JEE Main 22 Jan 2026, Shift 2

75 questions. Answers are hidden — tap “Show answer” under each one.

Physics

Q1 · MCQ · Units and MeasurementsOpen
If $\epsilon$ , E and t represent the free space permittivity, electric field and time respectively, then the unit of $\dfrac{\epsilon E}{t}$ will be :
1. (1)Am
2. (2) $\mathrm{Am^2}$
3. (3) $\mathrm{A/m^2}$
4. (4)A/m
Q2 · MCQ · OscillationsOpen
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 and time period T ?
1. (1)
2. (2)
3. (3)
4. (4)
Q3 · MCQ · Kinetic Theory of GasesOpen
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 molecule A is four times that of B. If the collision frequency in gas B is $32\times10^{8}$ /s then collision frequency in gas A is /s.
1. (1) $32\times10^{8}$
2. (2) $4\times10^{8}$
3. (3) $2\times10^{8}$
4. (4) $8\times10^{8}$
We corrected a printing error in the original paper
Source printed “ $32\times10^{18}$ /s”; corrected to the intended “ $32\times10^{8}$ /s” (all options and the source's solution use $10^{8}$ ; as printed no option fits).
Q4 · MCQ · Rotational MotionOpen
A uniform bar of length 12 cm and mass 20 $m$ lies on a smooth horizontal table. Two point masses m and 2 $m$ are moving in opposite directions with same speed of v and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency $\omega$ . The ratio of v and $\omega$ (in cm) is :
1. (1)33
2. (2) $2\sqrt{88}$
3. (3)66
4. (4)32
We corrected a printing error in the original paper
Source printed “The ratio of v and $\omega$ is” with unitless options ( $v/\omega$ is a length; 33 cm).
Q5 · MCQ · Electric Potential and CapacitanceOpen
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 :
1. (1) $1 : 3^{1/3}$
2. (2) $1 : 2^{2/3}$
3. (3) $3^{2/3} : 1$
4. (4) $1 : 3^{2/3}$
Q6 · MCQ · Ray OpticsOpen
In parallax method for the determination of focal length of a concave mirror, the object should always be placed :
1. (1)between the focus (F) and the centre of curvature (C) of the mirror ONLY
2. (2)at any point beyond the focus (F) of the mirror
3. (3)beyond the centre of the curvature (C) of the mirror ONLY
4. (4)between the pole (P) and the focus (F) of the concave mirror ONLY
Q7 · MCQ · AtomsOpen
The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly nm.
1. (1)1875
2. (2)1550
3. (3)1217
4. (4)1784
Q8 · MCQ · WavesOpen
In an open organ pipe $\nu_3$ and $\nu_6$ are $3^{\text{rd}}$ and $6^{\text{th}}$ harmonic frequencies, respectively. If $\nu_6 - \nu_3 = 2200$ Hz then length of the pipe is mm. (Take velocity of sound in air is 330 m/s.)
1. (1)275
2. (2)225
3. (3)200
4. (4)250
Q9 · MCQ · Mechanical Properties of FluidsOpen
When a part of a straight capillary tube is placed vertically in a liquid, the liquid rises 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 %.
1. (1) $-1$
2. (2) $+3$
3. (3) $-3$
4. (4) $+1$
We corrected a printing error in the original paper
Source printed “the liquid raises upto certain height”.
Q10 · MCQ · Semiconductor ElectronicsOpen
The correct truth table for the given input data of the following logic gate is :
1. (1)
  Inputs Output
  A B C D Y
  1 1 0 1 1
  0 0 1 1 0
  1 0 1 0 1
  1 1 1 1 0
2. (2)
  Inputs Output
  A B C D Y
  1 1 0 1 1
  0 0 1 1 0
  1 0 1 0 0
  1 1 1 1 1
3. (3)
  Inputs Output
  A B C D Y
  1 1 0 1 0
  0 0 1 1 0
  1 0 1 0 1
  1 1 1 1 1
4. (4)
  Inputs Output
  A B C D Y
  1 1 0 1 0
  0 0 1 1 1
  1 0 1 0 1
  1 1 1 1 1
Q11 · MCQ · Current ElectricityOpen
An electric power line having total resistance of $2\ \Omega$ , delivers 1 kW of power of 250 V. The percentage efficiency of transmission line is .
1. (1)96.9
2. (2)86.5
3. (3)100
4. (4)92.5
Q12 · MCQ · Ray OpticsOpen
The wavelength of light, while it is passing through water is 540 nm. The refractive index of water is $\dfrac43$ . The wavelength of the same light when it is passing through a transparent medium having refractive index of $\dfrac32$ is nm.
1. (1)380
2. (2)840
3. (3)480
4. (4)540
Q13 · MCQ · Electromagnetic InductionOpen
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.
1. (1)1
2. (2)zero
3. (3)3
4. (4)2
Q14 · MCQ · GravitationOpen
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 $T = 2\pi\sqrt{\dfrac{R_e}{g}}$ (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 :
1. (1)Both Statement I and Statement II are false
2. (2)Both Statement I and Statement II are true
3. (3)Statement I is true but Statement II is false
4. (4)Statement I is false but Statement II is true
Q15 · MCQ · Wave OpticsOpen
Which of the following are true for a single slit diffraction?
- (A)Width of central maxima increases with increase 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.
1. (1)A, C, E only
2. (2)A, D only
3. (3)B, D only
4. (4)B, C only
We corrected a printing error in the original paper
Source printed option (1) as “A, D, E only”; corrected to the intended “A, C, E only” (A, C, E are the true statements; as printed no option is correct).
Q16 · MCQ · Work, Energy and PowerOpen
Given below are two statements :
Statement I : An object moves from position $r_1$ to position $r_2$ under a conservative force field $\vec F$ . The work done by the force is $W = -\displaystyle\int_{r_1}^{r_2}\vec F\cdot\vec{dr}$ .
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 :
1. (1)Both Statement I and Statement II are true
2. (2)Statement I is false but Statement II is true
3. (3)Statement I is true but Statement II is false
4. (4)Both Statement I and Statement II are false
We corrected a printing error in the original paper
Answer corrected; the source key is (3) — the work done by a conservative force is $+\int\vec F\cdot\vec{dr}$ , so Statement I (with the minus sign) is false, and Statement II is false.
Q17 · MCQ · Electric Potential and CapacitanceOpen
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 ( $\vec E$ ) at the center O of the pentagon due to these five positive charges are :
1. (1) $V = \dfrac{5q}{4\pi\varepsilon_0 r}$ and $\vec E = 0$
2. (2) $V = \dfrac{5q}{4\pi\varepsilon_0 r}$ and $\vec E = \dfrac{5\sqrt3\,q}{8\pi\varepsilon_0 r^2}\hat r$
3. (3) $V = \dfrac{5q}{4\pi\varepsilon_0 r}$ and $\vec E = \dfrac{5q}{4\pi\varepsilon_0 r^2}\hat r$
4. (4) $V = 0$ and $\vec E = 0$
Q18 · MCQ · Electromagnetic WavesOpen
A laser beam has intensity of $4.0\times10^{14}\ \mathrm{W/m^2}$ . The amplitude of magnetic field associated with beam is T. (Take $\epsilon_0 = 8.85\times10^{-12}\ \mathrm{C^2/Nm^2}$ and $c = 3\times10^{8}$ m/s)
1. (1)2.0
2. (2)18.3
3. (3)5.5
4. (4)1.83
Q19 · MCQ · Dual Nature of Radiation and MatterOpen
Light is incident on a metallic plate having work function $110\times10^{-20}$ J. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is rad/s. ( $h = 6.63\times10^{-34}$ J.s)
1. (1) $1.04\times10^{16}$
2. (2) $1.04\times10^{13}$
3. (3) $1.66\times10^{16}$
4. (4) $1.66\times10^{15}$
Q20 · MCQ · Centre of Mass, Momentum and CollisionOpen
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. the origin and the kinetic energy of 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 :
1. (1)Both Statement I and Statement II are true
2. (2)Statement I is true but Statement II is false
3. (3)Statement I is false but Statement II is true
4. (4)Both Statement I and Statement II are false
We corrected a printing error in the original paper
Source printed “w.r.t. to the origin”.
Q21 · Numerical · Electromagnetic InductionOpen
A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a vertical 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. $\left(\text{Take } \pi = \dfrac{22}{7}\right)$
We corrected a printing error in the original paper
Assumption “vertical” (magnetic field) added; the source leaves the field direction relative to the horizontal position unstated, and the key 14 needs $e = BA\omega\sin30^\circ$ .
Q22 · Numerical · Rotational MotionOpen
Two masses m and 2m are connected by a light string going over a pulley (disc) of mass 30m with radius $r = 0.1$ m. 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 $g = 10\ \mathrm{m/s^2}$ )
Q23 · Numerical · Electric Potential and CapacitanceOpen
A capacitor $P$ with capacitance $10\times10^{-6}$ 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 $20\times10^{-6}$ F. The charge on capacitor $Q$ when equilibrium is established will be $\alpha\times10^{-5}$ C (assume capacitor $Q$ does not have any charge initially), the value of $\alpha$ is .
Q24 · Numerical · Current ElectricityOpen
A cylindrical conductor of length 2 m and area of cross-section $0.2\ \mathrm{mm^2}$ carries an electric current of 1.6 A when its ends are connected to a 2 V battery. Mobility of electrons in the conductor is $\alpha\times10^{-3}\ \mathrm{m^2/V.s}$ . The value of $\alpha$ is : (electron concentration $= 5\times10^{28}/\mathrm{m^3}$ and electron charge $= 1.6\times10^{-19}$ C)
Q25 · Numerical · Kinetic Theory of GasesOpen
An insulated cylinder of volume $60\ \mathrm{cm^3}$ is filled with a gas at $27^\circ$ C and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20\ \mathrm{cm^3}$ while allowing the temperature to rise to $77^\circ$ C. The final pressure is atmospheric pressure.

Chemistry

Q1 · MCQ · Some Basic ConceptsOpen
At T(K), 100 g of 98% $\ce{H2SO4}$ (w/w) aqueous solution is mixed with 100 g of 49% $\ce{H2SO4}$ (w/w) aqueous solution. What is the mole fraction of $\ce{H2SO4}$ in the resultant solution ?
(Given : Atomic mass H = 1 u ; S = 32 u; O = 16 u)
(Assume that temperature after mixing remains constant)
1. (1)0.9
2. (2)0.1
3. (3)0.337
4. (4)0.663
We corrected a printing error in the original paper
Answer corrected; the source key is (4) — 0.663 is the mole fraction of water; $\ce{H2SO4}$ = 147/98 = 1.5 mol, water = 53/18 = 2.94 mol, so x( $\ce{H2SO4}$ ) = 0.337.
Q2 · MCQ · HydrocarbonsOpen
Consider the following reaction :
The product Y formed is :
1. (1)2-methylhex-2-yne
2. (2)5-methylhex-2-yne
3. (3)2-methylhex-3-yne
4. (4)Isopropylbut-1-yne
Q3 · MCQ · Some Basic ConceptsOpen
$\ce{A + 2B -> AB2}$
36.0 g of ‘A' (Molar mass : 60 g mol $^{-1}$ ) and 56.0 g of ‘B' (Molar mass : 80 g mol $^{-1}$ ) are allowed to react. Which of the following statements are correct ?
- (A)‘A' is the limiting reagent
- (B)77.0 g of $\ce{AB2}$ is formed
- (C)Molar mass of $\ce{AB2}$ is 140 g 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 :
1. (1)C and D only
2. (2)A and C only
3. (3)B and D only
4. (4)A and B only
We corrected a printing error in the original paper
Source printed “limting reagent” in statement A.
Q4 · MCQ · d- and f-BlockOpen
Given below are two statements :
Statement-I : The first ionization enthalpy of Cr is lower than that of Mn.
Statement-II : The second and third ionization enthalpies of Cr are higher than those of Mn.
In the light of the above statements, choose the correct answer from the options given below :
1. (1)Both Statement-I and Statement-II are false.
2. (2)Statement-I is true but Statement-II is false.
3. (3)Both Statement-I and Statement-II are true.
4. (4)Statement-I is false but Statement-II is true.
We corrected a printing error in the original paper
Source printed the label “Statement-I L:” (stray letter).
Q5 · MCQ · AminesOpen
The final product [B] is :
1. (1)
2. (2)
3. (3)
4. (4)
Q6 · MCQ · Purification & CharacterisationOpen
When 1 g of compound (X) is subjected to Kjeldahl's method for estimation of nitrogen, 15 mL, 1M $\ce{H2SO4}$ was neutralized by ammonia evolved. The percentage of nitrogen in compound (X) is :
1. (1)21
2. (2)0.42
3. (3)42
4. (4)0.21
Q7 · MCQ · Chemical KineticsOpen
Correct statements regarding Arrhenius equation among the following are :
- (A)Factor $\mathrm{e}^{-\mathrm{Ea}/\mathrm{RT}}$ 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 $^\circ$ C doubles the rate of reaction.
- (D)Plot of log k vs $\dfrac{1}{\mathrm{T}}$ gives a straight line with slope $= -\dfrac{\mathrm{Ea}}{\mathrm{R}}$ .
Choose the correct answer from the options given below :
1. (1)B and D only
2. (2)A and B only
3. (3)A and C only
4. (4)B and C only
Q8 · MCQ · Organic Basics (GOC)Open
The IUPAC name of the following compound is :
1. (1)n-propyl-2-bromo-5-methylheptanoate
2. (2)2-bromo-5-methylhexylpropanoate
3. (3)2-bromo-5-methylpropanoate
4. (4)n-propyl-1-bromo-4-methylhexanoate
We corrected a printing error in the original paper
Source printed “the following comopound”.
Q9 · MCQ · p-Block (15–18)Open
Given below are two statements :
Statement-I : Element ‘X' and ‘Y' are the most and least electronegative elements, respectively among N, As, Sb and P. The nature of the oxides $\ce{X2O3}$ and $\ce{Y2O3}$ is acidic and amphoteric, respectively.
Statement-II : $\ce{BCl3}$ is covalent in nature and gets hydrolysed in water. It produces $\ce{[B(OH)4]^-}$ and $\ce{[B(H2O)6]^{3+}}$ in aqueous medium.
In the light of the above statements, choose the correct answer from the options given below :
1. (1)Both Statement-I and Statement-II are true.
2. (2)Statement-I is true but Statement-II is false.
3. (3)Both Statement-I and Statement-II are false.
4. (4)Statement-I is false but Statement-II is true.

Match List-I with List-II.

List-I	List-II
Reaction of glucose with	Product formed
A. Hydroxylamine	I. Gluconic acid
B. $\ce{Br2}$ water	II. Glucose pentaacetate
C. Excess acetic anhydride	III. Saccharic acid
D. Concentrated $\ce{HNO3}$	IV. Glucoxime

Choose the correct answer from the options given below :

(1)A-I, B-III, C-IV, D-II
(2)A-IV, B-I, C-II, D-III
(3)A-III, B-I, C-IV, D-II
(4)A-IV, B-III, C-II, D-I

We corrected a printing error in the original paper

Source printed “Glouconic acid” and “Glucose pentacetate”.

Q11 · MCQ · Chemical BondingOpen
Among $\ce{H2S}$ , $\ce{H2O}$ , $\ce{NF3}$ , $\ce{NH3}$ and $\ce{CHCl3}$ , identify the molecule (X) with lowest dipole moment value. The number of lone pairs of electrons present on the central atom of the molecule (X) is :
1. (1)2
2. (2)0
3. (3)1
4. (4)3
Q12 · MCQ · Classification & PeriodicityOpen
Given below are two statements :
Statement-I : C $<$ O $<$ N $<$ F is the correct order in terms of first ionization enthalpy values.
Statement-II : S $>$ Se $>$ Te $>$ Po $>$ O is the correct order in terms of the magnitude of electron gain enthalpy values.
In the light of the above statements, choose the correct answer from the options given below :
1. (1)Statement-I is false but Statement-II is true
2. (2)Both Statement-I and Statement-II are true.
3. (3)Both Statement-I and Statement-II are false.
4. (4)Statement-I is true but Statement-II is false.
Q13 · MCQ · EquilibriumOpen
Which of the following mixture gives a buffer solution with pH = 9.25 ?
Given : p $K_\mathrm{b}$ ( $\ce{NH4OH}$ ) = 4.75
1. (1)0.2M $\ce{NH4OH}$ (0.4 L) + 0.1M HCl (1L)
2. (2)0.2M $\ce{NH4OH}$ (0.5 L) + 0.1M HCl (0.5 L)
3. (3)0.5M $\ce{NH4OH}$ (0.2 L) + 0.2M HCl (0.5 L)
4. (4)0.4M $\ce{NH4OH}$ (1 L) + 0.1M HCl (1L)
Q14 · MCQ · Structure of AtomOpen
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 :
1. (1) $x^2$
2. (2) $\dfrac{x}{1.35}$
3. (3) $2x$
4. (4) $1.35\,x$
Q15 · MCQ · Practical / Qualitative AnalysisOpen
Identify the correct statements :
- (A)Hydrated salts can be used as primary standard.
- (B)Primary standard should not undergo any reaction with air.
- (C)Reactions of primary standard with another substance should be instantaneous and stoichiometric.
- (D)Primary standard should not be soluble in water.
- (E)Primary standard should have low relative molar mass.
Choose the correct answer from the options given below :
1. (1)A, B, C and E only
2. (2)A, B, and C only
3. (3)A, B and E only
4. (4)D and E only
Q16 · MCQ · Coordination CompoundsOpen
$\ce{[Ni(PPh3)2Cl2]}$ 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 $\ce{Ni(CO)4}$ .
Choose the correct answer from the options given below :
1. (1)A and B only
2. (2)A, B and D only
3. (3)C and D only
4. (4)C, D and E only
Q17 · MCQ · ElectrochemistryOpen
Consider the following reduction processes :
$\ce{Al^3+ + 3e- -> Al(s)}$ , $E^\circ = -1.66$ V
$\ce{Fe^3+ + e- -> Fe^2+}$ , $E^\circ = +0.77$ V
$\ce{Co^3+ + e- -> Co^2+}$ , $E^\circ = +1.81$ V
$\ce{Cr^3+ + 3e- -> Cr(s)}$ , $E^\circ = -0.74$ V
The tendency to act as reducing agent decreases in the order :
1. (1)Al $>$ Cr $>$ $\ce{Fe^2+}$ $>$ $\ce{Co^2+}$
2. (2)Al $>$ $\ce{Fe^2+}$ $>$ Cr $>$ $\ce{Co^2+}$
3. (3)Al $>$ Cr $>$ $\ce{Co^2+}$ $>$ $\ce{Fe^2+}$
4. (4)Cr $>$ $\ce{Fe^2+}$ $>$ Al $>$ $\ce{Co^2+}$
Q18 · MCQ · Aldehydes, Ketones & AcidsOpen
The compound A, $\ce{C8H8O2}$ reacts with acetophenone to form a single product via cross-Aldol condensation. The compound A on reaction with conc. NaOH forms a substituted benzyl alcohol. The compound A is :
1. (1)2-hydroxy acetophenone
2. (2)4-methoxy benzaldehyde
3. (3)4-hydroxy benzylaldehyde
4. (4)4-methyl benzoic acid
We corrected a printing error in the original paper
Source printed “forms a substituted benzyl alcohol as” (the question asked for A was missing; no option is a benzyl alcohol) and, in option (2), “4-methyoxy benzaldehyde”.
Q19 · MCQ · Alcohols, Phenols & EthersOpen
3, 3-Dimethyl-2-butanol cannot be prepared by :
- (A)
- (B)
- (C)
- (D)
- (E)
Choose the correct answer from the options given below :
1. (1)B only
2. (2)B and E only
3. (3)B and C only
4. (4)B, C and E only
We corrected a printing error in the original paper
Source printed “3, 3-Dimenthyl-2-butanol”.
Q20 · MCQ · HydrocarbonsOpen
The dibromo compound [P] (molecular formula : $\ce{C9H10Br2}$ ) when heated with excess sodamide followed by treatment with dilute HCl gives [Q]. On warming [Q] with mercuric sulphate and dilute sulphuric acid yields [R] which gives positive Iodoform test but negative Tollen's test. The compound [P] is :
1. (1)
2. (2)
3. (3)
4. (4)
We corrected a printing error in the original paper
Source printed “dilute sulphuric acid yield [R]”.
Q21 · Numerical · ElectrochemistryOpen
Consider the following electrochemical cell :
Pt $\mid$ $\ce{O2}$ (g) (1bar) $\mid$ HCl (aq) $\parallel$ $\ce{M^2+}$ (aq, 1.0 M) $\mid$ M(s)
The pH above which, oxygen gas would start to evolve at anode is (nearest integer).
[Given : $E^{0}_{\mathrm{M^{2+}/M}} = 0.994$ V and $E^{0}_{\mathrm{O_2/H_2O}} = 1.23$ V (standard reduction potential) and $\dfrac{RT}{F}(2.303) = 0.059$ V at the given condition]
Q22 · Numerical · ThermodynamicsOpen
If the enthalpy of sublimation of Li is 155 kJ mol $^{-1}$ , enthalpy of dissociation of $\ce{F2}$ is 150 kJ mol $^{-1}$ , ionization enthalpy of Li is 520 kJ mol $^{-1}$ , electron gain enthalpy of F is $-313$ kJ mol $^{-1}$ , standard enthalpy of formation of LiF is $-594$ kJ mol $^{-1}$ . The magnitude of lattice enthalpy of LiF is kJ mol $^{-1}$ (Nearest integer).
Q23 · Numerical · d- and f-BlockOpen
Among the following oxides of 3d elements, the number of mixed oxides is .
$\ce{Ti2O3}$ , $\ce{V2O4}$ , $\ce{Cr2O3}$ , $\ce{Mn3O4}$ , $\ce{Fe3O4}$ , $\ce{Fe2O3}$ , $\ce{Co3O4}$
We corrected a printing error in the original paper
Source printed “the number of mixed oxides are”.
Q24 · Numerical · AminesOpen
The mass of benzanilide obtained from the benzoylation reaction of 5.8 g of aniline, if yield of product is 82%, is g (nearest integer).
(Given molar mass in g mol $^{-1}$ H:1, C:12, N:14, O:16)
Q25 · Numerical · Chemical KineticsOpen
Consider $\ce{A ->[$k_1$] B}$ and $\ce{C ->[$k_2$] D}$ are two reactions. If the rate constant ( $k_1$ ) of the $\ce{A -> B}$ reaction can be expressed by the following equation $\log_{10} k = 14.34 - \dfrac{1.5\times10^{4}}{T/\mathrm{K}}$ and activation energy of $\ce{C -> D}$ reaction (Ea $_2$ ) is $\dfrac{1}{5}$ th of the $\ce{A -> B}$ reaction (Ea $_1$ ), then the value of (Ea $_2$ ) is kJ mol $^{-1}$ . (Nearest Integer)

Maths

Q1 · MCQ · Matrices & DeterminantsOpen
Let $n$ be the number obtained on rolling a fair die. If the probability that the system
$\begin{align*} x - ny + z &= 6\\ x + (n-2)y + (n+1)z &= 8\\ (n-1)y + z &= 1 \end{align*}$
Has a unique solution is $\dfrac{k}{6}$ , then the sum of $k$ and all possible values of $n$ is:
1. (1)21
2. (2)24
3. (3)20
4. (4)22
Q2 · MCQ · StatisticsOpen
If the mean deviation about the median of the numbers $k, 2k, 3k, \ldots, 1000k$ is 500, then $k^2$ is equal to:
1. (1)16
2. (2)4
3. (3)1
4. (4)9
Q3 · MCQ · Sets, Relations & FunctionsOpen
The number of elements in the relation $R = \{(x, y) : 4x^2 + y^2 < 52,\ x, y \in \mathbb{Z}\}$ is
1. (1)77
2. (2)89
3. (3)67
4. (4)86
Q4 · MCQ · Complex NumbersOpen
Let $S = \left\{z \in \mathbb{C} : 4z^2 + \bar{z} = 0\right\}$ . Then $\displaystyle\sum_{z\in S}\lvert z\rvert^2$ is equal to:
1. (1) $\dfrac{3}{16}$
2. (2) $\dfrac{7}{64}$
3. (3) $\dfrac{1}{16}$
4. (4) $\dfrac{5}{64}$
Q5 · MCQ · Limits, Continuity & DifferentiabilityOpen
If $\displaystyle\lim_{x\to0}\frac{e^{(a-1)x} + 2\cos bx + (c-2)e^{-x}}{x\cos x - \log_e(1+x)} = 2$ , then $a^2 + b^2 + c^2$ is equal to:
1. (1)5
2. (2)3
3. (3)7
4. (4)9
Q6 · MCQ · Differential EquationsOpen
If $y = y(x)$ satisfies the differential equation $16\left(\sqrt{x}\,\sqrt{9+\sqrt{x}}\right)\left(4 + \sqrt{9 + \sqrt{x}}\right)\cos y\,dy = (1 + 2\sin y)\,dx,\quad x > 0$ and $y(256) = \dfrac{\pi}{2}$ , $y(49) = \alpha$ , then $2\sin\alpha$ is equal to:
1. (1) $2\sqrt2 - 1$
2. (2) $2\left(\sqrt2 - 1\right)$
3. (3) $3\left(\sqrt2 - 1\right)$
4. (4) $\sqrt2 - 1$
We corrected a printing error in the original paper
Source printed the first factor as “ $\sqrt{x + 9\sqrt{x}}$ ”, with which none of the options is correct ( $2\sin\alpha \approx 1.466$ ); corrected to the intended “ $\sqrt{x}\,\sqrt{9+\sqrt{x}}$ ” (the source's own solution integrates with this factor), which gives the printed key (1).
Q7 · MCQ · Straight LinesOpen
Among the statements
- (S1): If $A(5, -1)$ and $B(-2, 3)$ are two vertices of a triangle, whose orthocentre is $(0, 0)$ , then its third vertex is $(-4, -7)$ and
- (S2): If positive numbers $2a$ , $b$ , $c$ are three consecutive terms of an A.P., then the lines $ax + by + c = 0$ are concurrent at $(2, -2)$ ,
1. (1)Only (S1) is correct
2. (2)Only (S2) is correct
3. (3)Both are incorrect
4. (4)Both are correct
Q8 · MCQ · VectorsOpen
Let $\vec a = 2\hat i - \hat j + \hat k$ and $\vec b = \lambda\hat j + 2\hat k$ , $\lambda \in \mathbb{Z}$ be two vectors, Let $\vec c = \vec a\times\vec b$ and $\vec d$ be a vector of magnitude 2 in $yz$ -plane. If $\lvert\vec c\rvert = \sqrt{53}$ , then the maximum possible value of $\left(\vec c\cdot\vec d\right)^2$ is equal to:
1. (1)26
2. (2)104
3. (3)208
4. (4)52
Q9 · MCQ · Matrices & DeterminantsOpen
If $X = \begin{bmatrix} x\\ y\\ z\end{bmatrix}$ is a solution of the system of equations $AX = B$ , where $\operatorname{adj} A = \begin{bmatrix} 4 & 2 & 2\\ -5 & 0 & 5\\ 1 & -2 & 3\end{bmatrix} \quad\text{and}\quad B = \begin{bmatrix} 4\\ 0\\ 2\end{bmatrix},$ then $\lvert x + y + z\rvert$ is equal to:
1. (1)3
2. (2) $\dfrac32$
3. (3)1
4. (4)2
Q10 · MCQ · 3D GeometryOpen
Let $L$ be the line $\dfrac{x+1}{2} = \dfrac{y+1}{3} = \dfrac{z+3}{6}$ and let $S$ be the set of all points $(a, b, c)$ on $L$ , whose distance from the line $\dfrac{x+1}{2} = \dfrac{y+1}{3} = \dfrac{z-9}{0}$ along the line $L$ is 7. Then $\displaystyle\sum_{(a,b,c)\in S}(a + b + c)$ is equal to:
1. (1)34
2. (2)28
3. (3)40
4. (4)6
Q11 · MCQ · Conic SectionsOpen
Let $P\left(10, 2\sqrt{15}\right)$ be a point on the hyperbola $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ , whose foci are $S$ and $S'$ . If the length of its latus rectum is 8, then the square of the area of $\Delta PSS'$ is equal to:
1. (1)4200
2. (2)900
3. (3)1462
4. (4)2700
Q12 · MCQ · Area under CurvesOpen
The area of the region $A = \{(x, y) : 4x^2 + y^2 \le 8 \text{ and } y^2 \le 4x\}$ is:
1. (1) $\dfrac{\pi}{2} + 2$
2. (2) $\pi + \dfrac23$
3. (3) $\pi + 4$
4. (4) $\dfrac{\pi}{2} + \dfrac13$
Q13 · MCQ · Quadratic EquationsOpen
Let $\alpha, \beta$ be the roots of the quadratic equation $12x^2 - 20x + 3\lambda = 0$ , $\lambda \in \mathbb{Z}$ . If $\dfrac12 \le \lvert\beta - \alpha\rvert \le \dfrac32$ , then the sum of all possible values of $\lambda$ is:
1. (1)6
2. (2)1
3. (3)3
4. (4)4
Q14 · MCQ · Sets, Relations & FunctionsOpen
Let the domain of the function $f(x) = \log_3\log_5\left(7 - \log_2(x^2 - 10x + 85)\right) + \sin^{-1}\left(\left\lvert\dfrac{3x - 7}{17 - x}\right\rvert\right)$ be $(\alpha, \beta]$ . Then $\alpha + \beta$ is equal to:
1. (1)10
2. (2)12
3. (3)9
4. (4)8
Q15 · MCQ · Limits, Continuity & DifferentiabilityOpen
Let $[\,\bullet\,]$ denote the greatest integer function, and let $f(x) = \min\left\{\sqrt2 x, x^2\right\}$ . Let $S = \{x \in (-2, 2) : \text{the function } g(x) = \lvert x\rvert\left[x^2\right] \text{ is discontinuous at } x\}$ . Then $\displaystyle\sum_{x\in S} f(x)$ equals:
1. (1) $2 - \sqrt2$
2. (2) $2\sqrt6 - 3\sqrt2$
3. (3) $1 - \sqrt2$
4. (4) $\sqrt6 - 2\sqrt2$
Q16 · MCQ · Conic SectionsOpen
Let $S$ and $S'$ be the foci of the ellipse $\dfrac{x^2}{25} + \dfrac{y^2}{9} = 1$ and $P(\alpha, \beta)$ be a point on the ellipse in the first quadrant. If $(SP)^2 + (S'P)^2 - SP\cdot S'P = 37$ , then $\alpha^2 + \beta^2$ is equal to:
1. (1)15
2. (2)11
3. (3)17
4. (4)13
Q17 · MCQ · Conic SectionsOpen
Let the locus of the mid-point of the chord through the origin $O$ of the parabola $y^2 = 4x$ be the curve $S$ . Let $P$ be any point on $S$ . Then the locus of the point, which internally divides $OP$ in the ratio $3:1$ , is:
1. (1) $3y^2 = 2x$
2. (2) $2y^2 = 3x$
3. (3) $3x^2 = 2y$
4. (4) $2x^2 = 3y$
Q18 · MCQ · Sets, Relations & FunctionsOpen
Let $f(x) = [x]^2 - [x + 3] - 3$ , $x \in \mathbb{R}$ where $[\,\bullet\,]$ is the greatest integer function. Then
1. (1) $f(x) > 0$ only for $x \in [4, \infty)$
2. (2) $f(x) < 0$ only for $x \in [-1, 3)$
3. (3) $\displaystyle\int_0^2 f(x)\,dx = -6$
4. (4) $f(x) = 0$ for finitely many values of $x$ .
Q19 · MCQ · Sets, Relations & FunctionsOpen
Let $f$ and $g$ be functions satisfying $f(x+y) = f(x)f(y)$ , $f(1) = 7$ and $g(x+y) = g(xy)$ , $g(1) = 1$ , for all $x, y \in \mathbb{N}$ . If $\displaystyle\sum_{x=1}^{n}\left(\frac{f(x)}{g(x)}\right) = 19607$ , then $n$ is equal to:
1. (1)7
2. (2)5
3. (3)6
4. (4)4
We corrected a printing error in the original paper
Source printed “ $f(l) = 7$ ” and “ $g(l) = 1$ ” (letter l for the number 1); the missing “If” added before “ $\sum \ldots = 19607$ ”.
Q20 · MCQ · Binomial TheoremOpen
Let $C_r$ denote the coefficient of $x^r$ in the binomial expansion of $(1 + x)^n$ , $n \in \mathbb{N}$ , $0 \le r \le n$ . If $P_n = C_0 - C_1 + \frac{2^2}{3}C_2 - \frac{2^3}{4}C_3 + \cdots + \frac{(-2)^n}{n+1}C_n,$ then the value of $\displaystyle\sum_{n=1}^{25}\frac{1}{P_{2n}}$ equals.
1. (1)580
2. (2)525
3. (3)650
4. (4)675
Q21 · Numerical · VectorsOpen
Let a vector $\vec a = \sqrt2\hat i - \hat j + \lambda\hat k$ , $\lambda > 0$ , make an obtuse angle with the vector $\vec b = -\lambda^2\hat i + 4\sqrt2\hat j + 4\sqrt2\hat k$ and an angle $\theta$ , $\dfrac{\pi}{6} < \theta < \dfrac{\pi}{2}$ , with the positive $z$ -axis. If the set of all possible values of $\lambda$ is $(\alpha, \beta) - \{\gamma\}$ , then $\alpha + \beta + \gamma$ is equal to .
Q22 · Numerical · Definite IntegrationOpen
Let $[\,\bullet\,]$ be the greatest integer function. If $\alpha = \displaystyle\int_0^{64}\left(x^{1/3} - \left[x^{1/3}\right]\right)dx$ , then $\frac{1}{\pi}\int_0^{\alpha\pi}\left(\frac{\sin^2\theta}{\sin^6\theta + \cos^6\theta}\right)d\theta$ is equal to .
Q23 · Numerical · TrigonometryOpen
Let $\cos(\alpha + \beta) = -\dfrac{1}{10}$ and $\sin(\alpha - \beta) = \dfrac38$ , where $0 < \alpha < \dfrac{\pi}{3}$ and $0 < \beta < \dfrac{\pi}{4}$ . If $\tan2\alpha = \dfrac{3\left(1 - r\sqrt5\right)}{\sqrt{11}\left(s + \sqrt5\right)}$ , $r, s \in \mathbb{N}$ , then $r + s$ is equal to .
Q24 · Numerical · Sequences & SeriesOpen
Suppose $a, b, c$ are in A.P. and $a^2, 2b^2, c^2$ are in G.P. If $a < b < c$ and $a + b + c = 1$ , then $9(a^2 + b^2 + c^2)$ is equal to .
Q25 · Numerical · Permutations & CombinationsOpen
Let $S$ be the set of the first 11 natural numbers. Then the number of elements in $A = \{B \subseteq S : n(B) \ge 2 \text{ and the product of all elements of } B \text{ is even}\}$ is .

Inputs				Output
A	B	C	D	Y
1	1	0	1	1
0	0	1	1	0
1	0	1	0	1
1	1	1	1	0

Inputs				Output
A	B	C	D	Y
1	1	0	1	1
0	0	1	1	0
1	0	1	0	0
1	1	1	1	1

Inputs				Output
A	B	C	D	Y
1	1	0	1	0
0	0	1	1	0
1	0	1	0	1
1	1	1	1	1

Inputs				Output
A	B	C	D	Y
1	1	0	1	0
0	0	1	1	1
1	0	1	0	1
1	1	1	1	1