JEE (Main + Advanced) Exam Question Paper

A uranium nucleus within a stationary train emits an alpha particle. A passenger measures the separation between the alpha particle and recoiling nucleus as x after time t. If the train moves at a constant velocity v, what separation will the passenger observe after the same time t?

Two identical spherical masses are positioned at a certain distance. What happens to the potential energy as one mass, m, is moved from the surface of one sphere to the surface of the other?

A uniform ring of mass m and radius a, and a sphere of mass M and radius a are released in free space. Considering only gravitational forces, what is the acceleration of the ring at the moment when the center of sphere and the center of the ring are $\sqrt{3}a$ apart?

A car travels on a road with regularly spaced small depressions every 8.0 meters. After four 80 kg passengers get in, the car lowers by 1.6 cm. At what speed might the car travel for the ride to become very uncomfortable?

Three tuning forks produce beats in the audible range. Forks B and C produce 7 Hz beats, A and C produce 8 Hz beats. If the frequency of B is 6% higher than that of A, what is the frequency of tuning fork C?

Two identical thin nichrome wires are fit into the side walls of communicating vertical vessels with cross-sectional areas S and 3S. An ideal battery with voltage U is connected to the lower ends of the wires. The vessels are filled to 50 cm and sealed with conductive pistons. An ammeter connects the pistons. Adding a 1 kg weight on the small piston results in a current $l_1 = 2.31$ A. Adding 3 such weights on the large piston results in a current $l_2 = 2.1$ A. What is true about this setup?

Three tigers begin to move simultaneously on a horizontal plane with constant speeds. The first tiger moves toward the second, the second toward the third, and the third toward the first. Initially, they form a right triangle with legs of length L. The first tiger's speed is v, and the speeds of the second and third tigers, $v_2$ and $v_3$, maintain constant angles in the tiger triangle. How long is it until the tigers meet?

As shown, a plano-convex lens with refractive index n is placed in air. The aperture radius is R. Point F is on the principal optical axis, where OF = f. If parallel light is incident along the principal optical axis, all light rays converge at point F. What is true about this lens?

An ice hemisphere of radius R and refractive index n sits on a warm flat table, melting slowly. The rate of heat transfer is proportional to the contact area. Complete melting occurs in time $T_o$. A laser beam shines vertically at a distance of R/2 from the axis of symmetry. Determine features of what happens.

A metallic rod of mass m and length L slides frictionlessly on two perpendicular wires, in a horizontal plane. A magnetic field, B, is perpendicular to the plane. The wires have negligible resistance compared to the rod, which has resistance R. The rod starts along one wire, with one end at the junction. An initial angular speed $\omega$ is imparted such that the rod slides until it aligns with the other wire, coming to rest. The value of $\omega$ is $\frac{3\pi B^2 L^2}{a m R}$. What is the value of 'a' (neglecting inductance)?

Two metal blocks with heat capacities $C_1 = 3$ J/K and $C_2 = 6$ J/K are connected by a rod of length l, cross-sectional area S, and thermal conductivity K. The system is thermally insulated. At t = 0, the temperature difference is $(\Delta T)_0$. If $\frac{\Delta T}{\Delta T_0} = e^{- \alpha t}$, what is $\alpha$, heat capacity of the rod is neglectable?

A sphere of mass m falls on three hemispheres symmetrically from height h. Each hemisphere has mass m/2 and radius R. Neglecting rebound, if the sphere stops after the collision, calculate the ratio of KE of the sphere before collision to the KE of each hemisphere after the collision. What mechanics are involved?

A syringe with cross-section $5 cm^2$ is filled to $20 cm^3$ with water. Its 90g piston moves upward at a constant rate, expelling water through a hole of $1 mm^2$ at 2 m/s. What is the work done by the agent? Friction can be ignored where g = 10 m/s².

A ring has a positive charge with constant density, inside it is a positive charge Q. What is $\sigma$, given an electric field cancels out?

Potential energy is approximated by mgh. We know the expression used isn't very close, so how wrong are we willing to mischaracterize this?

A uniform plank of mass m is on a solid cylinder in static equilibrium. What variables affect the plank and its oscillations?

A system contains two electrical situations. Which variables accurately characterize the different electrical setups?

Which of the following pairs both show stereo and structural isomerism?

Which of the following is not a disproportionation reaction?

The rate of effusion of two gases 'A' and 'B' under identical conditions of temperature and pressure are in the ratio of 2:1. What is th ratio of RMS velocity of their molecules if temperature of A & B are in ratio 2:1?

Consider the reaction sequence starting with a hydrocarbon A \rightarrow B \rightarrow C \rightarrow D + E, what structural feature is contained in A?

Starting With a benzene reactant, what nitrogen-containing structure has been added?

How does Thermal stability effect properties in specific materials?

Homolytic cleavage changes various properties. How can you distinguish how this happens?

Which of the following are correct at 298K?

Two products P1 from Hg(OAc)2 with H2O and NaBH4 and P2 from B2H6 with H2O2 with NaOH have been formed via reaction. What can you identify from their attributes?

What are some common things that certain materials have that cannot make f subshell?

A reaction involves CrI3 reacting with H2O2 in the presence of NaOH. What is it about, and what should you consider and look for?

Iodoform processes, what makes them happen?

If pKa values for protonated Lysine are pKa₁ = 2.18 ; pKa2 = 8.95 ; pKa3 = 10.79, then calculate vlue of the isoelectric point, what should we consider about the acid?

What are some typical ways we can find when one Carbon has started to bond with another? The reaction will create different behavior

For section on maximum electrons in orbitals... what principle are we considering?

What property affects how one element exists from crystal structure to crystal structure

For Column I and Column II where data is based on Schrondinger Wave model. How do we relate the systems, and what properties play into it?

Consider three sets A, B, and C. Determine probability product from one and sum from other two is prime number.

Two non-zero vector create 3x - 2y + z = 1 for co-terminous setup. What are we ultimately dealing with?

Consider potential expression for h which helps understand range of A, how is this value of range identified?

For the function what constraints or properties can we ensure?

H & P create tangent that touches hyperbola. What should guide and ensure which statement and property to identify?

Given that max has created certain condition and equation. What is meant to be derived?

4- |x| is maximum. We derive how the tangencies change, and tangent length that follows.

For 3cosx how does this guide

Derive and work value and understand functional relationship from the property