JEE Main 2019 Question Paper (09-Jan-2019) (Shift 1)

Question 1

A particle is moving with a velocity $ \overrightarrow{v} = K \left( y \widehat{i} + x \widehat{j} \right), $ where $ K $ is a constant. The general equation for its path is:

Accepted Answer

${y}^{2} = {x}^{2} + 	ext{constant}$

Answer

${y}^{2} = x + 	ext{constant}$

Answer

$xy = 	ext{constant}$

Answer

$y = x^{2} + 	ext{constant}$

Question 2

A conducting circular loop made of a thin wire has area $3.5 \times 10^{-2} \mathrm{m}^2$ and resistance $10  \Omega$. It is placed perpendicular to a time-dependent magnetic field $B(t) = (0.4  \mathrm{T}) \sin(50 \pi t)$. The field is uniform in space. Then the net charge flowing through the loop during $t = 0  \mathrm{s}$ and $t = 10  \mathrm{ms}$ is close to:

Accepted Answer

$1.4  mC$

Answer

$7  	ext{mC}$

Answer

$21  	ext{mC}$

Answer

$6  	ext{mC}$

Question 3

A rod of length $L$ at room temperature and uniform cross-sectional area $A$ is made of a metal having a coefficient of linear expansion $\alpha \; /°C$. It is observed that an external compressive force $F$ applied at each end prevents any change in the length of the rod when its temperature rises by $\Delta T \; \mathrm{K}$. Young's modulus, $Y$, for this metal is:

Accepted Answer

$ \frac{F}{A \alpha \Delta T} $

Answer

$\frac{F}{A \alpha \left(\Delta T - 273\right)}$

Answer

$ \frac{2F}{A \alpha \Delta T} $

Answer

$\frac{F}{2A \alpha \Delta T}$

Question 4

Three charges $ +Q, q, +Q $ are placed respectively, at distances $ 0, \frac{d}{2} $, and $ d $ from the origin, on the $ x $-axis. If the net force experienced by $ +Q $, placed at $ x=0 $, is zero, then the value of $ q $ is:

Accepted Answer

$-\frac{Q}{4}$

Answer

$+\frac{Q}{2}$

Answer

$+\frac{Q}{4}$

Answer

$ -\frac{Q}{2} $

Question 5

When the switch $S$ in the circuit shown is closed, then the value of current $i$ will be:

Accepted Answer

$5 \quad \mathrm{A}$

Answer

$2 \quad \mathrm{A}$

Answer

$3 \quad \mathrm{A}$

Answer

$4 \quad \mathrm{A}$