JEE Main 2019 Question Paper (12-Apr-2019) (Shift 2)

Question 1

A transparent cube of side $ d$, made of a material of refractive index $ {\mu }_{2}$, is immersed in a liquid of refractive index $ {\mu }_{1}\ (\ {\mu }_{1}<{\mu }_{2})$. A ray is incident on the face $ \mathrm{A}\mathrm{B}$ at an angle $ \theta $ (shown in the figure). Total internal reflection takes place at the point $ \mathrm{E}$ on the face $ \mathrm{B}\mathrm{C}.$

Accepted Answer

$ 	heta \mathit{<}{\mathrm{sin}}^{-1}\sqrt{\frac{{\mu }_{2}^{2}}{{\mu }_{1}^{2}}-1}$

Answer

$ 	heta \mathit{>}{\mathrm{sin}}^{-1}\frac{{\mu }_{1}}{{\mu }_{2}}$

Answer

$ 	heta \mathit{<}{\mathrm{sin}}^{-1}\frac{{\mu }_{1}}{{\mu }_{2}}$

Answer

$ 	heta \mathit{>}{\mathrm{sin}}^{-1}\sqrt{\frac{{\mu }_{2}^{2}}{{\mu }_{1}^{2}}-1}$

Question 2

A Carnot engine has an efficiency of $ \frac{1}{6} $. When the temperature of the sink is reduced by 62°{C}  its efficiency is doubled. The temperatures of the source and the sink are, respectively,

Accepted Answer

$	ext{37 ℃, } 99 	ext{ ℃}$

Answer

$	ext{124 ℃, } 62 	ext{ ℃}$

Answer

$	ext{99 ℃, } 37 	ext{ ℃}$

Answer

$	ext{62 ℃, } 124 	ext{ ℃}$

Question 3

A diatomic gas with rigid molecules does $10 \ \mathrm{J}$ of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process?

Accepted Answer

$35 \quad \mathrm{J}$

Answer

$40 \quad \mathrm{J}$

Answer

$25 \quad \mathrm{J}$

Answer

$30 \quad \mathrm{J}$

Question 4

A smooth wire of length $ 2\pi r $ is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed $ \omega $ about the vertical diameter $ AB $, as shown in the figure, the bead is at rest with respect to the circular ring at position $ P $ as shown. Then the value of $ \omega^{2} $ is equal to:

Accepted Answer

$\frac{2g}{r\sqrt{3}}$

Answer

$\frac{2\mathrm{g}}{\mathrm{r}}$

Answer

$\frac{\sqrt{3} g}{2 r}$

Answer

$\frac{g \sqrt{3}}{r}$

Question 5

Let a total charge $2Q$ be distributed in a sphere of radius $R$, with the charge density given by $\rho(r) = k r$, where $r$ is the distance from the centre. Two charges $A$ and $B$, of $-Q$ each, are placed on diametrically opposite points, at equal distance $a$ from the centre. If $A$ and $B$ do not experience any force, then:

Accepted Answer

$ \mathrm{a} = 8^{-0.25} \mathrm{R} $

Answer

$ \mathrm{a} = \frac{3\mathrm{R}}{2^{0.25}} $

Answer

$ \mathrm{a} = \frac{\mathrm{R}}{\sqrt{3}} $

Answer

$ \mathrm{a} = 2^{-0.25} \mathrm{R} $