JEE Main 2019 Question Paper (12-Jan-2019) (Shift 1)

Question 1

Two light identical springs of spring constant $ k $ are attached horizontally at the two ends of a uniform horizontal rod $ AB $ of length $ l $ and mass $ m $. The rod is pivoted at its center $ O $ and can rotate freely in the horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in the figure. The rod is gently pushed through a small angle and released. The frequency of the resulting oscillation is:

Accepted Answer

$\frac{1}{2\pi} \sqrt{\frac{6k}{m}}$

Answer

$\frac{1}{2\pi} \sqrt{\frac{3k}{m}}$

Answer

$\frac{1}{2\pi} \sqrt{\frac{k}{m}}$

Answer

$\frac{1}{2\pi} \sqrt{\frac{2k}{m}}$

Question 2

The galvanometer deflection, when key ${K}_{1}$ is closed but ${K}_{2}$ is open, equals ${\theta}_{0}$ (see figure). On closing ${K}_{2}$ also and adjusting ${R}_{2}$ to $5 \Omega$, the deflection in galvanometer becomes $\frac{{\theta}_{0}}{5}$. The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery]:

Accepted Answer

$22\,\Omega$

Answer

$12\,\Omega$

Answer

$5\,\Omega$

Answer

$25\,\Omega$

Question 3

The figure shows a capacitor of capacitance $C$ connected to a battery via a switch, having a total charge $Q_0$ on it, in steady-state. When the switch $S$ is turned from position $A$ to position $B$, the energy dissipated in the circuit is

Accepted Answer

$\frac{3}{8} \frac{(Q_0)^2}{C}$

Answer

$\frac{1}{8} \frac{(Q_0)^2}{C}$

Answer

$\frac{3}{4} \frac{(Q_0)^2}{C}$

Answer

$\frac{5}{8} \frac{(Q_0)^2}{C}$

Question 4

A $100\,V$ carrier wave is made to vary between $160\,V$ and $40\,V$ by a modulating signal. What is the modulation index?

Accepted Answer

$0.6$

Answer

$0.3$

Answer

$0.4$

Answer

$0.5$

Question 5

The least count of the main scale of a screw gauge is $1\mathrm{mm}$. The minimum number of divisions on its circular scale required to measure $5\mathrm{\mu m}$ diameter of a wire is:

Accepted Answer

$200$

Answer

$50$

Answer

$100$

Answer

$500$