the angle of incidence i less than a particular value $$i_m$$ are confined in the medium of refractive index $$n_1$$. The numerical aperture (NA) of the structureis defined as sin $$i_m$$.  


Question 19   


For two structures namely $$S_1$$ with $$n_1 = \frac{\sqrt 45}{4}$$ and $$n_2 = \frac{3}{2}$$, and $$S_2$$ with $$n_1 = \frac{8}{5}$$ and $$n_2 = \frac{7}{5}$$ and taking the refractive index of water to be $$\frac{4}{3}$$ and that of air to be 1, the correct option(s) is(are)

A

NA of $$S_1$$ immersed in water is the sameas that of $$S_2$$ immersed in liquid of refractive index $$\frac{16}{3\sqrt 15}$$

B

NA of $$S_1$$ immersed in liquid of refractive index $$\frac{6}{\sqrt 15}$$ is the same as that of $$S_2$$ immersed in water

C

NA of $$S_1$$ placed in air is the same as that of $$S_2$$ immersed in liquid of refractive index $$\frac{4}{\sqrt 15}$$

D

NA of $$S_1$$ placed in air is the same as that of $$S_2$$ placed in water

Question 20   


If two structures of same cross-sectional area, but different numerical apertures $$NA_1$$ and $$NA_2 (NA_2 < NA_1)$$ are joined longitudinally, the numerical aperture of the combined structure is

A

$$\frac{NA_1 NA_2}{NA_1 + NA_2}$$

B

$$NA_1 + NA_2$$

C

$$NA_1$$

D

$$NA_2$$