JEE Main 2016 Question Paper (10-Apr-2016)

Question 1

A conducting metal circular-wire loop of radius $r$ is placed perpendicular to a magnetic field which varies with time as $B = B_0 e^{-\frac{t}{	au}}$, where $B_0$ and $	au$ are constants at time $t = 0$. If the resistance of the loop is $R$, then the heat generated in the loop after a long time $\left(t 	o \inftyight)$ is

Accepted Answer

$\frac{\pi^{2} r^{4} B_{0}^{2}}{2 \tau R}$

Answer

$\frac{\pi^{2} r^{4} B_{0}^{4}}{2 \tau R}$

Answer

$\frac{\pi^{2} r^{4} B_{0}^{2} R}{\tau}$

Answer

$\frac{\pi^{2} r^{4} B_{0}^{2}}{\tau R}$

Question 2

Within a spherical charge distribution of charge density $ \rho(r) $, $ N $ equipotential surfaces of potential $ V_0, V_0 + \Delta V, V_0 + 2\Delta V, \dots, V_0 + N \Delta V (\Delta V > 0) $, are drawn and have increasing radii $ r_0,  r_1,  r_2, \dots, r_N $, respectively. If the difference in the radii of the surfaces is constant for all values of $ V_0 $ and $ \Delta V $, then:

Accepted Answer

$ \rho(r) \propto \frac{1}{r} $

Answer

$ ho(r) = 	ext{constant} $

Answer

$ \rho(r) \propto \frac{1}{r^{2}} $

Answer

$ \rho(r) \propto r $

Question 3

A thin $1\mathrm{m}$ long rod has a radius of $5\mathrm{mm}$. A force of $50 \pi 	imes 10^{3}\mathrm{N}$ is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is $0.01\mathrm{mm}$, which of the following statements is false?

Accepted Answer

The maximum value of $Y$ that can be determined is $2 	imes 10^{14} \mathrm{N} \mathrm{m}^{-2}$

Answer

$ \frac{\Delta Y}{Y} $ gets minimum contribution from the uncertainty in the length.

Answer

$ \frac{\Delta Y}{Y} $ gets its maximum contribution from the uncertainty in strain.

Answer

The figure of merit is the largest for the length of the rod.

Question 4

Concrete mixture is made by mixing cement, stone, and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to:
(Take the radius of the drum to be 1.25 m and its axle to be horizontal):

Accepted Answer

27.0

Answer

0.4

Answer

1.3

Answer

8.0

Question 5

The ratio $ R $ of output resistance $ r_0 $ and input resistance $ r_i $ in measurements of input and output characteristics of a transistor is typically in the range:

Accepted Answer

$R \sim 10^{2} - 10^{3}$

Answer

$R \sim 1 - 10$

Answer

$R \sim 0.1 	ext{ to } 1.0$

Answer

$R \sim 0.1 - 0.01$