JEE Main 2026 January 22, Shift 2 Question Paper with Solutions

Given below are two statements:

Statement-I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.

Statement-II: The time period of revolution of the satellite is $T=2\pi \sqrt{\frac{R_e}{g}}$ (for satellite very close to the earth surface), where $R_e$ radius of earth and g acceleration due to gravity.

In the light of the above statements, choose the correct answer from the options given below:

A uniform bar of length 12 cm and mass $20m$ lies on a smooth horizontal table. Two-point masses m and $2m$ are moving in opposite direction with same speed of v and in the same plane as the bar, as showing figure. These masses strike the bar simultaneously and got stuck to it. After collision the entire system is rotating with the angular frequency $\omega$. The ratio of v and $\omega$ is:

A Laser beam has intensity of $4.0\times 10^{14}W/m^2$. The amplitude of magnetic field associated with beam is ...... T. (Take ${ϵ}_0=8.85\times 10^{-12}{C}^2/N{m}^2$ and $c=3\times 10^{8}m/s$)

The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of $Paschen$ and $Balmer$ series is nearly ...... nm.

In an open organ pipe $v_3$ and $v_6$ are $3^{rd}$ and $6^{th}$ harmonic frequencies, respectively. If $v_6-v_3=2200$ Hz then length of the pipe is ______ mm. (Take velocity of sound in air is 330 m/s).

Figure shows the circuit that contains three resistances ($9\Omega$ each) and two inductors (4 mH each). The reading of ammeter at the moment switch K is turned ON, is ____ A.

The wavelength of light, while it is passing through the water of 540 nm. The refractive index of water is $\frac{4}{3}$. The wavelength of the same light when it is passing through a transparent medium having refractive index of $\frac{3}{2}$ is ______ nm.

An electric power line having total resistance of $2\Omega$, delivers 1kW of power at 250 V. The percentage efficiency of transmission line is ______

Five positive charges each having charge $q$ are placed at the vertices of a pentagon as shown in the figure. The electric potential ($V$) and the electric field ($E$) at the centre $O$ of the pentagon due to these five positive charges are:

Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is:

In parallax method for the determination of focal length of a concave mirror, the object should always be placed:

Given below are two statements:

Statement I: An object moves from position $r_1$ to position $r_2$ under a conservative force field F. The work done by the force is $W=-{\int }_{r_1}^{r_2}F\cdot dr$.

Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.

In the light of the above statements, choose the correct answer from the options given below:

Using a simple pendulum experiment $g$ is determined by measuring its time period T. Which of the following plots represent the correct relation between the pendulum length L & time period T?

When a part of a straight capillary tube is placed vertically in liquid, the liquid raises upto certain height $h$. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1% each, then the height of the liquid in the tube will change by ....... %

The correct truth table for the given input data of the following logic gate is: (Inputs A and B feed a NAND gate; inputs C and D feed an OR gate; the two outputs feed a final AND gate giving output Y.) The Boolean expression is $Y=\overline{(A\cdot B)}\cdot (C+D)$.

Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecules A is four times that of B. If the collision frequency in gas B is $32\times 10^{18}$ /s then collision frequency in gas A is ______ /s.

If $\epsilon$, E and t represent the free space permittivity, electric field and time respectively, then the unit of $\frac{\epsilon E}{t}$ will be:

Given below are two statements:
Statement-I: For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles.
Statement-II: The total kinetic energy can be the sum of kinetic energy of the center of mass w.r.t. to the origin and the kinetic energy of the all the particles w.r.t. the center of mass as the reference.
In the light of the above statements, choose the correct answer from the options given below:

Which of the following are true for a single slit diffraction? A. Width of central maxima increases with increasing in wavelength keeping slit width constant. B. Width of central maxima increases with decrease in wavelength keeping slit width constant. C. Width of central maxima increases with decrease in slit width at constant wavelength. D. Width of central maxima increases with increase in slit width at constant wavelength. E. Brightness of central maxima increases for decrease in wavelength at constant slit width.

Light is incident on a metallic plate having work function $110\times 10^{-20}$ J. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ....... rad/s. ($h=6.63\times 10^{-34}$ J/s)

A conducting circular loop is rotated about is diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5 T perpendicular to the axis of rotation. When the loop is rotated by $30^{\circ }$ from the horizontal position, the induced EMF is 15.4 mV. The radius of the loop is ______ mm. (Take $\pi =\frac{22}{7}$)

A capacitor P with capacitance $10\times 10^{-6}$ F is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor P is connected across another capacitor Q with capacitance $20\times 10^{-6}$ F. The charge on capacitor Q when equilibrium is established will be $\alpha \times 10^{-5}$ C (assume capacitor Q does not have any charge initially), the value of $\alpha$ is ______

An insulated cylinder of volume 60 $c{m}^3$ is filled with a gas at $27^{\circ }C$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as 20 $c{m}^3$ while allowing the temperature to rise to $77^{\circ }C$. The final pressure is ______ atmospheric pressure.

A cylindrical conductor of length 2 m and area of cross-section $0.2m{m}^2$ carries an electric current of 1.6 A when its ends are connected to a 2V battery. Mobility of electrons in the conductor is $\alpha \times 10^{-3}$ $m^2$/V.s. The value of $\alpha$ is: (electron concentration $=5\times 10^{28}/m^3$ and electron charge $=1.6\times 10^{-19}$ C)

Two masses m and 2m are connected by a light string going over a pulley (disc) of mass 30 m with radius $r=0.1m$. The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2m mass is released from rest and its speed when it has descended through a height of 3.6 m is ______ m/s. (Assume string does not slip and $g=10m/s^2$)

Cyclohexylmethanamine (cyclohexyl${\text{CH}}_2{\text{NH}}_2$) is treated with ${\text{C}}_6{\text{H}}_5\text{COCl}$ in presence of $\text{NaOH}$ to give [A], which on treatment with ${\text{LiAlH}}_4$ followed by ${\text{H}}_2\text{O}$ gives [B]. The final product [B] is: (Drawn structures in stem and all options.)

When 1 g of compound (X) is subjected to Kjeldahl's method for estimation of nitrogen, 15 mL 1 M ${\text{H}}_2{\text{SO}}_4$ was neutralized by ammonia evolved. The percentage of nitrogen in compound (X) is:

Which of the following mixture gives a buffer solution with pH = 9.25? Given: $\text{p}{K}_b({\text{NH}}_4\text{OH})=4.75$

At T (K), 100 g of 98% ${\text{H}}_2{\text{SO}}_4$ (w/w) aqueous solution is mixed with 100 g of 49% ${\text{H}}_2{\text{SO}}_4$ (w/w) aqueous solution. What is the mole fraction of ${\text{H}}_2{\text{SO}}_4$ in the resultant solution? (Given: Atomic mass H = 1 u; S = 32 u; O = 16 u) (Assume that temperature after mixing remains constant)

Given below are two statements:
Statement I: Elements 'X' and 'Y' are the most and least electronegative elements, respectively among N, As, Sb and P. The nature of the oxides ${\text{X}}_2{\text{O}}_3$ and ${\text{Y}}_2{\text{O}}_3$ is acidic and amphoteric, respectively.
Statement II: ${\text{BCl}}_3$ is covalent in nature and gets hydrolysed in water. It produces $[{\text{B(OH)}}_4{]}^{-}$ and $[{\text{B(H}}_2{\text{O)}}_6{]}^{3+}$ in aqueous medium.
In the light of the above statements, choose the correct answer from the options given below:

Consider the following reduction processes:
${\text{Al}}^{3+}+3e^{-}\to \text{Al(s)}$, $E^0=-1.66$ V
${\text{Fe}}^{3+}+e^{-}\to {\text{Fe}}^{2+}$, $E^0=+0.77$ V
${\text{Co}}^{3+}+e^{-}\to {\text{Co}}^{2+}$, $E^0=+1.81$ V
${\text{Cr}}^{3+}+3e^{-}\to \text{Cr(s)}$, $E^0=-0.74$ V
The tendency to act as reducing agent decreases in the order:

$[{\text{Ni(PPh}}_3{)}_2{\text{Cl}}_2]$ is a paramagnetic complex. Identify the INCORRECT statements about this complex. A. The complex exhibits geometrical isomerism. B. The complex is white in colour. C. The calculated spin-only magnetic moment of the complex is 2.84 BM. D. The calculated CFSE (Crystal Field Stabilization Energy) of Ni in this complex is $-0.8{\Delta }_0$. E. The geometrical arrangement of ligands in this complex is similar to that in ${\text{Ni(CO)}}_4$. Choose the correct answer from the options given below:

Correct statements regarding Arrhenius equation among the following are: A. Factor $e^{-Ea/RT}$ corresponds to fraction of molecules having kinetic energy less than Ea. B. At a given temperature, lower the Ea, faster is the reaction. C. Increase in temperature by about $10^0\text{C}$ doubles the rate of reaction. D. Plot of $\log k$ vs $\frac{1}{T}$ gives a straight line with slope $=-\frac{Ea}{R}$. Choose the correct answer from the options given below:

$\text{A}+2\text{B}\to {\text{AB}}_2$. 36.0 g of 'A' (Molar mass: 60 g ${\text{mol}}^{-1}$) and 56.0 g of 'B' (Molar mass: 80 g ${\text{mol}}^{-1}$) are allowed to react. Which of the following statements are correct? A. 'A' is the limiting reagent. B. 77.0 g of ${\text{AB}}_2$ is formed. C. Molar mass of ${\text{AB}}_2$ is 140 g ${\text{mol}}^{-1}$. D. 15.0 g of A is left unreacted after the completion of reaction. Choose the correct answer from the options given below:

The compound A, ${\text{C}}_8{\text{H}}_8{\text{O}}_2$ reacts with acetophenone to form a single product via cross-aldol condensation. The compound A on reaction with conc. $\text{NaOH}$ forms a substituted benzyl alcohol as one of the two products. The compound A is:

The energy of first (lowest) Balmer line of H atom is x J. The energy (in J) of second Balmer line of H atom is:

3,3-Dimethyl-2-butanol cannot be prepared by: (Each option A-E is a drawn reaction scheme.) A. (drawn carbonyl) $\underset{{\text{H}}_3{\text{O}}^{+}}{\overset{\text{MeMgBr-dry ether}}{\to }}$ ; B. (drawn alkene) $\stackrel{{\text{H}}_2\text{O}/{\text{H}}^{+}}{\to }$ ; C. (drawn alkene) $\underset{{\text{(ii) NaBH}}_4/\text{MeOH}}{\overset{{\text{(i) O}}_3/{\text{Zn-H}}_2\text{O}}{\to }}$ ; D. (drawn ketone) $\stackrel{{\text{LiAlH}}_4/{\text{H}}_3{\text{O}}^{\oplus }}{\to }$ ; E. (drawn alkyne) $\stackrel{{\text{H}}_2\text{O},{\text{Hg}}^{2+}/{\text{H}}^{+}}{\to }$ . Choose the correct answer from the options given below: