1
JEE Advanced 2022 Paper 1 Online
Numerical
+3
-0 A projectile is fired from horizontal ground with speed $v$ and projection angle $\theta$. When the acceleration due to gravity is $g$, the range of the projectile is $d$. If at the highest point in its trajectory, the projectile enters a different region where the effective acceleration due to gravity is $g^{\prime}=\frac{g}{0.81}$, then the new range is $d^{\prime}=n d$. The value of $n$ is ___________ .

2
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2 A medium having dielectric constant $K>1$ fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is $d$. The capacitor is connected to a battery of voltage $V$, as shown in Figure (a). Now, both the plates are moved by a distance of $\frac{d}{2}$ from their original positions, as shown in Figure (b). In the process of going from the configuration depicted in Figure (a) to that in Figure (b), which of the following statement(s) is(are) correct?

A
The electric field inside the dielectric material is reduced by a factor of $2 K$.
B
The capacitance is decreased by a factor of $\frac{1}{K+1}$.
C
The voltage between the capacitor plates is increased by a factor of $(K+1)$.
D
The work done in the process DOES NOT depend on the presence of the dielectric material.
3
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2 The figure shows a circuit having eight resistances of $1 \Omega$ each, labelled $R_{1}$ to $R_{8}$, and two ideal batteries with voltages $\varepsilon_{1}=12 \mathrm{~V}$ and $\varepsilon_{2}=6 \mathrm{~V}$. Which of the following statement(s) is(are) correct?

A
The magnitude of current flowing through $R_{1}$ is $7.2 \mathrm{~A}$.
B
The magnitude of current flowing through $R_{2}$ is $1.2 \mathrm{~A}$.
C
The magnitude of current flowing through $R_{3}$ is $4.8 \mathrm{~A}$.
D
The magnitude of current flowing through $R_{5}$ is $2.4 \mathrm{~A}$.
4
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2 An ideal gas of density $\rho=0.2 \mathrm{~kg} \mathrm{~m}^{-3}$ enters a chimney of height $h$ at the rate of $\alpha=$ $0.8 \mathrm{~kg} \mathrm{~s}^{-1}$ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_{1}=0.1 \mathrm{~m}^{2}$ and the upper end is $A_{2}=0.4 \mathrm{~m}^{2}$. The pressure and the temperature of the gas at the lower end are $600 \mathrm{~Pa}$ and $300 \mathrm{~K}$, respectively, while its temperature at the upper end is $150 \mathrm{~K}$. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take $g=10 \mathrm{~m} \mathrm{~s}^{-2}$ and the ratio of specific heats of the gas $\gamma=2$. Ignore atmospheric pressure. Which of the following statement(s) is(are) correct?

A
The pressure of the gas at the upper end of the chimney is $300 \mathrm{~Pa}$.
B
The velocity of the gas at the lower end of the chimney is $40 \mathrm{~m} \mathrm{~s}^{-1}$ and at the upper end is $20 \mathrm{~ms}^{-1}$.
C
The height of the chimney is $590 \mathrm{~m}$.
D
The density of the gas at the upper end is $0.05 \mathrm{~kg} \mathrm{~m}^{-3}$.
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