JEE Advanced 2026 Paper 2

A metal wire of cross-sectional area 0.5 mm2 and length 100 m is connected across a battery of e.m.f. 2 V and internal resistance 1 . The density, atomic mass and electrical conductivity of the metal are 6.35 103 kg m-3, 63.5 gm/mole and 2 108 mho m-1, respectively. Assuming one conduction electron per atom of the metal, the drift velocity (in mm s-1) of the electrons in the wire is: [Take Avogadro’s number as 6 1023 and charge of the electron as 1.6 10-19 C.]

1. 0.052
2. 0.104
3. 0.208
4. 0.156

A nuclear reactor starts producing a radioactive nuclide X from t=0, at a constant rate of per second. Each decay of X produces energy E0, which is utilized to heat a liquid of mass m and specific heat s. Assuming no heat loss from the liquid and taking as the decay constant of X, the rate of increase in the temperature of the liquid is:

1. E0m s (1-e- t )
2. E0m s (e t-1 )
3. E0m s (1-e- t )
4. E0m s ( - e- t )

A beam of polychromatic light passes through a thin prism of prism angle 6 . The refractive index of the material of the prism varies with wavelength ( ) as n( )= + 2, where =3 m-1 and =0.096 m2. If is the wavelength at which the angle of minimum deviation Dm is smallest, then the correct value of Dm at is

1. 6.4
2. 4.8
3. 3.2
4. 2.4

A particle of mass m, and angular momentum is moving in a circular orbit of radius r0 under the influence of an attractive force F(r)=- kr2 r. Keeping its angular momentum unchanged, the particle is displaced radially by a small distance r r0, due to which its radial distance varies periodically. The corresponding time period is:

1. 2 3mk2
2. 2 mk
3. 2 33mk2
4. 2 35mk2

In a vacuum chamber, a particle of charge 1 and mass 1 mg is projected with a velocity ( i+2 j) m s-1 from the XZ plane at time t=0 in an electric field of 1 i V m-1. At t=0.2 s, the electric field is switched off and a magnetic field of 6 j T is switched on. The acceleration due to gravity is -10 j m s-2. Correct option(s) is/are:

1. The vertical distance of the particle from the XZ plane at t=0.3 s is 15 cm.
2. The vertical distance of the particle from the XZ plane at t=0.4 s is 10 cm.
3. The radius of the trajectory of the particle for t>0.2 s is 20 cm.
4. The particle will be in the XZ plane at t=0.35 s.

Two charges Q1=q and Q2=mq are placed at the points P1(a,b) and P2(ma,mb), respectively, in the XY plane, where a,b 0 and m 0,1. If V1 is the potential at a point in the XY plane due to charge Q1 and V2 is the potential at that point due to charge Q2. Correct statement(s) for the points at which |V1|=|V2| is/are:

1. For m=-1, locus of these points is ax+by=0.
2. For m=2, the locus of these points is a circle of radius 23 a2+b2 centered at ( 23a, 23b )
3. For m=-2, the locus of these points is a circle of radius 2 a2+b2 centered at (2a,2b)
4. For m=-3, locus of these points is 3bx+3ay=0.

Consider an electric dipole comprising two charges +q and -q each with mass m, separated by a fixed distance d and initially at rest with its dipole moment pointing along i. A uniform electric field E j is turned on at time t=0 and it is turned off at t=tf, when the dipole moment makes an angle f with i. Neglecting any sources of energy loss, correct option(s) is/are:

1. The center of mass of the dipole is deflected towards j in the presence of the field.
2. If the magnitude of the final angular velocity f= 2qEmd, then f= 6.
3. If f= /3, then the change in kinetic energy of the dipole is given by 2 3 qEd.
4. For f= /4, the dipole rotates around its center of mass with a constant angular velocity after t>tf.

Two thin wires, Wire-1 of diameter 0.650 mm and Wire-2 of unknown diameter d are given. To obtain the value of d, the diameters of the two wires are measured with a screw gauge. The screw gauge has a pitch of 0.5 mm and there are 100 divisions on the circular scale (CS). The smallest division on the linear scale (LS) is 0.5 mm. The table shows the readings of LS and CS for the measurements. The value of d (in m) is: array|c|c|c| & 2c|Readings \ 2-3 & LS (mm) & CS \ Wire-1 & 0.5 & 42 \ Wire-2 & 1.5 & 95 \ array

In a single slit diffraction experiment, a slit of width (0.016 0.002) mm is used to measure the wavelength of a monochromatic light source. In the diffraction pattern, the angular distance between the central maximum and first minimum is measured to be (2 40'). The value of the fractional error in the measurement of wavelength is: [Given: (2 )=0.035]

In a new system of units, the units of mass, length, time and current are 5 kg, 5 m, 5 s and 5 A, respectively. If 0 and 0 are the permeability and permittivity of free space, respectively, then in this new system of units, the magnitude of one SI unit of 0/ 0, is:

Consider two isosceles prisms 1 and 2 with prism angles A1 and A2 and refractive indices n1 and n2, respectively, as shown in the figure. The faces a1b1 and a2b2 are parallel to each other and perpendicular to the mirror M. If a ray of light is incident on the face a1c1 and emerges from the face a2c2, then the correct statement(s) is/are: [figure]

1. If both the prisms are at minimum deviation condition, then n2n1= ( A12 )/ ( A22 ).
2. If prism 2 is at minimum deviation condition, then i1=n2 ( A22 ) is always true.
3. If both the prisms 1 and 2 are thin and are at minimum deviation condition with angles of deviation m1 and m2, respectively, then = m12(n1-1)+ m22(n2-1).
4. If prism 1 is at minimum deviation condition, then i2=n1 ( A12 ) is always true.

Ten moles of an ideal monoatomic gas, initially in state a at atmospheric pressure and temperature Ta=27 , is enclosed in a metal cylinder of volume V0 fitted with a frictionless piston. The gas is suddenly compressed to state b with volume V0/3. Now, keeping the piston stationary, the cylinder is submerged in a water bath of temperature 11 until the gas reaches the temperature of the water bath, which is denoted as state c. Finally, while still in the water bath, the piston is brought slowly to its initial position, which is denoted as state f. If R is universal gas constant, then the correct option(s) is/are: [Given: 91/3=2.08]

1. The schematic P-V diagram of the processes described above is: [figure]
2. The change in internal energy in going from state a to b is 4860R.
3. The net change in the internal energy in the whole process is -240R.
4. The pressure and temperature of the state b are 2.08 times the atmospheric pressure and 624 K, respectively.

As shown in the figure, a ray AB of unpolarized light enters from water of refractive index nw=4/3 into a medium of refractive index np=4/ 3 after passing through a glass plate of refractive index ng=1.5 and a layer of water. At a particular incident angle i the reflected ray CD is polarized in the direction as shown in the figure. The value of i (in degrees) is: [figure]

As shown in the figure, the resistance of a galvanometer G can be found by the half-deflection method. Here the resistance R2 is adjusted such that when the key K is closed the deflection in the galvanometer becomes half of the value as compared to when K is open. Half-deflection is obtained at R2=4 and thus the galvanometer resistance is found to be 6 . In this half-deflection condition the current (in mA) through the resistor R1 is: [figure]

The height (in m) of the liquid in left chamber at t=500 s is:

The difference in the capacitance (in F) between the metal plates at t=0 and that at t=500 s is (8-n) 0, where 0 is the permittivity of free space. The value of n is:

After the collision the disk starts to rotate around point C in the XY plane. The maximum change in the height (in m) of its center O is:

Amount of energy loss (in J) in the collision is:

At 300 K, the molar conductivities of the aqueous solutions of three salts at two different concentrations are given below: array|c|c|c| Salt & Concentration (M) & Molar conductivity ( S cm2 mol-1) \ NaNO3 & 0.01 & 111 \ & 0.04 & 101 \ NaCl & 0.01 & 117 \ & 0.04 & 107 \ AgNO3 & 0.01 & 125 \ & 0.04 & 116 \ array The conductivity of a saturated aqueous solution of AgCl is 1.40 10-6 S cm-1 at 300 K. If the solubility of AgCl in water at 300 K is X mol L-1, then 10(X-1) is (Assume that AgCl dissolved in water ionizes completely and that the molar conductivity of saturated AgCl solution is equal to its limiting molar conductivity.)

1. 3
2. 4
3. 5
4. 6

The correct order of ONO bond angle in the given species is

1. NO2+<NO2<NO3-<NO2-
2. NO2-<NO3-<NO2<NO2+
3. NO3-<NO2-<NO2<NO2+
4. NO2-<NO3-<NO2+<NO2

Correct statement(s) about the compounds P, Q and R is(are) Xe(g)+F2(g) (1:5 ratio) 873 K, 7 barP P+O2F2 143 KQ+O2 Q+H2O complete hydrolysisR+HF

1. P has two lone pairs of electrons on the central atom.
2. Q has a perfect octahedral geometry.
3. Q can act as a fluorinating agent.
4. The molecular structure of R is trigonal pyramidal.

The correct statement(s) regarding the periodic properties of elements is(are)

1. Second ionization enthalpy of carbon atom is less than that of boron atom.
2. Increasing order of ionic radii: Al3+<Mg2+<Na+
3. Under identical conditions, in solid state, the density of potassium metal is more than density of sodium metal.
4. The H–H bond is weaker than F–F bond.

The correct statement(s) regarding sugars is(are) Given: Specific rotations of L-(−)-glucose and L-(+)-fructose are -52.5 and +92.5 , respectively.

1. On treatment with HNO3, gluconic acid is oxidized to saccharic acid, whereas glucose is not oxidized to saccharic acid.
2. Fructose gives a positive Fehling's test because it isomerises to glucose and another aldohexose in the presence of Fehling's reagent.
3. Invert sugar is an equimolar mixture of D-glucose and D-fructose formed after hydrolysis of the corresponding disaccharide.
4. Specific rotation of invert sugar is -40 .

Xa+ and Yb+ are hydrogen-like species. The wavelength of light absorbed during the transition between the states with principal quantum numbers n=1 and n=2 of Xa+ is . The wavelength of light absorbed during the transition between the states with principal quantum numbers n=2 and n=4 of Yb+ is 9 . The lowest possible value of (a+b) is .

At a given temperature, 0.45 g of acetic acid in 50 mL of water is shaken with 1.0 g of charcoal and the pH of the resulting solution is 3.0. Assume, the adsorption of acetic acid from the aqueous solution by charcoal follows Freundlich isotherm, xm=kC1/n If the plot of 10(x/m) against 10C gives a straight line with slope 1, the value of k in L mol-1 is . Given: The molar mass of acetic acid is 60 g mol-1. The acid dissociation constant of acetic acid is 1.0 10-5 at the given temperature. x is the mass (in grams) of acetic acid adsorbed. m is the mass (in grams) of charcoal. C is the equilibrium concentration of acetic acid in the solution after the adsorption is complete. k and n are constants for acetic acid–charcoal system at the given temperature.

In a solvent S, a compound B is partially dissociated into C and D as given below: B 2C+2D B, C and D are non-volatile in nature. The molar mass of B is 10 times the molar mass of S. The standard boiling point and the standard enthalpy of vaporization of S are 400 K and 10R J mol-1, respectively (R is the gas constant in J K-1 mol-1). A solution of B in S with an initial concentration of B as 0.25% (mass/mass) has a boiling point of 408 K at 1 bar pressure. In this solution, the mole percent of B that has been dissociated is .

Consider that the coordinating atoms of the ligands in cis-[Co(NH3)4Cl2]Cl and mer-[Co(NH3)3Cl3] octahedral complexes are at the vertices of an octahedron. The sum of total number of the triangular faces in both the complexes having one N atom and two Cl atoms at their corners is .

At 300 K, the ratio of the molar volume of pure B in vapour phase to its molar volume in liquid phase is .

The mole fraction of B in vapour phase which is in equilibrium with this solution is .

Natural rubber on complete ozonolysis ( O3/Zn-H2O) gives compound X as the major product. X gives positive iodoform and Tollen's tests. X on heating with aqueous NaOH gives Y as the major product. Y is

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A known artificial sweetener X is composed of 4-chloro-4-deoxy-α-D-galactose and 1,6-dichloro-1,6-dideoxy-β-D-fructose joined by a glycosidic linkage. Structure of D-galactose is given below: [figure] The correct structure of X is

1. [figure]
2. [figure]
3. [figure]
4. [figure]

For a first-order reaction R P at a given temperature, k is the rate constant. For this reaction, at the given temperature, the concentrations of R and P at a time t are [R] and [P], respectively. The correct graphical representation(s) for this reaction is(are)

1. [figure]
2. [figure]
3. [figure]
4. [figure]

The volume of 1 M aqueous H2SO4 required to completely neutralize the ammonia evolved from 5.72 g of L in Kjeldahl's method of nitrogen estimation is mL.

In sulphur estimation by Carius method, the amount of BaSO4 formed from 3.79 g of M is g.

In the following reaction sequence, P, Q, S and T are the major products. [figure] The correct statement(s) about P, Q, S and T is(are)

1. Q on treatment with ethanol generates an aromatic aldehyde.
2. S gives positive phthalein dye test.
3. P is a dinitro compound.
4. T is a coloured compound.

In the following reaction sequence, major products X and Y are acyclic monomers. CH3I [ 3. Red P, Br2\ 4. NH3 (excess)] 1. KCN\ 2. H3O+, X [figure] 500 mol of X completely reacts with 500 mol of Y to give 1 mol of a single biodegradable acyclic copolymer Z as the only product. The amount of Z formed in grams is . Given: Atomic mass (in amu): H : 1, C : 12, N : 14, O : 16, Br : 80

Let a, b be two vectors, and let P, Q and R be the points with position vectors a, b and a+ b, respectively, with respect to the origin O. If | a+ b|= 21, | a- b|=3, and a and ( a- b) are perpendicular to each other, then the area of the triangle OPR is

1. 3
2. 32
3. 3 32
4. 32

Let T be the tangent to the parabola y2=16x at the point (64,32). Let L be the tangent to the same parabola at another point (x1, y1) on the parabola. If L and T are perpendicular to each other, then the distance between the point (x1, y1) and the focus of the parabola, is

1. 154
2. 4
3. 174
4. 5

Let y:(- , ) (0, ) be the solution of the differential equation dydx= e5xy3+y3ex+exy4, satisfying y(0)= 1 2. Then the value of y( e 2) is

1. 5+ 352
2. 7+ 532
3. 7+ 532
4. 5+ 352

The value of the definite integral 02 13x+3 dx is

1. 12
2. 13
3. e 33
4. e 32

Let R denote the set of all real numbers. Consider the polynomial function f: R R defined by f(x)= d10dx10 ((x2-1)10 ), for all x R. Here d10dx10 ((x2-1)10 ) is the 10th order derivative of the function (x2-1)10. Then which of the following statements is (are) TRUE ?

1. The coefficient of x8 in the polynomial f(x) is (-10) ( 18!8! )
2. The value of f(1)+f(-1) is equal to 10! 211
3. The degree of the polynomial f(x) is 10
4. The constant term of the polynomial f(x) is - ( 10!5! )

Let a, b, c be positive integers in arithmetic progression such that the equation ax2+bx+c=0 has only integer solutions. Then which of the following statements is (are) TRUE ?

1. c-b is an integer multiple of a
2. Both the roots of the equation ax2+bx+c=0 are odd integers
3. If c=15, then ab=8
4. If b=8, then x=3 is a root of the equation ax2+bx+c=0

Let L be the straight line joining the points P(1,2,-1) and Q(2,3,1). Let S be the foot of the perpendicular drawn from the point R(4,-1,5) to the line L. Another line passing through R intersects L at a point T such that the point S divides the line segment PT internally in the ratio |PS|:|ST|=1:2, where |PS| and |ST| are the lengths of the line segments PS and ST, respectively. Then which of the following statements is (are) TRUE ?

1. The orthocentre of the triangle PRT is ( 235,-4, 315 )
2. The orthocentre of the triangle PRT is (4,3,5)
3. The area of the triangle PRT is 6 5
4. The area of the triangle PRT is 18 5

Let y=f(x) be the real valued function defined on the interval (0, ), satisfying y(1)=0 and the differential equation x dydx=y-x3. Then which of the following statements is (are) TRUE ?

1. The function f has a local minimum at x= 1 3
2. The function f has a local maximum at x= 1 3
3. The function f is increasing in the interval (1, 2)
4. If g(x)=4x3-5x2+ 32x for x>0, then the number of elements in the set \x (0, ): f(x)=g(x)\ is 2

Let R denote the set of all real numbers and let i= -1. Consider the matrices S= bmatrix 0 & -1 \ 1 & 0 bmatrix and T= bmatrix 1 & 1 \ 0 & 1 bmatrix. Let a,b,c,d be real numbers such that ST= bmatrix a & b \ c & d bmatrix. Let H=\x+iy: x,y R and y>0\. Then which of the following statements is (are) TRUE ?

1. b+iad+ic=i
2. If = -1+i 32, then a +bc +d=
3. If m is an integer greater than 2 such that (ST)2=(ST)m, then m is an integer multiple of 8
4. If z H, then az+bcz+d H

Let N denote the set of all positive integers. Consider the sets A=\1,2,3,4,5\ and B=\1,2,3,4,5,6,7\. Let S be the set of all functions f:A B such that f(2) 2 and f(4) 4. Consider the set T=\f S: there exists a function g:B N such that g(f(x))=2x for all x A\. Then the number of elements in the set T is .

A bookshelf contains 6 distinct books of Mathematics and 5 distinct books of Physics. From these 11 books, 6 books are chosen at random. Let X be the absolute value of the difference between the number of Mathematics books chosen and the number of Physics books chosen. If is the mean of the random variable X, then the value of 77 is .

Consider a data consisting of 10 observations x1,x2, ,x10, whose mean is 5 and variance is 7. If the mean and the variance of the first 8 observations x1,x2, ,x8 are 4 and 3.5, respectively, and x9<x10, then the value of 3x9+2x10 is .

Consider the ellipse E given by x218+ y212=1. Let H be the hyperbola whose eccentricity is the reciprocal of the eccentricity of E and whose foci are the same as that of E. Let P and Q be the points of intersection of H and the parabola 5 y=x2 in the first quadrant. Let d be the distance between P and Q. If a and b are the integers such that d2=a+b 5, then the value of a-b is .

For a real number , let [ ] denote the greatest integer less than or equal to . For a finite set S, let |S| denote the number of elements in the set S. Consider the functions f:(-3,3) (- , ) and g:(-3,3) (- , ) defined by f(x)=[x3] e (1+ 2 ( (x-[x]) ) ) and g(x)=x3 2 ( e(1+x-[x]) ). Let A=\x (-3,3): f is discontinuous at x\ and B=\x (-3,3): g is discontinuous at x\. Then the value of |A|+2|B|-|A B| is .

The value of n is .

Let be the area of the region enclosed between the curves C1, C2, and the lines x= 1 and x= 4. Then the value of - 1 e ( -2 e- 2 ) is .

Let P be the point in the first quadrant where the given ellipses intersect. If is the acute angle between the tangents to the given ellipses at the point P, then the value of 4 is .

If is the area of the common region that lies inside both the given ellipses, then the value of is .