JEE Advanced Previous Year Questions (2018 - 2023): Simple Harmonic Motion | Physics for JEE Main & Advanced PDF Download

2023

So, we can calculate the focal length :

Next, we need to calculate the error in the determination of the focal length. For that, we find the differential of the lens formula :
Then, the derivative of the equation gives us the change in the focal length (df) in terms of the changes in the object distance (du) and the image distance (dv): 

For maximum error, we get :

This equation tells us how errors in (u) and v propagate to an error in f. Now, when you compute the relative error in the focal length, you get :

Plugging in your values of  u = 10 cm,  du =0.1 cm,  v = 20 cm,  dv = 0.2 cm, and  f = 20/3 cm, you indeed get: 

So, the error in the focal length of the lens is indeed 1% (i.e., n = 1).

2022

Q1: In a particular system of units, a physical quantity can be expressed in terms of the electric charge e, electron mass m_e, Planck's constant ℎ, and Coulomb's constant , where ε₀ is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is . The value of α + β + γ + δ is______.     [JEE Advanced 2022 Paper 2]
Ans: 

Compare :

On Solving:

2019

∴ f = 20 cm Also,  

= 50/36
= 1.38 and 1.39 (both)

2018

We know that

where W is weight or load = mg = 1.2 × 10 = 12 kg m s⁻², Y is Young's modulus = 2 × 10¹¹ N m⁻², L is length of wire with load = 1.0 m, A is area of steel wire
=

Therefore,

Now, least count of vernier scale =

Therefore, Vernier reading =
Vernier reading = 0.3 mm / 0.1 mm = 3
Therefore, 3^rd vernier scale division coincides with the main scale division.