JEE Main 2023: Top 200 Questions

• A list of top 200 selected questions for JEE Main 2023, covering January and April sessions, has been prepared.
• The list is compiled from a total of 720 questions.
• The question PDF link is available in the description box for download.
• Students should aim to solve all 200 questions within a maximum of 8 hours.
• The PDF's third page contains an index with chapter names, the number of questions per chapter, and corresponding page numbers.
• The PDF contains chapter-wise questions, totaling 200 questions.
• A significant number of questions are from Modern Physics and Current Electricity, with some from EMI.
• The PDF includes a fill-in-the-blank answer key for students to record answers.
• Official answer keys are provided in the final pages for cross-verification.
• Discussion videos are available to analyze incorrect answers.

Dimensional Analysis Example

• The velocity of light (c), universal gravitational constant (G), and Planck's constant (h) are chosen as fundamental quantities.
• The dimension of mass (M) in the new system is to be determined.
• M ∝ c^a * G^b * h^c, where a, b, and c are exponents to be found.
• Dimensions of speed of light: c = LT⁻¹
• Dimensions of gravitational constant: Derived from F = G(m₁m₂)/r², G = Fr²/m² = M⁻¹L³T⁻²
• Dimensions of Planck's constant derived from E = h*frequency: h = E/frequency = ML²T⁻¹
• After substituting these dimensions and comparing powers on both sides, one can solve for a, b, and c.
• Comparing powers of M, L, and T on both sides gives three equations:
  • For M: -b + c = 1
  • For L: a + 3b + 2c = 0
  • For T: -a - 2b - c = 0
• Solving these equations yields a = 1/2, b = -1/2, c = 1/2.
• Therefore, the dimension of mass M is proportional to c^(1/2) * G^(-1/2) * h^(1/2).

Cross Product and Unit Vector

• The question involves finding the unit vector in the direction of p x q, given vectors p and q.
• First, calculate the cross product p x q using the determinant method:
  • p x q = | i j k | | 3√3 2 √3 2.5 | | 4 √3 2.5 |
• Calculate the components: i(2.5√3 - 2√3) - j(3 * 2.5 - 8) + k(3√3 * √3 - 4√3)
• Simplify to √3/2 i + 0.5 j - √3 k
• Calculate the magnitude: |p x q| = √((√3/2)² + (1/2)² + (-√3)²) = √((3/4) + (1/4) + 3) = √4 = 2
• Convert to unit vector by dividing by the magnitude resulting in (√3/4)i + (1/4)j - (√3/2)k
• After this identify the common factors and rewrite the expression in the required form by factoring out 1/4
• After factoring, identify the value for 'x' corresponding to the unit vector in the form given

Vernier Calipers and Error Analysis

• Refractive index (μ) is the ratio of real thickness (d) to apparent thickness (d'): μ = d / d'.
• Real thickness of the glass slab is 5.25 mm, and apparent depth is 5 mm so the refractive index will be 5.25/5 = 21/20
• The microscope has 20 divisions in 1 cm on the main scale; thus, 1 MSD = 1 cm / 20 = 0.05 cm = 0.5 mm.
• 50 Vernier scale divisions (VSD) match 49 main scale divisions (MSD); hence, 1 VSD = (49/50) MSD.
• Least count is 1 MSD - 1 VSD = 0.5 mm - (49/50) * 0.5 mm = 0.01 mm.
• Relative error in refractive index Δμ/μ = Δd/d + Δd'/d'
• Δd = Δd' = Least Count (LC) = 0.01 mm.
• Calculate Δμ/μ to find the value

Screw Gauge Calculations

• There are 100 divisions on the circular scale and the main scale moves 5 mm on a complete rotation of the circular scale.
• Pitch = 5 mm, Number of circular scale divisions = 100.
• Least Count (LC) = Pitch / Number of circular scale divisions = 5 mm / 100 = 0.05 mm.
• The zero of the scale lies six divisions below the line of graduation, indicating a positive zero error.
• Error = 6 * LC = 6 * 0.05 mm = 0.3 mm
• Four linear scale divisions are visible with 46th division of circular scale coinciding
• Reading = (4 * 5) + (46*.05) – Error
• Simplify and determine the required answer

Resistance and Percentage Error

• Parallel resistance equation: 1/R = 1/R₁ + 1/R₂
• Differentiate to find error propagation: ΔR/R² = ΔR₁/R₁² + ΔR₂/R₂²
• Solve for ΔR: ΔR = R²(ΔR₁/R₁² + ΔR₂/R₂²)
• Percentage error is (ΔR/R) * 100.

Positive Zero Error

• List count is 0.01 cm and to calculate the zero error multiply error with the list count.
• Find total reading by adding the zero error and the main reading
• Subtract the zero reading to get reading for further calculations

Pressure, Volume, and Energy

• Dimensional analysis to find equivalent physical quantity for ratio a/b Given x = (a/y^2) and with x as pressure
• Dimension of a/b equals dimension x * y which equals Pressure Volume
• Energy dimension is equivalent to the Pressure multiply Volume, that will determine the equality

Wave Speed and Dimensional Analysis

• Wave speed related to wavelength, gravitational constant, and density
• Dimensional Formula for velocity = [LT^-1]
• Equate to the dimensions of right-hand side parameters to get equation
• With these equations find dimensions of each parameter

Breaking Distance

• Find retardation using formula (v^2 = u^2 +2as) for the situation when brakes are applied first at mentioned distance.
• Use this retardation to find how much distance the train can travel the final distance (when brakes are applied at half of mentioned distance)

Average Acceleration/ Error Calculation (Conceptual)

• First find the entry Speed (v) using height. Just before the impact and after it.
• a = (change in velocity) / time
• Take appropriate sign convention to correctly find change it. If velocity down Is taken negative
• Change in velocity = Final velocity – Initial velocity, then (Entry) Velocity = -√2gh

Average Speed

• Let total distance covered be x.
• First half took 5ms. speed and other half speed is changing after = time T1 and T2. And using the given condition to relate these parameters and get

Graph Comprehension Tips

• Graphs represent information, so read them carefully.
• Consider each statement one at a time relative to graph to see if it's right/ wrong.
• Be weary of statements that use qualifying wording like ‘All’ or ‘None’
• Look for relative slopes in X – Y graphs (Velocity, Acceleration)

Projectile Motion

• In projectile motion, vertical displacement (h) is same at two different times (3s and 5s)
• Use H = ut -+ 1/2 at^2 to make required expression for the value u in this

Train Crossing Tunnels

• Total time calculated when the trains enter and leave the tunnel for calculations to happen correctly
• Express distance in a relative term and make the expression out of them.
• The time an observer Sees trains depends on the relative motion of the observer, when he/ She sits in other train to View

Inextensible Strings, Forces Equilibrium

• Identify force components and make relative expressions for the tension
• Force in strings (y) in both side = T * SIN(angle), as tension will cancel each others component.
• In (X) net force will (Tension – Force in Y from both strings will equalize)

Work Done Calculation

• F=2Cos(kx), Calculate Force in DX = F*DX AND THEN integrate both parameter to do so
• Limits need to apply in expression for value assessment

Time Derivative for Motion Involving Friction

• V= ut - friction, and finally V=u - μgt, V will end.
• Use work done/Energy theorem to equate parameters. V^2= U^2 -2aS

Spring Calculation

• Spring related question, so it's a MUST that final energy will become U.
• Use the formula to calculate the U and then use it further to equate with force

Momentum Conservation

• Momentum conservation requires that the mass M time speed V
• The speed equation and values need substituting appropriately and precisely.

Scrue and screw drivers

• All these questions require a little bit of conceptual understanding
• Make sure to know the definitions and terminology involved

Error Calculation and Combination

• Find the error parameter which are to be calculated from screw gauge and screw parameter and implement for result.
• Get values using given data.

Power & Constant Force

• Use power P definition = F. V. Also use velocity as intergral of F/ m
• Multiply terms vectorically to get final outcome

Tension / Equilibrium

• Find net force, then equate with Tension and finally evaluate

Circular Motion Numerical

• Tangental Accelaration = V * dv / Ds and then integrate
• Tangential acceleration will allow speed Vs function expression to get equated.

Constant power Application

• P=F . D And equate parameters from this expression and solve them accordingly

Elastic Potential Energy

• Elastic potential energy stored in a string is
• 1 / 2 * STRESS * STRAIN * VOLUME. Use value, put In it and calculated carefully.

Average Velocity - Conceptual

• Average VELOCITY of something over short is related parameter that needs addressing to find answer from

Momentum Conservation / Friction - Conceptual

• Momentum conservation principle: m1v1 = (M+m)V, find speed for common mass-speed post-sticking
• Use work theorem to establish further data

Spring Force and Displacement

• Force for Spring follows Hook's law: F = -kx.
• F is proportional to d / t vectorially, find relationship using this

Potential Energy

• Change in PE from top - bottom + KE need equating PE - Loss = GME / R^2
• Change in PE can then evaluate using formula in calculation.

Speed in Medium / Refractive Index

• Refractive index is always C/VM; use this approach with velocity

Collision

• Collision requires momentum relation, and it’s speed related with change velocity, mass

Power/Time derivative

• Deriving time based equations give the solution about the system behavior

SHM

• SHM (Simple Harmonic Motion) questions check how effectively can Use data Given To calculate Parameters and make expressions.
• Remember main equations involved

Angular SHM

• Angular momentum require equating and comparing expression and understand relation of velocity
• Torque = I Alpha can be used to prove Angular speed is in short range

Time Constant.

• Time constant questions are a must, the expression needs Remembering

Doppler Shift

• Apparent shift with changing observer is calculated accurately after equating frame based and then implementing

Solid Cylinder Rolling

• Solid cylinders have specific equations, carefully try solving it using conservation force theorem
• Concepts require some very basic vector skills.

Circular Motion / Angular Momentum

• Circular motion questions mostly depend on direction and how speed changes depending on direction and it’s component.

Collision / Relative Velocity, conceptual, approach

• Mostly depends/involves on direction and relative speed in expression, consider sign convention

Collisions and Trajectories

• Use KINEMATICS properly; equate all components for perfect solutions

Thermodynamics Laws

• Apply thermodynamic laws first for a perfect solution and accurate expressions
• Thermodynamic variable must be implemented for results

Carnot Engine

• Carnot Engine formulas, efficiency related formula are very basic and important to know for expression

Process Types ( Adiabatic )

• For the adiabatic process: TV^GAMMA, use to relate these parameter

RMS / Power factors ( with L & R )

• Power factors expressions and the way we equate RMS value are essential to understand for proper usage.
• This calculation requires many steps for proper evaluations. This concept, though small takes a significant memory and time.

Angular momentum

• Angular Momentum equal to MVR
• Carefully regard sign Convention

Graph reading / Data Analysis

• Check graph reading carefully for final conclusion
• Ensure perfect mapping of X and Y data. Don’t go for assumption

Wave theory

• Wave theory and SHM (Simple Harmonic) are important as there are so many small formulas

Fluid

• Fluid and viscosity related questions like the terminal velocity depend a lot what the surrounding are.
• There is a buoyant force and viscosity contributes in opposite direction

Poiseuille's Law

• Find variables, equate and calculate for find answers

Error In lens instrument and SHIFT concept

• Implement mirror related expressions to the surface
• A shift formula used mostly

Wave optics ( YDS, etc)

• Wave optics and formula involving wave parameter for effective solution with minimal mistakes
• YDS require knowing difference angles created, phase difference. Path length affects calculations and equate

Lens / Reflection ( Mix conceptual)

• First identify refraction reflection, which is playing virtual role before incident.
• Use this approach without having to memorize, however, it requires patience

Brewster angel

• Remember tangent of the Brewster angle must be ratio index relation, also remember angel is = 90 degree as well.
• Use all information for solving the questions

Average and Angular velocity

• Average speed Vs Tangential Component is another area of confusion, have conceptual knowledge for such situation

Work done

• Learn simple diagram for such kind of difficult questions

Viscosity

• Viscosity formula and value need substituting carefully; know the meaning

Gravity

• G force calculation requires knowing which body is under examination
• Also remember gravitational formulas regarding them

KVL and electric loop

• Apply all values and the loop formula; use the series relations well

Meter Instrument reading like Voltammeter/ Ameter

• Learn all conversions and value. Make basic circuit and you should be good to solve this
• Then implement conversion formula in calculations

Electromagnetic Radiation

• Relation between E . B= C^2 where C is component value.
• Directional formula understanding is needed

Logic circuit

• Logic circuit requires every AND/ OR gate understanding also De Morgan's laws are needed.
• Understand small parameters with them

EM WAVE

• Find expression with derivatives, and solve accordingly.
• Em wave power transfer, field component relation, and values given help for a directional graph related approach

EM related question

• EM, electrodynamics related mostly has formula to remember; few concepts are very essential

AC CURRENT

• AC series formulas and component is very essential, must know them before attempting
• Take down data and use formulas as well

Logic Gate Analysis and Boolean Algebra Simplification

• Diagram represents a combination of logic gates with inputs A and B, leading to an output Y.
• The initial expression derived from the gate combination is (A NAND B) NAND B, equivalent to ((A·B)')'.B)'.
• De Morgan's laws are applied to simplify the Boolean expression.
• Applying De Morgan's Law: (A•B)' = A' + B'.
• ((A·B)')'.B)' simplifies to (A' + B') + B.
• Further simplification yields A' + A'·B + B'·B, where B'·B equals zero.
• The expression simplifies to A'·B, matching the behavior of an XOR gate.
• XOR gate truth table: Output is 1 only when inputs are different (0,1 or 1,0) and 0 when inputs are the same.

Circuit Analysis and Logic Gate Equivalence

• Circuit involves switches A and B connected to a bulb, with a 5V potential and a grounded point.
• "1" means switch is closed (on), "0" means switch is open, Y represents bulb's state.
• If both switches are open (0,0), the bulb lights up (Y=1) due to complete circuit.
• If A is closed (1) and B is open (0), current bypasses the bulb through A switch with no resistance, bulb doesn't light (Y=0)
• If A is open (0) and B is closed (1), current bypasses the bulb through B switch, bulb doesn't light (Y=0).
• If both A and B are closed (1,1), current continues to bypass the bulb, bulb doesn't light (Y=0).
• The truth table represents a NOR gate: output is 1 only when both inputs are 0, and 0 otherwise.

Logic Gate Combination and Output Waveform

• The logic gate combination is identified as an OR gate.
• Combination includes NAND and NOT gates.
• Boolean algebra is used to simplify the gates structure.
• DeMorgan's Theorem simplifies to A + B (an OR gate).
• Given the input signal A is '0' then signal B equals '0', the output is zero
• If A = 0 and B = 1, the output is 1 (due to OR gate logic).
• If A = 1 and B = 0, the output is again 1.
• Lastly, if A = 1 and B = 1, the output remains at 1.
• The resulting waveform matches the behavior of an OR gate.

Diode Circuit and Current Relationships

• Diodes have a forward bias resistance of 25 ohms, reverse bias assumed as infinite resistance.
• Positive terminal indicates forward biasing, and negative shows reverse biasing.
• Reverse-biased diode is an open circuit.
• The reverse-biased diode acts as an infinite resistance.
• Diodes D2 and D4 are forward biased and replaced by 25-ohm resistors.
• i2 and i4 branch from i1: same voltage across both branches, currents are the same
• Current relationship: i1 = i2 / 2 and i1 = i4 / 2.
• Given that i2 = i1 / 2, therefore i1 = 2 * i2.

Hydrogen Atom Energy Levels and Angular Momentum Transitions

• Hydrogen atom absorbs 12.75 eV energy while in ground state (n=1).
• Hydrogen atom moves to an excited state.
• The amount of energy absorbed dictates the final state.
• Hydrogen atom energy transition is n=1 -> n=4, since the energy difference is 12.75 eV.
• Angular momentum in the excited state is given by L= nh/2π.
• With n=4, calculate L = (4/2) * h/π.
• Further simplification results in the value x is linked to the calculation of momentum.

Nuclear Fission and Energy Release Calculation

• Fission of a single nucleus of 240X releases 200 MeV of energy.
• Given 120 grams of substance, calculate the number of atoms undergoing fusion.
• Number of moles is mass / atomic mass.
• The mass comes out to be one-half a mole
• Number of atoms is one-half a mole multiplied by the Avogadro number (6 x 10^23).
• The released energy is the number of atoms multiplied by the energy released per atom.
• Final calculation yields 6 x 10^25 MeV of total energy released.

Wavelength Calculation in Electron Transitions

• Wavelength emitted is λ0 when an electron jumps from the 2nd excited state (n=3) to the 1st excited state (n=2.)
• 1/λ0 = R·z^2 (1/4 - 1/9), where R is the Rydberg constant.
• Simplifies to 1/λ0 = R·z^2 · 5/36.
• When the electron jumps from the 3rd excited state (n=4) to the 2nd orbit (n=2), the wavelength emitted is a different amount
• Calculate 1/λ1 = R·z^2 (1/4 - 1/16).
• Lambda equals R*z^2 multiplied by 3 divided by 16
• By dividing the two equations wavelength is calculated.
• The value x, when solving resulting equations, equals 27.

Energy Level Transitions and Photon Emission

• Atom energy levels shown in a diagram.
• Emission of a photon with a wavelength of 124.1 nm.
• Use formula E = 1243/λ (in nm) to find energy change in eV.
• Divided by 124.1 nm yields an approximate 10 eV transition.
• The D transition (from -4 eV to -14 eV) results in emission of a photon

Nuclear Disintegration and Velocity Ratio

• Original nucleus breaks into two smaller parts with velocity ratios of 3:2.
• If velocity of part 1 is 3v, velocity of part 2 is 2v (opposite directions to conserve momentum).
• Magnitudes need to be equal i.e m1(3v)= m2(2v)
• Resulting equation: 3m1= 2m2.
• Nuclear density is constant, and thus, mass is proportional to volume.
• Thus Mass is equal to 4/3piradius cubed.
• Size means radius ratio calculation
• Given the initial mass relationship and density equation calculate to find radius and the value equals 2.

Photoelectric Emission and Threshold Wavelength

• Photoelectric emission occurs when the incident energy exceeds the work function.
• The photoelectric emission will not happen when the threshold is not met.
• Given the threshold wavelength of 5500 angstroms the photoelectric emission can be calculated
• Relate incident wavelength to threshold wavelength: λ < λth.
• UV has 400 nm to 1 nm, or 4000 Å to 10 Å.
• The threshold wavelength of ultraviolet must then be less than the incident wavelength
• Infrared range stretches over vast range.
• Ultraviolet radiation will result in emission from the material when illuminated.

Radioactive Decay and Half-Life

• Substance A: atomic mass number 16, half-life of 1 day.
• Substance B: atomic mass number 32, half-life of half a day.
• Both A and B undergo radioactivity simultaneously, starting with 320g each.
• Initial state is defined as a total number of atoms.
• The moles multiplied by Avogadro's number gives you number of atoms.
• a decays in one day and b decays in a half day.
• Given two days after, the same rate is used with number of atoms to calculate new amounts and the new total combined atoms is approximately 3x10^24.

Small Object Absorbing Light Pulse

• A small object at rest absorbs a light pulse.
• Light pulse parameters are given.
• Full absorption occurs.
• Given Force = Power / Speed of light, use value of power multiplied by time, divided speed.
• Use equation momentum change equals force times the time.
• After calculations, the final calculated momentum equals 2x10^-11.

Hemispherical Surface and Light Force

• Point source placed at center of a curvature, with hemispherical surface and surface is reflective
• Surface will have a force on light
• To find value of force, find light component
• Find force across area and element to a surface area.
• The end result is the vertical point which is equal to one
• Total for acting when one integrates, with equation to describe all forces
• Intesity = power by area also calculated
• Equation simplified results is equal to the power divided by two times the speed
• Substituting the givens.

Radioactive Nuclei Decay Processes and Half-Life

• Radioactive nucleus decays at two different rates.
• Process 1 half-life 5 minutes and Process 2 half life 30 seconds.
• Overall constant needs to be determined
• Overall rate is equal to each amount added.
• Log functions are used.
• Time is calculated using the rates.

Photoelectric Effect on Metals and Work Functions

• Metals A and B are exposed to radiation.
• Wave length is given.
• The work function defines metal a and metal b.
• The same formula is the kinetic energy is related to that value of frequency
• The metal with the higher energy will emit more particles

Bohr Atom Radius Proportionality

• Radius for the electron in the 2nd orbit for Bohr equals R
• Third orbit radius is determined via value
• A formula is used along with calculating the ratio

Energy Levels in a Hydrogen Atom and Shortest Wavelength

• Hydrogen energy with ladder diagram
• Find the amount on one transition
• Energy is related with an inverse value to wavelength
• Shortest wavelength must be determined

Circular Orbit Movement with Potential Energy

• Movement follows a constant relation
• Radius formula of the particle can be calculated
• The potential energy equation is also derived.

Nuclear Breakup and Binding Energies

• Nucleus with mass one has a binding energy
• Nucleus breaks in two
• Each Nuclei binding energy.
• Total energy is then calculated

De Broglie Wavelength and Temperature

• De Broglie Wavelength dependence on temperature is evaluated
• A value is calculated
• The Temperature formula is then used

Variation of Stopping Potential

• Variation of stopping potential follows frequency
• Stopping Potential is v
• Then kinetic energy is calculates
• Then stopping potential is derived

Threshold Wavelength Calculation

• The question is a threshold energy based question
• Two situations are provided
• The corresponding equations are then equated for a solution through calculation

Ratio of Decay Constants Calculation

• The ratio of two decay amount is needed
• Average halfife mean given as such and need to equated