JEE Main 2018 Question Paper (08-Apr-2018)

Question 1

Three concentric metal shells $ A, \ B $ and $ C $ of respective radii $ a, \ b $ and $ c \ (a < b < c) $ have surface charge densities $ +\sigma, \ -\sigma $ and $ +\sigma $ respectively. The potential of shell $ B $ is:

Accepted Answer

$ \frac{\sigma}{\epsilon_0} \left[ \frac{a^2 - b^2}{b} + c \right] $

Answer

$ \frac{\sigma}{\epsilon_0} \left[ \frac{b^2 - c^2}{c} + a \right] $

Answer

$ \frac{\sigma}{\epsilon_0} \left[ \frac{a^2 - b^2}{a} + c \right] $

Answer

$ \frac{\sigma}{\epsilon_0} \left[ \frac{b^2 - c^2}{b} + a \right] $

Question 2

Seven identical circular planar disks, each of mass $ M $ and radius $ R $, are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point $ P $ is:

Accepted Answer

$\frac{181}{2} M R^{2}$

Answer

$\frac{19}{2} \quad M R^{2}$

Answer

$\frac{55}{2} M R^{2}$

Answer

$\frac{73}{2} M R^{2}$

Question 3

From a uniform circular disc of radius $ R $ and mass $ 9M $, a small disc of radius $ \frac{R}{3} $ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the centre of the disc is:

Accepted Answer

$4M R^{2}$

Answer

$\frac{37}{9} M R^{2}$

Answer

$\frac{40}{9} M R^{2}$

Answer

$10M R^{2}$

Question 4

The reading of the ammeter for a silicon diode in the given circuit is:

Accepted Answer

$11.5\,\mathrm{mA}$

Answer

$13.5\,\mathrm{mA}$

Answer

$0$

Answer

$15\,\mathrm{mA}$

Question 5

Unpolarized light of intensity $I$ passes through an ideal polariser $A$. Another identical polariser $B$ is placed behind $A$. The intensity of light beyond $B$ is found to be $\frac{I}{2}$. Now another identical polariser $C$ is placed between $A$ and $B$. The intensity beyond $B$ is now found to be $\frac{I}{8}$. The angle between polarisers $A$ and $C$ is

Accepted Answer

$45^\circ$

Answer

$60^\circ$

Answer

$0^\circ$

Answer

$30^\circ$