NEET 2023 Question Paper Step-by-Step Solutions

An inductor stores energy in its magnetic field when a current flows through it. The work done in establishing current I against the self-induced back emf is obtained by integrating dW = L i di from 0 to I:

Substitute the given numerical parameters into the expression with appropriate SI conversion:

Convert Joules into microjoules (μJ) using 1 μJ = 10⁻⁶ J:

The activity A of a radioactive sample at time t is related to its initial activity A₀ through the number of elapsed half-lives n:

Given that the activity drops to 1/16th of its initial value:

Multiply the number of half-lives by the duration of one half-life:

Gas law relations must strictly be calculated in Kelvin (absolute temperature):

Root mean square velocity of an ideal gas molecule of molar mass M is given by:

The velocity increases BY 3 times its initial value, which makes the new velocity 4 times the original:

Square the velocity ratio to find the final absolute temperature, then convert back to Celsius:

Convert back to degrees Celsius:

An open pipe of length L has antinodes at both open ends and a displacement node at the center. The pipe length accommodates half a wavelength:

A closed pipe of length L has a displacement node at the closed end and an antinode at the open end. The pipe length accommodates one-quarter of a wavelength:

Divide the two fundamental frequencies for pipes of identical length:

Resonance in a series LCR circuit occurs when inductive reactance equals capacitive reactance, causing impedance to become purely resistive (Z = R):

Substitute inductance L = 10 × 10⁻³ H and capacitance C = 10⁻⁶ F:

Convert angular frequency ω₀ (in rad/s) to cyclic frequency f₀ (in Hz):

The wavelength λ of radiation emitted during an electronic transition from state n₂ to state n₁ in hydrogen is given by the Rydberg formula:

The shortest wavelength corresponds to the maximum energy transition, which occurs from n₂ = ∞ to the ground level of that series (n₁):

For the Balmer series, n₁ = 2. For the Brackett series, n₁ = 4:

Substitute 1/R into the expression for Brackett series limit:

Angular acceleration α⃗ is defined as the time rate of change of angular velocity ω⃗:

Angular velocity ω⃗ is an axial vector perpendicular to the orbital plane of rotation, pointing along the axis of rotation by the right-hand screw rule. Since α⃗ is the derivative of ω⃗ with respect to scalar time t, it must be parallel (if speeding up) or antiparallel (if slowing down) to ω⃗:

In circular motion, the linear acceleration consists of centripetal acceleration (radially inwards) and tangential acceleration (tangent to the circle), whereas angular acceleration governs rotational rate and is purely axial:

The opposition offered by a capacitor to alternating current is capacitive reactance X_C:

When the operating frequency f decreases, the capacitive reactance X_C increases inversely:

The alternating current in the circuit (conduction current i_c) is determined by Ohm's law in AC circuits:

Inside the capacitor plates, the changing electric flux generates displacement current i_d, which identically equals the conduction current i_c at every instant:

Since f decreases, i_d decreases proportionally:

In physics measurements, experimental errors are broadly categorized into Systematic Errors and Random Errors:

According to the standard NCERT physics syllabus, random errors are errors that occur irregularly and are random with respect to sign and size. They arise due to unpredictable fluctuations in experimental conditions such as voltage supply variations, temperature fluctuations, and mechanical vibrations.

Instrumental errors arise from zero error or calibration defects; Personal errors arise from human bias or parallax; Least count errors are associated with instrument resolution. None of these arise from unpredictable ambient fluctuations.

When the galvanometer G shows zero deflection, the current flowing through its branch is zero (i_g = 0). By Kirchhoff's Current Law at the junction, the secondary branch is completely isolated in terms of current flow:

All current from the 10 V source circulates exclusively through the series combination of 400 Ω and R:

The potential drop across resistor R is given by Ohm's law and must balance the 2 V battery:

Solve the linear equation for resistance R:

The work done against the restoring spring force F = -kx in stretching a spring of spring constant k by displacement x is stored as elastic potential energy:

Write expressions for initial state x₁ = 2 cm and final state x₂ = 8 cm:

Take the ratio of final to initial potential energy:

Average speed is fundamentally defined as total distance travelled divided by total time elapsed:

Let the total distance be 2d. Each half of the journey has distance d:

Add the two time intervals together using a common denominator:

Divide total distance 2d by total time:

A photovoltaic device (solar cell) operates on the principle of the photovoltaic effect. When incident photons of energy hν > E_g strike the junction, electron-hole pairs are generated in the depletion region. The built-in junction electric field separates electrons to the n-side and holes to the p-side, establishing a photo-voltage across an external load without any external bias:

A Zener diode is a special-purpose semiconductor diode that is heavily doped on both p and n sides, resulting in a very thin depletion layer (~10⁻⁶ m) and intense junction electric field (~5 × 10⁶ V/m). It is specifically designed to operate under reverse bias in the Zener breakdown region, where the voltage across it remains virtually constant despite sharp variations in current, serving as a voltage stabilizer:

Since both Statement I and Statement II represent foundational, canonical principles of semiconductor devices, Option (2) is the uniquely correct choice.

Resolve the initial velocity vector u along the vertical y-axis:

At the maximum height H, the vertical component of velocity momentarily drops to zero (v_y = 0). Applying the third equation of kinematics for vertical motion:

Substitute the given values into the formula with g = 9.8 m/s²:

Let the neutral point P be located at distance x from mass m and (R - x) from mass 9m along the line joining them. At P, the net gravitational field is zero:

Taking the square root on both sides (since distance must lie between the masses):

The distances from the respective masses are:

Gravitational potential is a scalar quantity. The total potential V at point P is the algebraic sum of the potentials due to m and 9m:

An electron of charge e accelerated from rest through potential difference V acquires kinetic energy:

In continuous X-ray production (Bremsstrahlung), the minimum wavelength λ_min corresponds to the maximum photon energy, occurring when the entire kinetic energy of the electron is transferred to a single photon in a single collision:

Solve for λ_min in terms of potential difference V:

A Venturi-meter is a device used for measuring the speed of flow of an incompressible fluid in a pipe. It consists of a broad entrance tube of area A₁, a constricted throat of area A₂, and a manometer to record the pressure difference between the two sections.

By the equation of continuity, as area decreases at the throat (A₂ < A₁), the fluid velocity increases (v₂ > v₁):

For horizontal streamline flow, Bernoulli's principle states that the total mechanical energy per unit volume is constant:

Thus, the functioning of a Venturi-meter is fundamentally based on Bernoulli's principle.

Standard 4-band carbon resistors encode resistance as R = (AB × 10^C ± D%) Ω, where A and B are the first two significant figures, C is the decimal multiplier, and D is the tolerance percentage:

Comparing with the standard colour-code format:

Using the canonical mnemonic "B B R O Y of Great Britain has Very Good Wife":

Unlike a solid liquid drop which has only one outer surface, a soap bubble has a hollow spherical air pocket inside and air outside, creating two distinct liquid-air interfaces of virtually identical surface area:

The work done W required to form the bubble from a soap solution is equal to the surface energy created:

Substitute radius r = 2 × 10⁻² m and surface tension T = 0.03 N/m:

Using π ≈ 3.1416:

The output of a full-wave rectifier consisting of two p-n junction diodes and a center-tapped transformer is unidirectional but pulsates periodically with twice the input frequency (ripple frequency = 2f). This output consists of a desired DC component superimposed with unwanted AC ripple harmonics.

To obtain a steady DC voltage without fluctuations, a filter circuit is employed. A capacitor filter is connected in parallel with the load resistance R_L. Its capacitive reactance is frequency-dependent:

For the high-frequency AC ripple components, X_C is very low, providing an easy low-impedance bypass path. For DC (f = 0), X_C → ∞, meaning zero DC current leaks through the capacitor, forcing steady DC voltage across the load resistance R_L:

Gauss's law for magnetism is one of the four fundamental Maxwell equations governing classical electrodynamics. It states that the net magnetic flux Φ_B through any closed surface S is identically zero:

In electrostatics, Gauss's law allows net flux because isolated positive and negative charges exist (∮ E · dA = q_enclosed / ε₀). In magnetism, magnetic poles always occur in equal and opposite dipoles (North and South). The net magnetic charge enclosed by any closed volume is always zero:

Magnetic field lines form continuous closed loops without beginning or end. Every field line that enters a closed surface must necessarily emerge from it, ensuring total incoming flux equals total outgoing flux.

According to Einstein's quantum theory of the photoelectric effect, an incident photon transfers its entire energy E = hν to a single conduction electron. Photoelectric emission can occur only if this energy exceeds the minimum energy required to liberate the electron from the metal surface (the work function Φ₀):

Compare the incident radiation energy E = 2.20 eV with the work functions of all three photosensitive alkali metals:

Only Caesium satisfies the condition E ≥ Φ₀, meaning photoelectrons are emitted from the Caesium surface only.

By Newton's second law of motion, the net external force F⃗ acting on the player is directly proportional to the rate of change of linear momentum, and therefore points in the direction of the change in velocity vector Δv⃗:

Let the positive x-axis represent East (+î), positive y-axis represent North (+ĵ), and negative y-axis represent South (-ĵ). With initial speed v:

Subtract the initial velocity vector from the final velocity vector:

The vector v î + v ĵ has equal positive components along East and North, forming an angle of 45° between East and North:

Inspect the right branch of the circuit: two identical capacitors of capacitance 3 μF are connected in parallel across the same potential nodes. The equivalent capacitance of a parallel combination is the direct sum:

The parallel block C_p = 6 μF is connected in series with the first capacitor C_1 = 3 μF between terminals A and B. The equivalent series capacitance is given by the reciprocal formula:

Inverting yields the net equivalent capacitance:

When an electric dipole of dipole moment p⃗ = q(2a⃗) is placed in a uniform electric field E⃗ at an angle θ, it experiences a restoring torque given by the vector cross product:

Substitute torque τ = 4 N m, length 2a = 2 × 10⁻² m, electric field E = 2 × 10⁵ N/C, and angle θ = 30°:

Evaluate the trigonometric and metric terms using sin 30° = 1/2:

Solve for charge q and express in millicoulombs (1 mC = 10⁻³ C):

The electric flux Φ through a closed Gaussian surface S is geometrically defined as the net count of electric field lines penetrating the surface. Inward-directed lines contribute negative flux, while outward-directed lines contribute positive flux:

The problem states that the number of field lines entering the closed surface equals the number of field lines leaving it. Therefore:

According to Gauss’s Law of electrostatics, the net electric flux through any closed Gaussian surface in vacuum is directly proportional to the total net charge q_enc enclosed within the surface:

Equating the net flux to zero yields:

In Fraunhofer single-slit diffraction produced by a slit of width a, the condition for the first diffraction minimum is given by a sin θ = λ. For small diffraction angles (sin θ ≈ θ in radians), the angular width of the central maximum is 2θ = 2λ/a, and the angular separation of adjacent fringes is:

Linear fringe separation on the screen is y = D θ = λ D / a, which is directly proportional to D. However, the ANGULAR separation θ depends strictly on the ratio λ/a and is completely independent of the distance D between the slit plane and the screen:

From the governing formula θ = λ / a, the angular separation is directly proportional to the wavelength of light used:

Statement I correctly asserts that angular separation does not change when the screen is moved away. Statement II incorrectly claims that angular separation decreases with increasing wavelength (it actually increases). Therefore, Statement I is true and Statement II is false.

The given circuit is a single closed loop ABCDA. All components (the 2 Ω resistor, the 10 V cell, junction E, the 5 V cell, the 1 Ω resistor, and the 7 Ω resistor) are connected in series.

The positive terminal of the 10 V source faces towards E (pushing current from left to right, i.e., from A towards B), while the 5 V source faces into E with its positive terminal pushing opposite. Because they are in opposition, the net driving EMF is the difference:

By Ohm’s Law / Kirchhoff’s Loop Rule applied to the single closed path:

Since E₁ (10 V) is greater than E₂ (5 V), the net current flows in the direction driven by the 10 V battery: flowing clockwise through the loop, which corresponds to travelling from A to B through point E.

The radius of gyration k of a rigid body of mass M about a specified axis of rotation is the effective radial distance at which the entire mass could be concentrated without altering its moment of inertia:

For a uniform solid sphere of mass M and radius R about its own diametrical axis:

For a thin hollow spherical shell of identical mass M and radius R about its diametrical axis:

Evaluating the ratio k₁ / k₂:

None of the four printed options contained the square root sign. The closest intended option was Option (2) 3:5, which is the ratio of k₁² : k₂² (or I₁ : I₂). Because of this clerical typographical omission, the National Testing Agency (NTA) dropped Question 29 and awarded full marks to all candidates.

In an ideal transformer, energy losses due to flux leakage, eddy currents, hysteresis, and Joule heating in windings are assumed to be zero. Consequently, the input electrical power fed into the primary winding equals the output power delivered by the secondary winding:

The power delivered to the primary winding from the AC supply is given by the product of the primary RMS voltage and primary RMS current (assuming unity power factor for the resistive lamp load):

Substitute the primary mains voltage V_p = 220 V and the secondary load power P_s = 60 W:

Divide both sides by 220 to isolate I_p:

When light travels from an optically denser medium of refractive index μ into an optically rarer medium (air, μ_air ≈ 1), total internal reflection occurs at the critical angle of incidence θ_c where the angle of refraction is 90°:

By the wave definition of refractive index, μ is the ratio of the speed of light in air (v_1) to the speed of light in the denser medium (v_2):

Using the kinematic relation speed = distance / time for each medium:

Substitute v_1 and v_2 into the critical angle relation:

When an external deforming force is applied to a body, an internal restoring force equal in magnitude and opposite in direction develops within the material across every plane of cross-section. Stress σ is defined as this internal restoring force per unit area:

For a wire of negligible mass suspended from a rigid ceiling and carrying a weight W at its free end, make an imaginary horizontal cut at any point along the wire. For the lower portion to remain in static equilibrium, the internal tension T across the cross-sectional area A must balance the weight W: