1

JEE Advanced 2023 Paper 2 Online

Numerical

+4

-0

An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius $0.1 \mathrm{~mm}$ is dipped vertically into the liquid through the airtight piston hole, as shown in the figure. The air in the container is isothermally compressed from its original volume $V_0$ to $\frac{100}{101} V_0$ with the movable piston. Considering air as an ideal gas, the height $(h)$ of the liquid column in the capillary above the liquid level in $\mathrm{cm}$ is _______.

[Given: Surface tension of the liquid is $0.075 \mathrm{~N} \mathrm{~m}^{-1}$, atmospheric pressure is $10^5 \mathrm{~N} \mathrm{~m}^{-2}$, acceleration due to gravity $(\mathrm{g})$ is $10 \mathrm{~m} \mathrm{~s}^{-2}$, density of the liquid is $10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ and contact angle of capillary surface with the liquid is zero]

[Given: Surface tension of the liquid is $0.075 \mathrm{~N} \mathrm{~m}^{-1}$, atmospheric pressure is $10^5 \mathrm{~N} \mathrm{~m}^{-2}$, acceleration due to gravity $(\mathrm{g})$ is $10 \mathrm{~m} \mathrm{~s}^{-2}$, density of the liquid is $10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ and contact angle of capillary surface with the liquid is zero]

Your input ____

2

JEE Advanced 2020 Paper 2 Offline

Numerical

+3

-1

A train with cross-sectional area S

p

_{t}is moving with speed vt inside a long tunnel of cross-sectional area S_{0}(S_{0}= 4S_{t}). Assume that almost all the air (density $$\rho $$) in front of the train flows back between its sides and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be p_{0}. If the pressure in the region between the sides of the train and the tunnel walls is p, thenp

_{0}- p = $${7 \over {2N}}\rho v_t^2$$. The value of 𝑁 is ________.Your input ____

3

JEE Advanced 2020 Paper 2 Offline

Numerical

+3

-1

A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total
mass is 480 kg. Its effective volume giving the balloon its buoyancy is V. The balloon is floating at
an equilibrium height of 100 m. When N number of sandbags are thrown out, the balloon rises to a
new equilibrium height close to 150 m with its volume V remaining unchanged. If the variation of
the density of air with height h from the ground is

$$\rho \left( h \right) = {\rho _0}{e^{ - {h \over {{h_0}}}}}$$, where $$\rho $$

$$\rho \left( h \right) = {\rho _0}{e^{ - {h \over {{h_0}}}}}$$, where $$\rho $$

_{0}= 1.25 kg m^{−3}and h_{0}= 6000 m, the value of N is _________.Your input ____

4

JEE Advanced 2020 Paper 2 Offline

Numerical

+4

-0

A cubical solid aluminium (bulk modulus = $$ - V{{dP} \over {dV}} = 70GPa$$) block has an edge length of 1 m on the surface of the earth. It is kept on the floor of a 5 km deep ocean. Taking the average density of water and the acceleration due to gravity to be 10

^{3}kg m^{-3}and 10 ms^{-2}, respectively, the change in the edge length of the block in mm is _______.Your input ____

Questions Asked from Properties of Matter (Numerical)

Number in Brackets after Paper Indicates No. of Questions

JEE Advanced Subjects

Physics

Mechanics

Units & Measurements
Motion
Laws of Motion
Work Power & Energy
Impulse & Momentum
Rotational Motion
Properties of Matter
Heat and Thermodynamics
Simple Harmonic Motion
Waves
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Modern Physics

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Physical Chemistry

Some Basic Concepts of Chemistry
Structure of Atom
Redox Reactions
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Inorganic Chemistry

Periodic Table & Periodicity
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Quadratic Equation and Inequalities
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Trigonometry

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Calculus