WBJEE 2026 Paper 2 (Physics & Chemistry) Question Paper with Solutions

A body of density＇$𝜌$＇is dropped slowly on the surface of a lake of depth $𝑑$ ．If the density of the lake water be＇${𝜌}^{\prime \prime }({𝜌}^{\prime }<𝜌)$ then the time taken by the body to reach the bottom of the lake is ‘

Beyond what distance，the ray optics is sufficiently valid when the aperture is 6 mm wide and the wavelength is $6000\stackrel{o}{A}$ ？

A plano－convex lens fits exactly into a plano－concave lens．Their plane surfaces are parallel to each other．If lenses are made of different materials of refractive indices ${𝜇}_1$ and ${𝜇}_2$ and $𝑅$ is the radius of curvature of the curved surface of the lenses，then the focal length of the combination is

Consider a fuse wire of length $𝑙$ and radius $𝑟$ ．The time of heating $\left(𝑡\right)$ for passing the maximum current will depend on

Density and volume of a body are given as $(20\pm 4)\mathrm{gm}/{\mathrm{cm}}^3$ and $(10\pm 1){\mathrm{cm}}^3$ respectively. The absolute error in measurement of mass is

If a vector $\overrightarrow{𝑣}=3\widehat{𝑖}$ is rotated in the $𝑥-𝑧$ plane by an angle $𝜃$ with respect to $𝑥$－axis in the clockwise direction，then for an observer at $+𝑦$ axis the vector will be

A circular coil, carrying current, has radius $𝑅$. The distance from the centre of the coil on the axis where the magnetic induction will be $\frac{1}{27}$ th of its value at the centre of the coil is

A square of side $𝐿$ lies in the $𝑥-𝑦$ plane，where the magnetic field is given by $𝐵={𝐵}_0(2\widehat{𝑖}+3\widehat{𝑗}+4\widehat{𝑘})$ where ${𝐵}_0$ is constant．The magnetic flux passing through the square is $𝐿$

A resistor of resistance＇$𝑅$＇draws power＇$𝑃$＇when connected to an AC source．If an inductance is now placed in series with $𝑅$ ，such that the impedance of the circuit becomes＇$𝑍$＇，the power drawn will be

A simple pendulum of length $𝑙$ has a bob of mass $𝑚$ ，with a charge $𝑞$ ．On it a vertical sheet of charge， with surface charge density＇$𝜎$＇passes through the point of suspension．At equilibrium，if the string makes an angle $𝜃$ with the vertical，then

The equation of a transverse wave is $𝑦={𝑦}_0\sin 2𝜋(𝑓𝑡-\frac{𝑥}{𝜆})$ ．If the maximum particle velocity be four times that of wave velocity then

A uniform but time varying magnetic field is present in a circular region of radius ' $𝑅$ '. The magnetic field is perpendicular and into the plane of loop and the magnitude of field is increasing at a constant rate $𝛼$. There is a straight conducting rod of length 2 R placed as shown in figure. The magnitude of induced emf across the rod is

From a tower of height $𝐻$ ，a particle is thrown vertically upwards with a speed $𝑢$ ．The time taken by the particle to hit the ground is $𝑛$ times that taken by it to reach the highest point of its path．The relation between $𝐻,𝑢$ and $𝑛$ is

There is a ring of radius $𝑟$ having linear charge density $𝜆$ and rotating with a uniform angular velocity $𝜔$. The magnitude of the magnetic field produced by this ring at its own centre would be ( ${𝜇}_0=$ permeability of air)

Three vectors $\overrightarrow{𝑎},\overrightarrow{𝑏}$ and $\overrightarrow{𝑐}$ are such that $\left|\overrightarrow{𝑎}\right|=1,\left|\overrightarrow{𝑏}\right|=2$ and $\left|\overrightarrow{𝑐}\right|=4$ along with $\overrightarrow{𝑎}+\overrightarrow{𝑏}+\overrightarrow{𝑐}=0$ ．Then，the value of $4\overrightarrow{𝑎}\cdot \overrightarrow{𝑏}+3\overrightarrow{𝑏}\cdot \overrightarrow{𝑐}+3\overrightarrow{𝑐}\cdot \overrightarrow{𝑎}$ will be

Two identical metal bars are heated in two different temperatures and allowed to cool in the same surroundings. Which one of the following figures correctly shows their cooling curves?

The inputs to a digital circuit are as shown below. The output Y is

The velocity $𝑣$ of a particle at time $𝑡$ is given by $𝑣=𝑎𝑡+\frac{𝑏}{𝑡+𝑐}$, where $𝑎,𝑏$ and $𝑐$ are constants. The dimension of $𝑎,𝑏$ and $𝑐$ are, respectively

A body initially at rest and sliding along a frictionless track from a height＇$ℎ$＇（as shown in figure） just completes a vertical circle of diameter $\mathrm{AB}=𝑑$ ．The height＇$ℎ$＇is equal to

The I-V characteristics graph shown below is exhibited by

A person has a minimum distance of distinct vision of 50 cm ．The power of lenses required to read a book at a distance of 25 cm is

Three blocks of masses ${𝑚}_1=2\mathrm{kg},{𝑚}_2=3\mathrm{kg}$ and ${𝑚}_3=5\mathrm{kg}$ are placed on a horizontal frictionless surface and a force of 30 N pulls the system as shown below．The value of tension $𝑇$ will be

Which one of the following graphs represents the velocity-time $(𝑣-𝑡)$ graph of a small spherical body falling in a viscous liquid?

A ray of light travelling in air is incident on one face of a parallel glass slab of thickness $𝑡$ and refractive index $𝜇$ at an angle of incidence $𝑖$ ．Total time spent by the ray inside the slab is

Radiation of wavelength $𝜆$ is incident on a photocell．The fastest emitted electron has speed $𝑣$ . If the wavelength is changed to $\frac{3𝜆}{4}$ ，then the speed of the fastest emitted electron will be

Two spherical soap bubbles of radii ${𝑟}_1$ and ${𝑟}_2$ in vaccum coalesce under isothermal condition．The newly formed bubble has a radius（ $𝑟$ ）given by

A radioactive element ${}_{242}^{92}X$ emits two $𝛼$－particles，one electron and two positrons．The transformed nucleus is represented by ${}_{234}^{𝑃}𝑌$ ．The value of $𝑃$ is

The magnetic moment of an iron bar is $𝑀$. It is now bent in such a way that it forms an arc section of a circle subtending an angle of ${60}^{\circ }$ at the centre. The magnetic moment of the arc section is

A uniform $\mathrm{rod}𝐴𝐵$ is suspended from a point $𝑃$ ，at a variable distance $𝑥$ ，from $𝐴$ ，as shown in figure． To make the rod horizontal，a mass＇$𝑚$＇is suspended from its end $𝐴$ ．Which set of variables will give a straight line when they are plotted？

A pipe $𝐴$ is connected with other pipes $𝐵$ and $𝐶$ as shown in the figure．The areas of cross－section of $𝐴,𝐵$ and $𝐶$ are respectively $𝛼,\frac{𝛼}{2}$ and $\frac{𝛼}{4}$ ．If the velocities of flow of water through $𝐴$ and $𝐵$ are $10m/\sec$ and $6m/\sec$ ，respectively，then velocity of flow，${𝑉}_{𝑐}$ along $𝐶$ is

A particle of mass $𝑚$ is suspended from a point O by a string of length $𝑅$ ．It is given a velocity $𝑢=3\sqrt{\surd 𝑔𝑅}$ at the bottom．The difference in tension at point $𝐵$ and at the point $𝐶$ is $𝑚$

The de-Broglie wavelength of an electron in 4th orbit is (where $𝑟=$ radius of the 1st orbit)

An electromagnetic wave，whose wave normal makes an angle of ${45}^{\circ }$ with the vertical，is travelling in air and strikes a horizontal liquid surface．While travelling through the liquid，it gets deviated by ${15}^{\circ }$ ．If the speed of electromagnetic wave in air is $3\times {10}^{8}m/s$ ，then the speed of electromagnetic wave in the liquid will be

The circuit has two oppositely connected ideal diodes in parallel as shown in the figure．What is the current flowing in the circuit？

2 moles of an ideal gas with $\frac{{𝐶}_{𝑝}}{{𝐶}_{𝑣}}=\frac{5}{3}$ are mixed with 3 moles of another ideal gas with $\frac{{𝐶}_{𝑝}}{{𝐶}_{𝑣}}=\frac{4}{3}$ ．The value of $\frac{{𝐶}_{𝑝}}{{𝐶}_{𝑣}}$ for the mixture is

Which of the velocity-time $(𝑣-𝑡)$ graph(s) can possibly represent one-dimensional motion of a particle?

The moment of inertia of a thin disc about axes $𝑎,𝑏,𝑐,𝑑$ are ${𝐈}_1,{𝐈}_2,{𝐈}_3$ and ${𝐈}_4$ respectively，as shown in figure．If the moment of inertia about an axis passing through the centre and perpendicular to the plane of the disc is I then，

The displacement current flows through a capacitor when the voltage across its plates

Two points of monochromatic and coherent sources of light of wavelength $𝜆$ each, are placed as shown in figure. The initial phase difference between the sources is zero, $(𝐷\gg 𝑑)$. Mark the correct statement(s).

For Boolean variables $𝐴$ and $𝐵,𝐴\oplus 𝐵=𝐴\overline{𝐵}+\overline{𝐴}𝐵$ ．Then，which of the following statements is / are correct？

The major products U and V in the following reaction are

Among $N_{2}O,{\mathrm{ClF}}_{-}^2,{\mathrm{SO}}_2$ and $I_{+}^3$, the species having the linear structures are

In the following sequence of reactions, what is the end product ' $𝑍$ '?

A compound $\left(X\right)$ when treated with ${\mathrm{CuSO}}_4$ solution yields a brown precipitate．On adding hypo solution the precipitate turns white．The compound $\left(X\right)$ is

Three engines $A,B$ and C take steam at ${130}^{\circ }C$ and reject it at ${20}^{\circ }C,{40}^{\circ }C$ and ${50}^{\circ }C$ respectively．The most efficient engine will be

In a conductance experiment, aqueous ${\mathrm{AgNO}}_3$ solution is added to aqueous KCl solution gradually and simultaneously the molar conductivity ( ${𝜆}_m$ ) is measured. The correct plot of ${𝜆}_m$ versus volume of ${\mathrm{AgNO}}_3$ solution is

Indicate the major product of the following reaction:

The van't Hoff Factor (i) for a dilute aqueous solution of ${\mathrm{Na}}_2{\mathrm{SO}}_4$ is

Which of the following is the structure of pyrosulphuric acid?

Peroxide ion is

How many isomers can a compound with molecular formula $C_3{H}_5\mathrm{Br}$ have？

Which one of the following cations gives a chocolate brown precipitate upon addition of aqueous solution of $K_4\left[\mathrm{Fe}\right(\mathrm{CN}{)}_6]$ ？

A compound contains two types of atoms $𝐴$ and $𝐵$ ．Its crystal structure is a cubic lattice with＇$𝐴$＇ atoms at the corner of the unit cells and＇$𝐵$＇atoms at the body centres．The simplest formula of the compound will be

The plot of radial probability density（ $4𝜋{𝑟}^2{𝑅}^2$ ）against $𝑟$ for an electron in $𝑛𝑝$ orbital of a many electron atom is given below．

The value of $𝑛$ is

A buffer solution contains 100 ml of $0.01\left(M\right){\mathrm{CH}}_3\mathrm{COOH}$ and 200 ml of $0.02\left(M\right){\mathrm{CH}}_3{\mathrm{COONa}}_{𝑎}.700\mathrm{ml}$ of water is added subsequently to the buffer solution．The pH before and after dilution are ［given，$𝑝{𝐾}_{𝑎}=4.74;\log 2=0.301$ ］