1

JEE Advanced 2022 Paper 1 Online

Numerical

+3

-0

Two spherical stars $A$ and $B$ have densities $\rho_{A}$ and $\rho_{B}$, respectively. $A$ and $B$ have the same radius, and their masses $M_{A}$ and $M_{B}$ are related by $M_{B}=2 M_{A}$. Due to an interaction process, star $A$ loses some of its mass, so that its radius is halved, while its spherical shape is retained, and its density remains $\rho_{A}$. The entire mass lost by $A$ is deposited as a thick spherical shell on $B$ with the density of the shell being $\rho_{A}$. If $v_{A}$ and $v_{B}$ are the escape velocities from $A$ and $B$ after the interaction process, the ratio $\frac{v_{B}}{v_{A}}=\sqrt{\frac{10 n}{15^{1 / 3}}}$. The value of $n$ is __________ .

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2

JEE Advanced 2021 Paper 2 Online

Numerical

+4

-0

The distance between two stars of masses 3M

_{S}and 6M_{S}is 9R. Here R is the mean distance between the centers of the Earth and the Sun, and M_{S}is the mass of the Sun. The two stars orbit around their common center of mass in circular orbits with period nT, where T is the period of Earth's revolution around the Sun. The value of n is __________.Your input ____

3

JEE Advanced 2015 Paper 2 Offline

Numerical

+4

-0

A large spherical mass M is fixed at one position and two identical masses m are kept on a line passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of length l and this assembly is free to move along the line connecting them.

All three masses interact only through their mutual gravitational interaction. When the point mass nearer to M is at a distance r = 3l from M the tension in the rod is zero for m = $$k\left( {{M \over {288}}} \right)$$. The value of k is

All three masses interact only through their mutual gravitational interaction. When the point mass nearer to M is at a distance r = 3l from M the tension in the rod is zero for m = $$k\left( {{M \over {288}}} \right)$$. The value of k is

Your input ____

4

JEE Advanced 2015 Paper 1 Offline

Numerical

+4

-0

A bullet is fired vertically upwards with velocity v from the surface of a spherical planet. When it reaches
its maximum height, its acceleration due to the planet’s gravity is $${\left( {{1 \over 4}} \right)^{th}}$$ of its value at the surface of the
planet. If the escape velocity from the planet is $${v_{esc}} = v\sqrt N $$, then the value of N is (ignore energy loss due
to atmosphere)

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Questions Asked from Gravitation (Numerical)

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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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Optics

Modern Physics

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Some Basic Concepts of Chemistry
Structure of Atom
Redox Reactions
Gaseous State
Equilibrium
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States of Matter
Thermodynamics
Chemical Kinetics and Nuclear Chemistry
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Inorganic Chemistry

Periodic Table & Periodicity
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d and f Block Elements
Coordination Compounds
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Organic Chemistry

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Vector Algebra and 3D Geometry
Statistics
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Trigonometry

Coordinate Geometry

Calculus