JEE Main 2 Apr 2026, Shift 2

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

Physics

Q1 · MCQ · Units and MeasurementsOpen
Dimensions of universal gravitational constant (G) in terms of Planck's constant ( $h$ ), distance ( $L$ ), mass ( $M$ ) and time ( $T$ ) are .
1. (1) $[\mathrm{hTLM^{-2}}]$
2. (2) $[\mathrm{hT^{-1}LM^{-2}}]$
3. (3) $[\mathrm{hTL^{2}M^{-2}}]$
4. (4) $[\mathrm{h^{-1}T^{-1}LM^{-2}}]$
Q2 · MCQ · Circular MotionOpen
A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is 5 rad/s. The coefficient of friction between the drum's inner wall surface and mass is . (Take $g = 10\ \mathrm{m/s^2}$ )
1. (1)0.1
2. (2)0.5
3. (3)0.7
4. (4)0.3
Q3 · MCQ · Newton's Laws of MotionOpen
Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass in 2 s is m. (Take $g = 10\ \mathrm{m/s^2}$ )
1. (1)3.33
2. (2)3.12
3. (3)2.22
4. (4)1.42
Q4 · MCQ · Moving Charges and MagnetismOpen
A particle having charge $10^{-9}$ C moving in $x$ – $y$ plane in fields of $0.4\,\hat{\jmath}$ N/C and $4\times10^{-3}\,\hat{k}$ T experiences a force of $\left(4\hat{\imath} + 2\hat{\jmath}\right)\times10^{-10}$ N. The velocity of the particle at that instant is m/s.
1. (1) $50\hat{\imath} + 100\hat{\jmath}$
2. (2) $100\hat{\imath} + 50\hat{\jmath}$
3. (3) $-50\hat{\imath} + 100\hat{\jmath}$
4. (4) $50\hat{\imath} - 100\hat{\jmath}$
We corrected a printing error in the original paper
Source printed the magnetic field as “ $4\times10^{-3}\ k$ T” (unit vector $k$ without a hat).
Q5 · MCQ · Semiconductor ElectronicsOpen
If X and Y are the inputs, the given circuit works as .
1. (1)OR gate
2. (2)AND gate
3. (3)NAND gate
4. (4)NOR gate
Q6 · MCQ · GravitationOpen
If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy ( $k$ ) on reaching the surface of earth. The values of v and k respectively are . (Take radius of earth to be 6400 km and $g = 9.8\ \mathrm{m/s^2}$ )
1. (1)11.2 km/s; $6.27\times10^{7}$ J
2. (2)11.2 km/s; $12.54\times10^{7}$ J
3. (3)8.8 km/s; $6.27\times10^{7}$ J
4. (4)8.8 km/s; $12.54\times10^{7}$ J
Q7 · MCQ · Units and MeasurementsOpen
In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are 100 divisions in circular scale and pitch of screw gauge is 0.1 mm. When diameter of a sphere is measured, the reading of main scale is 5 mm and $50^{\text{th}}$ division of circular scale coincides with the reference line of main scale. The diameter of sphere is mm.
1. (1)5.045
2. (2)5.055
3. (3)5.450
4. (4)5.550
Q8 · MCQ · Mechanical Properties of FluidsOpen
The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is $\alpha\pi\times10^{-4}$ J. The value of $\alpha$ is . (Take $\pi = 3.14$ )
1. (1)0.86
2. (2)0.64
3. (3)1.92
4. (4)7.68
Q9 · MCQ · Kinetic Theory of GasesOpen
A mixture of carbon dioxide and oxygen has volume $8310\ \mathrm{cm^3}$ , temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are . (Assume both carbon dioxide and oxygen gases behave like ideal gases) [ $R = 8.31$ J/mol.K]
1. (1)0.15 and 0.18
2. (2)0.25 and 0.08
3. (3)0.21 and 0.12
4. (4)0.13 and 0.20
We corrected a printing error in the original paper
Source printed “carbondioxide”.
Q10 · MCQ · Mechanical Properties of FluidsOpen
If an air bubble of diameter 2 mm rises steadily through a liquid of density $2000\ \mathrm{kg/m^3}$ at a rate of 0.5 cm/s, then the coefficient of viscosity of liquid is Poise. (Take $g = 10\ \mathrm{m/s^2}$ )
1. (1)0.88
2. (2)8.8
3. (3)88.8
4. (4)0.088
Q11 · MCQ · Work, Energy and PowerOpen
A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is N. (Take $g = 10\ \mathrm{m/s^2}$ )
1. (1)1980
2. (2)2020
3. (3)2000
4. (4)1000
We corrected a printing error in the original paper
Assumption “(Take $g = 10\ \mathrm{m/s^2}$ )” added; the source leaves it unstated, and with $g = 9.8\ \mathrm{m/s^2}$ option (1) would be correct.
Q12 · MCQ · Electromagnetic WavesOpen
An electromagnetic wave travels in free space along the $x$ -direction. At a particular point in space and time, $\vec{B} = 2\times10^{-7}\,\hat{\jmath}$ T is associated with this wave. The value of corresponding electric field $\vec{E}$ at this point is V/m.
1. (1) $60\,\hat{k}$
2. (2) $-60\,\hat{k}$
3. (3) $30\,\hat{k}$
4. (4) $-600\,\hat{k}$
Q13 · MCQ · Current ElectricityOpen
Two resistors of $200\ \Omega$ and $400\ \Omega$ are connected in series with a battery of 100 V. A bulb rated at 200 V, 100 W is connected across the $400\ \Omega$ resistance. The potential drop across the bulb is V.
1. (1)25
2. (2)50
3. (3)66.6
4. (4)100
Q14 · MCQ · Electric Charges and FieldsOpen
Two metal plates (A, B) are kept horizontally with separation of $\left(\dfrac{12}{\pi}\right)$ cm, with plate A on the top. An atomizer jet sprays oil (density $1.5\ \mathrm{g/cm^3}$ ) droplets of radius 1 mm horizontally. All oil droplets carry a charge 5 nC. The potentials $V_A$ and $V_B$ are required on plates A and B respectively in order to ensure the droplets do not descend. The values of $V_A$ and $V_B$ are . (Neglect the air resistance to the droplets and take $g = 10\ \mathrm{m/s^2}$ )
1. (1)100 V and 580 V
2. (2)580 V and 100 V
3. (3)60 V and 400 V
4. (4)0 V and $-200$ V
Q15 · MCQ · Electric Charges and FieldsOpen
Two point charges $8\ \mu$ C and $-2\ \mu$ C are located at $x = 2$ cm and $x = 4$ cm, respectively on the x-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is .
1. (1) $4:1$
2. (2) $3:4$
3. (3) $4:3$
4. (4) $4:5$
Q16 · MCQ · Ray OpticsOpen
One side of an equilateral prism is painted by a transparent material of refractive index $n_2$ . The refractive index of prism is 1.6. The maximum value of $n_2$ required for total internal reflection from painted face is .
1. (1) $\dfrac{3\sqrt3}{1.6}$
2. (2) $\sqrt3$
3. (3) $\dfrac{3.2}{\sqrt3}$
4. (4) $\dfrac{4\sqrt3}{5}$
We corrected a printing error in the original paper
Source printed “minimum value of $n_2$ ”; corrected to the intended “maximum value of $n_2$ ” (TIR at the painted face needs $n_2 \le 1.6\sin60^\circ$ ).
Q17 · MCQ · Alternating CurrentOpen
The figure given below shows an LCR series circuit with two switches $S_1$ and $S_2$ . When switch $S_1$ is closed keeping $S_2$ open, the phase difference ( $\phi$ ) between the current and source voltage is $30^\circ$ and phase difference is $60^\circ$ when $S_2$ is closed keeping $S_1$ open. The value of $(3L_1 - L_2)$ is H.
1. (1) $\dfrac92$
2. (2) $\dfrac29$
3. (3) $\dfrac13$
4. (4)3
Q18 · MCQ · Electromagnetic InductionOpen
A circular current loop of radius R is placed inside square loop of side length L ( $L \gg R$ ) such that they are co-planar and their centers coincide. The permeability of free space is $\mu_0$ . The mutual inductance between circular loop and square loop is .
1. (1) $2\sqrt2\,\dfrac{\mu_0 L^2}{R}$
2. (2) $\sqrt2\,\dfrac{\mu_0 L^2}{R}$
3. (3) $\sqrt2\,\dfrac{\mu_0 R^2}{L}$
4. (4) $2\sqrt2\,\dfrac{\mu_0 R^2}{L}$
Q19 · MCQ · NucleiOpen
The binding energy per nucleon of $^{209}_{\ 83}\mathrm{Bi}$ is MeV. [Take $m\left(^{209}_{\ 83}\mathrm{Bi}\right) = 208.980388$ u, $m_p = 1.007825$ u, $m_n = 1.008665$ u, $1\,\mathrm{u} = 931\ \mathrm{MeV}/c^2$ ]
1. (1)7.48
2. (2)7.84
3. (3)8.79
4. (4)6.94
Q20 · MCQ · OscillationsOpen
The equation of motion of a particle is given by $x = a\sin\left(50t + \pi/3\right)$ cm. The particle will come to rest at time $t_1$ and it will have zero acceleration at time $t_2$ . The $t_1$ and $t_2$ respectively are .
1. (1) $\dfrac{\pi}{300}$ s, $\dfrac{\pi}{75}$ s
2. (2) $\dfrac{\pi}{75}$ s, $\dfrac{\pi}{300}$ s
3. (3) $\dfrac{\pi}{300}$ s, $\dfrac{\pi}{25}$ s
4. (4) $\dfrac{\pi}{50}$ s, $\dfrac{\pi}{100}$ s
Q21 · Numerical · Wave OpticsOpen
In a Young's double slit experiment, the intensity at some point on the screen is found to be $\dfrac34$ times of the maximum of the interference pattern. The path difference between the interfering waves at this point is $\dfrac{\lambda}{x}$ where $\lambda$ is wavelength of the incident light. The value of $x$ is .
Q22 · Numerical · AtomsOpen
Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the $2^{\text{nd}}$ and $4^{\text{th}}$ orbits of hydrogen atom .
We corrected a printing error in the original paper
Answer corrected; the source key is (64) — $B = \mu_0 I/2r$ with $I = ev/2\pi r$ gives $B \propto 1/n^5$ , so $B_2/B_4 = 2^5 = 32$ ; the source solution evaluates $4^5/2^5$ as 64.
Q23 · Numerical · ThermodynamicsOpen
5 moles of unknown gas is heated at constant volume from $10^\circ$ C to $20^\circ$ C. The molar specific heat of this gas at constant pressure $c_p = 8$ cal/mol. $^\circ$ C and $R = 8.36$ J/mol. $^\circ$ C. The change in the internal energy of the gas is calorie.
Q24 · Numerical · Ray OpticsOpen
If sunlight is focused on a paper using convex lens (take the lens to be equiconvex), it starts burning the paper in shortest time when the lens is kept at 30 cm above the paper. If the radius of curvature of the lens is 60 cm then the refractive index of the lens material is $\dfrac{\alpha}{10}$ . The value of $\alpha$ is .
We corrected a printing error in the original paper
Assumption “(take the lens to be equiconvex)” added; the source leaves the lens shape unstated (a plano-convex lens would give $\alpha = 30$ ).
Q25 · Numerical · Rotational MotionOpen
Moment of inertia about an axis AB for a rod of mass 40 kg and length 3 m is same as that of a solid sphere of mass of 10 kg and radius R about an axis parallel to AB axis with separation of 3 m as shown in figure below. The value of R is given as $\sqrt{\dfrac{\alpha}{2}}$ . The value of $\alpha$ is .

Chemistry

Q1 · MCQ · Some Basic ConceptsOpen
The ratio of mass percentage (w/w) of C : H in a hydrocarbon is 12 : 1. It has two carbon atoms. The weight (in g) of $\ce{CO2}$ (g) formed when 3.38 g of this hydrocarbon is completely burnt in oxygen is :
(Given : Molar mass in g mol $^{-1}$ C : 12, H : 1, O : 16)
1. (1)5.68
2. (2)11.44
3. (3)22.74
4. (4)17.05
Q2 · MCQ · EquilibriumOpen
The first and second ionization constants of a weak dibasic acid $\ce{H2A}$ are $8.1\times10^{-8}$ and $1.0\times10^{-13}$ respectively. 0.1 mol of $\ce{H2A}$ was dissolved in 1L of 0.1 M HCl solution. The concentration of $\ce{HA-}$ in the resultant solution is :
1. (1)0.1 M
2. (2) $9.53\times10^{-6}$ M
3. (3) $8.1\times10^{-8}$ M
4. (4) $1.0\times10^{-13}$ M
Q3 · MCQ · Chemical BondingOpen
$\ce{SF4}$ is isostructural with :
- (A) $\mathrm{BrF}_4^{\ominus}$
- (B) $\ce{CH4}$
- (C) $\mathrm{IF}_4^{\oplus}$
- (D) $\ce{XeF4}$
- (E) $\ce{XeO2F2}$
Choose the correct answer from the options given below :
1. (1)C only
2. (2)C and E only
3. (3)A and D only
4. (4)B and E only
Q4 · MCQ · ThermodynamicsOpen
Gas ‘A' undergoes change from state ‘X' to state ‘Y'. In this process, the heat absorbed and work done by the gas are 10 J and 18 J respectively. Now gas is brought back to state ‘X' by another process during which 6 J of heat is evolved. In the reverse process of ‘Y' to ‘X',
1. (1)18 J of the work is done by the gas ‘A'.
2. (2)2 J of the work is done by the gas ‘A'.
3. (3)12 J of the work is done on the gas ‘A' by the surrounding.
4. (4)14 J of the work is done on the gas ‘A' by the surrounding.
We corrected a printing error in the original paper
Source printed “the heat absorbed and work done by the gas is 10 J and 18 J”.
Q5 · MCQ · SolutionsOpen
Solution A is prepared by dissolving 1 g of a protein (molar mass = 50000 g mol $^{-1}$ ) in 0.5 L of water at 300 K. Its osmotic pressure is x bar. Solution B is made by dissolving 2 g of same protein in 1 L of water at 300 K. Osmotic pressure of solution B is y bar. Entire solution of A is mixed with entire solution of B at same temperature. The osmotic pressure of resultant solution is z bar. x, y and z respectively are :
( $R = 0.083$ L bar mol $^{-1}$ K $^{-1}$ )
1. (1) $9.96\times10^{-4}$ ; $9.96\times10^{-4}$ ; $9.96\times10^{-4}$
2. (2) $9.96\times10^{-4}$ ; $9.96\times10^{-4}$ ; $19.92\times10^{-4}$
3. (3) $4.98\times10^{-4}$ ; $4.98\times10^{-4}$ ; $9.96\times10^{-4}$
4. (4) $4.98\times10^{-4}$ ; $4.98\times10^{-4}$ ; $4.98\times10^{-4}$
Q6 · MCQ · EquilibriumOpen
At 25 $^\circ$ C, 20.0 mL of 0.2 M weak monoprotic acid HX is titrated against 0.2 M NaOH. The pH of the solution (a) at the start of the titration (when NaOH has not been added) and (b) when 10 mL of NaOH is added respectively, are :
Given : $K_\mathrm{a} = 5\times10^{-4}$ , p $K_\mathrm{a} = 3.3$ , $\alpha \ll 1$
1. (1)0.7, 2.0
2. (2)2.0, 3.3
3. (3)1.1, 2.2
4. (4)3.0, 2.2
Q7 · MCQ · Chemical KineticsOpen
Consider the reaction $\ce{aX -> bY}$ , for which the rate constant at 30 $^\circ$ C is $1\times10^{-3}$ mol $^{-1}$ L s $^{-1}$ . Which of the following statements are true ?
- (A)When concentration of ‘X' is increased to four times, the rate of reaction becomes 16 times.
- (B)The reaction is a second order reaction.
- (C)The half-life period is independent of the concentration of X.
- (D)Decomposition of $\ce{N2O5}$ is an example of the above reaction.
- (E) is valid for the above reaction.
Choose the correct answer from the options given below :
1. (1)A and B only
2. (2)A, B and C only
3. (3)A, B, D and E only
4. (4)C and D only
Q8 · MCQ · Classification & PeriodicityOpen
The correct set that contains all kinds (basic, acidic, amphoteric and neutral) of oxides is :
1. (1) $\ce{Na2O}$ , $\ce{K2O}$ , $\ce{Al2O3}$ and $\ce{As2O3}$
2. (2) $\ce{Al2O3}$ , $\ce{As2O3}$ , CO and NO
3. (3) $\ce{K2O}$ , $\ce{Cl2O7}$ , $\ce{As2O3}$ and NO
4. (4) $\ce{Na2O}$ , $\ce{N2O}$ , $\ce{Al2O3}$ and CO
Q9 · MCQ · Classification & PeriodicityOpen
Given below are two statements :
Statement-I : The second ionization enthalpy of B, Al and Ga is in the order of B $>$ Al $>$ Ga.
Statement-II : The correct order in terms of first ionization enthalpy is Si $<$ Ge $<$ Pb $<$ Sn.
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)Both Statement-I and Statement-II are false.
3. (3)Statement-I is true but Statement-II is false.
4. (4)Statement-I is false but Statement-II is true.
Q10 · MCQ · d- and f-BlockOpen
Given below are two statements :
Statement-I : Among Zn, Mn, Sc and Cu, the energy required to remove the third valence electron is highest for Zn and lowest for Sc.
Statement-II : The correct order of the following complexes in terms of CFSE is
$\ce{[Co(H2O)6]^2+}$ $<$ $\ce{[Co(H2O)6]^3+}$ $<$ $\ce{[Co(en)3]^3+}$ .
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)Both Statement-I and Statement-II are false.
3. (3)Statement-I is true but Statement-II is false.
4. (4)Statement-I is false but Statement-II is true.
Q11 · MCQ · Coordination CompoundsOpen
Which of the following complexes will show coordination isomerism ?
(Take coordination isomerism as the interchange of ligands between the cationic and anionic entities of different metals.)
- (A) $\ce{[Ag(NH3)2][Ag(CN)2]}$
- (B) $\ce{[Co(NH3)6][Cr(CN)6]}$
- (C) $\ce{[Co(NH3)6][Co(CN)6]}$
- (D) $\ce{[Fe(NH3)6][Co(CN)6]}$
- (E) $\ce{[Co(NH3)6][Fe(CN)6]}$
Choose the correct answer from the options given below :
1. (1)B, C and D Only
2. (2)B, D and E Only
3. (3)A, C and D Only
4. (4)C, D and E Only
We corrected a printing error in the original paper
Assumption “(Take coordination isomerism as the interchange of ligands between the cationic and anionic entities of different metals.)” added and answer corrected; the source states no definition and its key accepts (1), (2) and (4), since in the broad sense C (two Co centres) also qualifies and no option lists B, C, D and E; with the textbook definition only B, D and E qualify.
Q12 · MCQ · Purification & CharacterisationOpen
Complete combustion of X g of an organic compound gave 0.25 g of $\ce{CO2}$ and 0.12 g of $\ce{H2O}$ . If the % of carbon is 25% and of hydrogen is 4.89%, then X = $\times10^{-3}$ g. (Nearest integer)
(Molar mass of C, H and O are 12, 1 and 16 g mol $^{-1}$ respectively.)
1. (1)273
2. (2)27
3. (3)2730
4. (4)227
Q13 · MCQ · Organic Basics (GOC)Open
Given below are two statements :
Statement I : In
, the
carbocation is stabilised by +R effect of $\ce{-OCH3}$ group.
Statement II : In
, the
carbanion is stabilised by $-$ R effect of $\ce{-NO2}$ group.
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)Both Statement I and Statement II are false
3. (3)Statement I is true but Statement II is false
4. (4)Statement I is false but Statement II is true
Q14 · MCQ · HydrocarbonsOpen
The compound (X) on
- (i)on heating in the presence of anhydrous $\ce{AlCl3}$ and HCl gas gives 2, 4–dimethyl pentane
- (ii)aromatization gives toluene and
- (iii)cyclisation gives methyl cyclohexane
The correct name of compound (X) is :
1. (1)Hept-2-ene
2. (2)Hept-1,3,5-triene
3. (3)Heptane
4. (4)Hept-2,4,6-triene
Q15 · MCQ · Haloalkanes & HaloarenesOpen
Correct statements regarding alkyl halides (R–X) among the following are :
- (A)Alcohol being less polar solvent as compared to water, alcoholic KOH favours elimination reaction with R–X.
- (B)Order of reactivity towards S $_\mathrm{N}$ 1 mechanism is $\ce{C6H5-CH2-Cl}$ $>$ $\ce{C6H5-CHCl-C6H5}$ .
- (C)Non substituted aryl halides exhibit properties similar to alkyl halides.
- (D)Vinyl chloride is an example of haloalkene and allyl chloride is an example of haloalkyne.
- (E)R–Cl can be prepared by reacting R–OH with $\ce{SOCl2}$ but Ar–Cl cannot be prepared by reacting Ar–OH with $\ce{SOCl2}$ .
Choose the correct answer from the options given below :
1. (1)A, B and C Only
2. (2)B and D Only
3. (3)A and E Only
4. (4)D and E Only
Q16 · MCQ · Aldehydes, Ketones & AcidsOpen
An organic compound “x” where molar ratio of C, O and H are equal, on treatment with 50% KOH under reflux followed by acidification produced “y”. The most likely structure of “y” is:
[Molar mass of ‘x' is 58 g mol $^{-1}$ ]
1. (1)
2. (2) $\ce{CH3-CH=CH-CH=O}$
3. (3)
4. (4)
Q17 · MCQ · Aldehydes, Ketones & AcidsOpen
A molecule (X) with following structure under mild acidic condition is hydrolysed to produce (Y) and (Z). Identify the correct statements about (Y) and (Z).
- (A)Both (Y) and (Z) have same molar mass
- (B)(Y) and (Z) can be distinguished from each other by $\ce{NaHCO3}$
- (C)(Y) and (Z) react with HCN with same rates
- (D)(Y) and (Z) undergo addition reaction with 2, 4-DNP
Choose the correct answer from the options given below :
1. (1)A, B and C Only
2. (2)B and C Only
3. (3)C and D Only
4. (4)A and D Only
Q18 · MCQ · AminesOpen
Identify compounds A and E in the following reaction sequence.
1. (1)
2. (2)
3. (3)
4. (4)
Q19 · MCQ · BiomoleculesOpen
Identify the correct pair having amino acid (A) and the hormone (B) that is iodinated derivative of the amino acid (A).
(T and Y represent one letter code for amino acids)
Amino acid (A) – Hormone (B)
1. (1)T – Insulin
2. (2)T – Thyroxine
3. (3)Y – Thyroxine
4. (4)Y – Insulin
We corrected a printing error in the original paper
Source printed “Insuline” in options (1) and (4).
Q20 · MCQ · Practical / Qualitative AnalysisOpen
Among $\ce{Fe^2+}$ , $\ce{Fe^3+}$ , $\ce{Cr^2+}$ and $\ce{Zn^2+}$ , the ion that shows positive borax bead test and with highest ionisation enthalpy is:
1. (1) $\ce{Fe^2+}$
2. (2) $\ce{Zn^2+}$
3. (3) $\ce{Cr^2+}$
4. (4) $\ce{Fe^3+}$
Q21 · Numerical · Structure of AtomOpen
The surface of sodium metal is irradiated with radiation of wavelength x nm. The kinetic energy of ejected electrons is $2.8\times10^{-20}$ J. The work function of sodium is 2.3 eV. The value of x is $\times10^{2}$ nm. (Nearest integer)
(Given : $h = 6.6\times10^{-34}$ J s; 1eV $= 1.60\times10^{-19}$ J; $c = 3.0\times10^{8}$ m s $^{-1}$ )

Consider the following gas phase reaction being carried out in a closed vessel at 25 $^\circ$ C.

$\ce{2A(g) -> 4B(g) + C(g)}$

$\dfrac{\text{time}}{\text{(min)}}$	$\dfrac{\text{total pressure of the system}}{\text{(mm Hg)}}$
30	300
$\infty$	600

The pressure of C(g) at 30 minutes time interval would be mm Hg. (Nearest integer)

Q23 · Numerical · ElectrochemistryOpen
Consider the following two half-cell reactions along with the standard reduction potential given :
$\ce{CO2 + 6H+ + 6e- -> CH3OH + H2O}$ $E^\circ_\mathrm{red} = 0.02$ V
$\dfrac{1}{2}$ $\ce{O2 + 2H+ + 2e- -> H2O}$ $E^\circ_\mathrm{red} = 1.23$ V
The fuel cell was set up using the above two reactions such that the cell operates under the standard condition of 1 bar pressure and 298 K temperature. The fuel cell works with 80% efficiency. If the work derived from the cell using 1 mol of $\ce{CH3OH}$ is used to compress an ideal gas isothermally against a constant pressure of 1kPa, then the change in the volume of the gas, $\lvert\Delta V\rvert$ = m $^3$ . (Nearest integer)
Given : $F = 96500$ C mol $^{-1}$
We corrected a printing error in the original paper
Source printed “ $\Delta V$ =”; corrected to the intended magnitude “ $\lvert\Delta V\rvert$ =” (the gas is compressed, so $\Delta V = -560$ m $^3$ ; the key 560 is its magnitude).
Q24 · Numerical · d- and f-BlockOpen
Number of paramagnetic ions among the following d- and f-block metal ions is .
$\ce{Mn^2+}$ , $\ce{Cu^2+}$ , $\ce{Zn^2+}$ , $\ce{Yb^2+}$ , $\ce{Sc^3+}$ , $\ce{La^3+}$ , $\ce{Gd^3+}$ , $\ce{Lu^3+}$ , $\ce{Ti^4+}$ , $\ce{Ce^4+}$
(Atomic number of Mn = 25, Cu = 29, Zn = 30, Yb = 70, Sc = 21, La = 57, Gd = 64, Lu = 71, Ti = 22, Ce = 58)
Q25 · Numerical · AminesOpen
Consider the following reaction sequence
When the product (P) is subjected to Carius analysis using $\ce{AgNO3}$ , 1.0 g of the product (P) will produce g of the precipitate of AgBr. (Nearest integer)
(Given : molar mass in g mol $^{-1}$ C : 12, H : 1, O : 16, N : 14, Br : 80, Ag : 108)
We corrected a printing error in the original paper
Source printed “the following reactions sequence” and “(Nearest interger)”.

Maths

Q1 · MCQ · Quadratic EquationsOpen
Let $\alpha, \beta$ be the roots of the equation $x^2 - 3x + r = 0$ , and $\dfrac{\alpha}{2}, 2\beta$ be the roots of the equation $x^2 + 3x + r = 0$ . If the roots of the equation $x^2 + 6x = m$ are $2\alpha + \beta + 2r$ and $\alpha - 2\beta - \dfrac{r}{2}$ , then $m$ is equal to:
1. (1) $-135$
2. (2) $-567$
3. (3)135
4. (4)567
Q2 · MCQ · Complex NumbersOpen
Let the circles $C_1 : \lvert z\rvert = r$ and $C_2 : \lvert z - 3 - 4i\rvert = 5$ , $z \in \mathbb{C}$ , be such that $C_2$ lies within $C_1$ . If $z_1$ moves on $C_1$ , $z_2$ moves on $C_2$ and $\min\lvert z_1 - z_2\rvert = 2$ , then $\max\lvert z_1 - z_2\rvert$ is equal to:
1. (1)12
2. (2)17
3. (3)22
4. (4)24
We corrected a printing error in the original paper
Source printed “Let the circle $C_1$ … and $C_2$ …” (singular for two circles).
Q3 · MCQ · Matrices & DeterminantsOpen
If the system of equations
$\begin{align*} x + 5y + 6z &= 4,\\ 2x + 3y + 4z &= 7,\\ x + 6y + az &= b \end{align*}$
has infinitely many solutions, then the point $(a, b)$ lies on the line
1. (1) $y - x = 3$
2. (2) $x - y = 3$
3. (3) $x + y = 11$
4. (4) $x + y = 12$
Q4 · MCQ · Sequences & SeriesOpen
Let $a_1, a_2, a_3, \ldots$ be an A.P. and $g_1 = a_1, g_2, g_3, \ldots$ be an increasing G.P. If $a_1 = a_2 + g_2 = 1$ and $a_3 + g_3 = 4$ , then $a_{10} + g_5$ is equal to:
1. (1)81
2. (2)76
3. (3)62
4. (4)55
Q5 · MCQ · Sequences & SeriesOpen
The sum $\dfrac{1^3}{1} + \dfrac{1^3 + 2^3}{1 + 3} + \dfrac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \ldots$ up to 8 terms, is:
1. (1)70
2. (2)71
3. (3)72
4. (4)73
Q6 · MCQ · Permutations & CombinationsOpen
If for $3 \le r \le 30$ , $\left({}^{30}C_{30-r}\right) + 3\left({}^{30}C_{31-r}\right) + 3\left({}^{30}C_{32-r}\right) + \left({}^{30}C_{33-r}\right) = {}^{m}C_{r},$ then $m$ equals:
1. (1)31
2. (2)32
3. (3)33
4. (4)34
Q7 · MCQ · Permutations & CombinationsOpen
Let $p_n$ denote the total number of triangles formed by joining the vertices of an $n$ -sided regular polygon. If $p_{n+1} - p_n = 66$ , then the sum of all distinct prime divisors of $n$ is:
1. (1)7
2. (2)8
3. (3)5
4. (4)6
We corrected a printing error in the original paper
Source printed “an $n$ -side regular polygon”.
Q8 · MCQ · ProbabilityOpen
A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for each tail he throws. If the probability that he gets exactly 30 points is $\dfrac{m}{n}$ , $\gcd(m, n) = 1$ , then $m + n$ is equal to:
1. (1)53
2. (2)55
3. (3)107
4. (4)105
Q9 · MCQ · StatisticsOpen
The mean and variance of $n$ observations are 8 and 16, respectively. If the sum of the first $(n-1)$ observations is 48 and the sum of squares of the first $(n-1)$ observations is 496, then the value of $n$ is:
1. (1)21
2. (2)16
3. (3)13
4. (4)7
Q10 · MCQ · CirclesOpen
Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines $x + (k-1)y + 3 = 0$ and $2x + k^2y - 4 = 0$ . If the line $x - y + 2 = 0$ intersects the circle at the points $A$ and $B$ , then $(AB)^2$ is equal to:
1. (1)10
2. (2)27
3. (3)18
4. (4)34
Q11 · MCQ · Conic SectionsOpen
Let $O$ be the origin, and $P$ and $Q$ be two points on the rectangular hyperbola $xy = 12$ such that the mid point of the line segment $PQ$ is $\left(\dfrac12, -\dfrac12\right)$ . Then the area of the triangle $OPQ$ equals:
1. (1) $\dfrac32$
2. (2) $\dfrac52$
3. (3) $\dfrac72$
4. (4) $\dfrac92$
Q12 · MCQ · Quadratic EquationsOpen
Let the parabola $y = x^2 + px + q$ passing through the point $(1, -1)$ be such that the distance between its vertex and the $x$ -axis is minimum. Then the value of $p^2 + q^2$ is:
1. (1)2
2. (2)4
3. (3)5
4. (4)8
Q13 · MCQ · TrigonometryOpen
Let $P = \{\theta \in [0, 4\pi] : \tan^2\theta \neq 1\}$ and $S = \{a \in \mathbb{Z} : 2(\cos^8\theta - \sin^8\theta)\sec2\theta = a^2,\ \theta \in P\}.$ Then $n(S)$ is:
1. (1)0
2. (2)1
3. (3)2
4. (4)3
Q14 · MCQ · VectorsOpen
Let the vectors $\vec a = -\hat i + \hat j + 3\hat k$ and $\vec b = \hat i + 3\hat j + \hat k$ . For some $\lambda, \mu \in \mathbb{R}$ , let $\vec c = \lambda\vec a + \mu\vec b$ . If $\vec c\cdot(3\hat i - 6\hat j + 2\hat k) = 10$ and $\vec c\cdot(\hat i + \hat j + \hat k) = -2$ , then $\lvert\vec c\rvert^2$ is equal to:
1. (1)8
2. (2)12
3. (3)14
4. (4)15
Q15 · MCQ · 3D GeometryOpen
Let the point $A$ be the foot of perpendicular drawn from the point $P(a, b, 0)$ on the line $\dfrac{x-1}{2} = \dfrac{y-2}{1} = \dfrac{z-\alpha}{3}$ . If the midpoint of the line segment $PA$ is $\left(0, \dfrac34, \dfrac{-1}{4}\right)$ , then the value of $a^2 + b^2 + \alpha^2$ is equal to:
1. (1)1
2. (2)2
3. (3)6
4. (4)9
Q16 · MCQ · VectorsOpen
Two adjacent sides of a parallelogram $PQRS$ are given by $\overrightarrow{PQ} = \hat j + \hat k$ and $\overrightarrow{PS} = \hat i - \hat j$ . If the side $PS$ is rotated about the point $P$ by an acute angle $\alpha$ in the plane of the parallelogram so that it becomes perpendicular to the side $PQ$ , then $\sin^2\left(\dfrac{5\alpha}{2}\right) - \sin^2\left(\dfrac{\alpha}{2}\right)$ is equal to:
1. (1) $\dfrac12$
2. (2) $\dfrac{\sqrt3}{2}$
3. (3) $\dfrac{\sqrt3}{4}$
4. (4) $\dfrac{2\sqrt3}{5}$
Q17 · MCQ · Definite IntegrationOpen
The value of $\displaystyle\int_0^{20\pi}(\sin^4x + \cos^4x)\,dx$ is equal to:
1. (1) $\dfrac{15\pi}{2}$
2. (2) $25\pi$
3. (3) $15\pi$
4. (4) $\dfrac{25\pi}{2}$
Q18 · MCQ · Applications of DerivativesOpen
Let $f(x)$ be a polynomial of degree 5, and have extrema at $x = 1$ and $x = -1$ . If $\displaystyle\lim_{x\to0}\left(\frac{f(x)}{x^3}\right) = -5$ , then $f(2) - f(-2)$ is equal to:
1. (1)0
2. (2)50
3. (3)92
4. (4)112
Q19 · MCQ · Indefinite IntegrationOpen
Let $f(x) = \displaystyle\int\left(\frac{16x + 24}{x^2 + 2x - 15}\right)dx$ . If $f(4) = 14\log_e(3)$ and $f(7) = \log_e(2^{\alpha}\cdot3^{\beta})$ , $\alpha, \beta \in \mathbb{N}$ , then $\alpha + \beta$ is equal to:
1. (1)31
2. (2)37
3. (3)39
4. (4)41
Q20 · MCQ · Differential EquationsOpen
Let $x = x(y)$ be the solution of the differential equation $2y^2\dfrac{dx}{dy} - 2xy + x^2 = 0$ , $y > 1$ , $x(e) = e$ . Then $x(e^2)$ is equal to:
1. (1) $\dfrac32e^2$
2. (2) $\dfrac23e^2$
3. (3) $e^2$
4. (4) $2e^2$
Q21 · Numerical · Sets, Relations & FunctionsOpen
Let $A = \{2, 3, 4, 5, 6\}$ . Let $R$ be a relation on the set $A \times A$ given by $(x, y)R(z, w)$ if and only if $x$ divides $z$ and $y \le w$ . Then the number of elements in $R$ is .
Q22 · Numerical · Matrices & DeterminantsOpen
Consider the matrices $A = \begin{bmatrix} 2 & -2\\ 4 & -2\end{bmatrix} \quad\text{and}\quad B = \begin{bmatrix} 3 & 9\\ 1 & 3\end{bmatrix}.$ If matrices $P$ and $Q$ are such that $PA = B$ and $AQ = B$ , then the absolute value of the sum of the diagonal elements of $2(P + Q)$ is .
We corrected a printing error in the original paper
Source printed “B” directly followed by the matrix, without the “=” sign.
Q23 · Numerical · Conic SectionsOpen
Let $A$ be the point $(3, 0)$ and circles with variable diameter $AB$ touch the circle $x^2 + y^2 = 36$ internally. Let the curve $C$ be the locus of the point $B$ . If the eccentricity of $C$ is $e$ , then $72e^2$ is equal to .
Q24 · Numerical · Area under CurvesOpen
If the area of the region bounded by $16x^2 - 9y^2 = 144$ and $8x - 3y = 24$ is $A$ , then $3(A + 6\log_e(3))$ is equal to .
Q25 · Numerical · Limits, Continuity & DifferentiabilityOpen
The number of points in the interval $[2, 4]$ , at which the function $f(x) = \left[x^2 - x - \dfrac12\right]$ , where $[\,\cdot\,]$ denotes the greatest integer function, is discontinuous, is .