JEE Main 6 Apr 2026, Shift 2

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

Physics

Q1 · MCQ · Units and MeasurementsOpen
The percentage error in the calculated volume of a sphere, if there is 2% error in its diameter measurement, is .
1. (1)1
2. (2)2
3. (3)6
4. (4)8

Match List-I with List-II.

	List-I		List-II
A.	Boltzmann constant	I.	$[\mathrm{M^{-1}L^{3}T^{-2}}]$
B.	Stefan's constant	II.	$[\mathrm{M\,L^{2}T^{-1}}]$
C.	Planck's constant	III.	$[\mathrm{ML^{2}T^{-2}K^{-1}}]$
D.	Gravitational constant	IV.	$[\mathrm{ML^{0}T^{-3}K^{-4}}]$

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

Q3 · MCQ · Rotational MotionOpen
A solid sphere (A) of mass, $5m$ and spherical shell (B) of mass $m$ , both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of A and B, they start rolling without slipping with an acceleration of $a_A$ and $a_B$ , respectively. The ratio of $a_A$ and $a_B$ is .
1. (1) $5 : 21$
2. (2) $6 : 10$
3. (3) $21 : 25$
4. (4) $1 : 5$
Q4 · MCQ · Work, Energy and PowerOpen
A body of mass 1 kg moves along a straight line with a velocity $v = 2x^2$ . The work done on the body during displacement from $x = 0$ to 5 m is J.
1. (1)0
2. (2)250
3. (3)1250
4. (4)1000
We corrected a printing error in the original paper
Source printed “The work done by the body”; corrected to the intended “The work done on the body” (the key 1250 J is the gain in kinetic energy; the work done by the body would be $-1250$ J).
Q5 · MCQ · ThermodynamicsOpen
A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same $P$ , $V$ , $T$ . Heating is started from left side until pressure changes to $\dfrac{27P}{8}$ . If initial volume of each compartment was 9 litres then the final volume in right-hand side compartment is litres. (for this ideal gas $C_P/C_V = 1.5$ )
1. (1)3
2. (2)4
3. (3)14
4. (4)9
Q6 · MCQ · Electromagnetic WavesOpen
For an electromagnetic wave propagating through vacuum, $\vec k$ , $\vec E$ and $\omega$ represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated with this wave is represented by:
1. (1) $\dfrac{\vec E\times\vec k}{\omega}$
2. (2) $\dfrac{\vec k\times\vec E}{\omega}$
3. (3) $\omega\left(\vec E\times\vec k\right)$
4. (4) $\omega\left(\vec k\times\vec E\right)$
Q7 · MCQ · Centre of Mass, Momentum and CollisionOpen
Two identical bodies A and B of equal masses have initial velocities $\vec v_1 = 4\hat i\ \mathrm{m/s}$ and $\vec v_2 = 4\hat j\ \mathrm{m/s}$ respectively. The body A has acceleration $\vec a_1 = 6\hat i + 6\hat j\ \mathrm{m/s^2}$ while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in path.
1. (1)circular
2. (2)parabolic
3. (3)straight line
4. (4)elliptical
Q8 · MCQ · Mechanical Properties of SolidsOpen
Figure represents the extension ( $\Delta l$ ) of a wire of length 1 meter, suspended from the ceiling of the room at one end with load W connected to the other end. If the cross-sectional area of the wire is $10^{-5}\ \mathrm{m^2}$ then the Young's modulus of the wire is $\mathrm{N/m^2}$ .
1. (1) $1.0\times10^{11}$
2. (2) $2.0\times10^{10}$
3. (3) $1.0\times10^{10}$
4. (4) $2.0\times10^{11}$
Q9 · MCQ · Mechanical Properties of FluidsOpen
A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is 528 $\mathrm{dm^3}$ (dm : decimeter). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at 70 cm below the top of water level, then horizontal range of water falling on the ground in the beginning is cm.
1. (1) $120\sqrt2$
2. (2) $140\sqrt2$
3. (3) $140\sqrt3$
4. (4) $120\sqrt3$
Q10 · MCQ · Kinetic Theory of GasesOpen
If 2 mole of an ideal monoatomic gas at temperature $T$ , is mixed with 6 mole of another ideal monoatomic gas at temperature $2T$ then the temperature of mixture is:
1. (1) $\dfrac52 T$
2. (2) $\dfrac54 T$
3. (3) $\dfrac72 T$
4. (4) $\dfrac74 T$
We corrected a printing error in the original paper
Source printed “is maxed with 6 mole”.
Q11 · MCQ · OscillationsOpen
A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the system and maximum energy in the spring are Hz and J, respectively. (Take $g = 10\ \mathrm{m/s^2}$ )
1. (1) $\dfrac{5\sqrt{50}}{\pi}$ and $8\times10^{-3}$
2. (2) $\dfrac{5\sqrt{50}}{\pi}$ and 8
3. (3) $10\sqrt{50}$ and $2\times10^{-3}$
4. (4) $\dfrac{5\sqrt{50}}{\pi}$ and $16\times10^{-3}$
Q12 · MCQ · Electric Potential and CapacitanceOpen
The electric potential as a function of $x$ , $y$ is given by $V = 5(x^2 - y^2)$ V. The electric field at a point (2, 3) m is V/m.
1. (1) $(-20\hat i + 30\hat j)$
2. (2) $(20\hat i - 30\hat j)$
3. (3) $(20\hat i + 45\hat j)$
4. (4) $(-4\hat i + 6\hat j)$
Q13 · MCQ · Moving Charges and MagnetismOpen
A current of 30 A each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of 8 cm. The magnetic field at the mid point between the two wires is $\mu$ T.
( $\dfrac{\mu_0}{4\pi} = 10^{-7}\ \mathrm{N/A^2}$ )
1. (1)30
2. (2)300
3. (3)150
4. (4)0.1
Q14 · MCQ · Electromagnetic InductionOpen
A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as $B = 0.4\sin(300t)$ Tesla. The normal to the plane of loop makes an angle of $60^\circ$ with the field. The maximum induced emf produced in the loop is mV.
1. (1)12
2. (2)18
3. (3)21
4. (4)24
Q15 · MCQ · Electric Potential and CapacitanceOpen
A sphere of capacitance 100 pF is charged to a potential of 100 V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is $\alpha\times10^{-7}$ J. The value of $\alpha$ is . (combined capacitance of spheres is 200 pF).
1. (1)5
2. (2) $\dfrac52$
3. (3) $\dfrac72$
4. (4) $\dfrac92$
We corrected a printing error in the original paper
Source printed “Another identical undercharged metal sphere”.
Q16 · MCQ · NucleiOpen
The energy released if hydrogen atoms are combined to form ${}^{4}_{2}\mathrm{He}$ is MeV.
(Take binding energies per nucleon of ${}^{2}_{1}\mathrm{H}$ and ${}^{4}_{2}\mathrm{He}$ as 1.1 MeV and 7.2 MeV, respectively).
1. (1)6.1
2. (2)24.4
3. (3)26.6
4. (4)5
We corrected a printing error in the original paper
Source printed helium as a fraction “ $\frac{4}{2}$ He”; “1.1 meV”; no unit after the blank (MeV added).
Q17 · MCQ · Ray OpticsOpen
Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is .
1. (1)1.5
2. (2) $\sqrt3$
3. (3) $\sqrt2$
4. (4)1.65
We corrected a printing error in the original paper
Source printed “angle of prism is an equilateral prism”; “refreactive”.
Q18 · MCQ · Semiconductor ElectronicsOpen
Refer to the logic circuit given below. For two inputs ( $A = 1$ , $B = 1$ ) and ( $A = 0$ , $B = 1$ ), output ( $Y$ ) will be .
1. (1)1, 0 respectively
2. (2)0, 1 respectively
3. (3)0, 0 respectively
4. (4)1, 1 respectively
We corrected a printing error in the original paper
Source printed option (2) “rsepectively” and a stray fifth option “(5) 0.0” (duplicate of (3)), omitted.
Q19 · MCQ · Newton's Laws of MotionOpen
The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is m/s. Assume pulley is massless and string is light and inextensible (Take $g = 10\ \mathrm{m/s^2}$ ).
1. (1)7.74
2. (2)7.20
3. (3)6.55
4. (4)4.50
Q20 · MCQ · Wave OpticsOpen
In a Young double slit experiment, the wavelength of incident light is 6000 Å, the separation between slits $S_1$ and $S_2$ is 5 cm, the distance between slits plane and screen is 50 cm, as shown in the figure below. If the resultant intensity at P is equal to the intensity due to individual slits, the minimum path difference between interfering waves is Å.
1. (1)4000
2. (2)3000
3. (3)2000
4. (4)1000
We corrected a printing error in the original paper
Source printed “the wavelength of incident of incident light”; “the separation between slits $S_1$ and 5 cm the distance”; “the path different” — corrected to the intended “the minimum path difference” (4000 Å, option (1), also gives the single-slit intensity; the key 2000 Å is the least).
Q21 · Numerical · Newton's Laws of MotionOpen
A block takes $t$ time to slide down a plane inclined at $45^\circ$ to the horizontal. If the surface is made smooth (frictionless), the block takes time $\dfrac{t}{2}$ to slide down the plane. The coefficient of friction between the block and the inclined plane is $\left(\dfrac{\alpha}{100}\right)$ . The value of $\alpha$ is .
We corrected a printing error in the original paper
Source printed “the block takes times $t/2$ ”; “coeffcient”.
Q22 · Numerical · Dual Nature of Radiation and MatterOpen
The de Broglie wavelength for an electron accelerated through the potential difference $V_1$ volt is $\lambda_1$ . When the potential difference is changed to $V_2$ volt, the associated de Broglie wavelength is increased by 50%. If $(V_1/V_2) = (9/\alpha)$ , then the value of $\alpha$ is .
We corrected a printing error in the original paper
Source printed “The de Broglie weave length”.
Q23 · Numerical · Moving Charges and MagnetismOpen
A moving coil of a galvanometer when shunted with $2\ \Omega$ resistance gives a full scale deflection for a current of 500 mA. When a resistance of $470\ \Omega$ is connected in series it gives a full scale deflection for 10 V potential applied on it. The value of resistance of galvanometer coil is $\Omega$ .
We corrected a printing error in the original paper
Source printed “golvanometer”.
Q24 · Numerical · Current ElectricityOpen
Two cells of emfs 1 V and 2 V and internal resistances $2\ \Omega$ and $1\ \Omega$ , respectively connected in parallel, gave current of 1 A through an external resistance. If the polarity of one cell is reversed, then value of current through the external resistance will be $\dfrac{\alpha}{5}$ A. The value of $\alpha$ is .
We corrected a printing error in the original paper
Source printed “internal reseistance”.
Q25 · Numerical · Ray OpticsOpen
A concave mirror of focal length 10 cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is cm.
We corrected a printing error in the original paper
Source printed “froms an image”.

Chemistry

Q1 · MCQ · Some Basic ConceptsOpen
Which of the following contain the same number of atoms ?
(Given : Molar mass in g mol $^{-1}$ of H, He, O and S are 1,4,16 and 32 respectively)
- (A)2g of $\ce{O2}$ gas
- (B)4g of $\ce{SO2}$ gas
- (C)1400 mL of $\ce{O2}$ at STP
- (D)0.05 L of He at STP
- (E)0.0625 mol of $\ce{H2}$ gas
Choose the correct answer from the options given below :
1. (1)A and B only
2. (2)B and C only
3. (3)C and D only
4. (4)A, C and E only
We corrected a printing error in the original paper
Source printed “4g fo $\ce{SO2}$ gas”.
Q2 · MCQ · Structure of AtomOpen
The Bohr radius of a hydrogen like species is 70.53 pm. The species and the stationary state(n) are respectively
(Given: Hydrogen atom Bohr radius is 52.9 pm)
1. (1) $\ce{Li^{2+}}$ , 3
2. (2) $\ce{He+}$ , 3
3. (3) $\ce{He+}$ , 2
4. (4) $\ce{Li^{2+}}$ , 2
Q3 · MCQ · Chemical BondingOpen
Given below are two statements:
Statement I : The number of compounds among $\ce{SO2}$ , $\ce{SO3}$ , $\ce{SF4}$ , $\ce{SF6}$ and $\ce{H2S}$ in which sulphur does not obey the Octet rule is 3.
Statement II : Among [ $\ce{H2O}$ , $\ce{ClF3}$ , $\ce{SF4}$ ], [ $\ce{NH3}$ , $\ce{BrF5}$ , $\ce{SF4}$ ], [ $\ce{BrF5}$ , $\ce{ClF3}$ , $\ce{XeF4}$ ] and [ $\ce{XeF4}$ , $\ce{ClF3}$ , $\ce{H2O}$ ], the number of sets in which all the molecules have one lone pair of electrons on the central atom is 1.
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
We corrected a printing error in the original paper
Source printed options (3) and (4) as “Statement I is true Statement II is false” and “Statement I is false Statement II is true”.

Q4 · MCQ · ThermodynamicsOpen

Match List-I with List-II

Given $V_1$ and $V_2$ are initial and final volumes respectively:

List-I		List-II
(Isothermal process)		(Expression)
A.	Reversible expansion	I.	$q = 0$
B.	Free expansion	II.	$q = nRT\ln\dfrac{V_2}{V_1}$
C.	Irreversible Compression	III.	$w = -p_\mathrm{ext}\left(V_2 - V_1\right)$
D.	Cyclic reversible	IV.	$\dfrac{q_\mathrm{rev}}{T} = 0$

Choose the correct answer from the options given below :

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

We corrected a printing error in the original paper

Source printed expression III as “ $w = -p_\mathrm{ext}(V_1 - V_2)$ ” (wrong sign for $V_1$ initial, $V_2$ final); corrected to the intended “ $w = -p_\mathrm{ext}(V_2 - V_1)$ ”.

Q5 · MCQ · SolutionsOpen
Given below are two statements :
Chamber 1 Chamber 2
18 g glucose in 100 mL aqueous solution Semi-permeable membrane 30 g glucose in 250 mL aqueous solution
Statement I : $\ce{H2O}$ molecules move from the chamber 1 to chamber 2.
Statement II : The osmotic pressure of a solution prepared by dissolving 50 mg of potassium sulphate (molar mass = 174 g/mol) in 2 L of water (at 27 $^\circ$ C) is 0.0107 bar. (Given : $R = 0.083$ dm $^3$ bar K $^{-1}$ mol $^{-1}$ and assume complete dissociation of electrolyte)
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
Q6 · MCQ · EquilibriumOpen
Given is a concentrated solution of a weak electrolyte $\mathrm{A}_x\mathrm{B}_y$ of concentration ‘ $c$ ' and dissociation constant ‘ $K$ '. the degree of dissociation is given by:
1. (1) $\left[K\times c^{x+y-1}x^xy^y\right]^{x+y}$
2. (2) $\left(\dfrac{K}{c^{x+y-1}x^xy^y}\right)^{\frac{1}{x+y}}$
3. (3) $\left(\dfrac{c^{x+y-1}x^xy^y}{K}\right)^{x+y}$
4. (4) $\left(\dfrac{c^{x+y-1}x^xy^y}{K}\right)^{\frac{1}{x+y}}$
Q7 · MCQ · ElectrochemistryOpen
For a general redox reaction
Anode $\mathrm{Red_1 \rightarrow Ox_1^{\,n_1^+} + n_1e^-}$
Cathode $\mathrm{Ox_2 + n_2e^- \rightarrow Red_2^{\,n_2^-}}$
Which of the following statement is incorrect ?
1. (1)
  The overall reaction can be written as
  $\mathrm{n_2\,Red_1 + n_1Ox_2 \rightleftharpoons n_2Ox_1^{\,n_1^+} + n_1\,Red_2^{\,n_2^-}}$
2. (2)The electrons do not appear in the overall reaction because electrons produced at the anode are consumed at the cathode.
3. (3)
  Here $n$ is the number of electrons transferred in redox reaction.
4. (4)If the reaction is carried out reversibly, the electrical work done is equal to the ratio of charge and potential difference through which charge is moved.
We corrected a printing error in the original paper
Option (3) graph: source printed the $y$ -axis label as “(E $-$ E $^\circ$ )/(RT/E)”; corrected in the figure to the intended “(E $-$ E $^\circ$ )/(RT/F)” (F = Faraday constant).
Q8 · MCQ · Classification & PeriodicityOpen
In a period, the first ionisation enthalpy of the element at extreme left and the negative electron gain enthalpy of the extreme right element, except noble gases, are respectively.
1. (1)lowest and lowest
2. (2)highest and lowest
3. (3)lowest and highest
4. (4)highest and highest
Q9 · MCQ · Chemical BondingOpen
Given below are two statements :
Statement I : $\ce{F2O}$ $<$ $\ce{H2O}$ $<$ $\ce{Cl2O}$ is the correct trend in terms of bond angle.
Statement II : $\ce{SiF4}$ , $\ce{SnF4}$ and $\ce{PbF4}$ are ionic in nature.
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
The correct order of first ( $\Delta_\mathrm{i}H_1$ ) and second ( $\Delta_\mathrm{i}H_2$ ) ionisation enthalpy values of Cr and Mn is :
- (A) $\Delta_\mathrm{i}H_1$ : Cr $>$ Mn
- (B) $\Delta_\mathrm{i}H_2$ : Cr $>$ Mn
- (C) $\Delta_\mathrm{i}H_1$ : Mn $>$ Cr
- (D) $\Delta_\mathrm{i}H_2$ : Mn $>$ Cr
Choose the correct answer from the options given below :
1. (1)A and B only
2. (2)B and C only
3. (3)A and D only
4. (4)C and D only
We corrected a printing error in the original paper
Source printed “ionisation enthalpy values of cr and Mn are”.
Q11 · MCQ · Coordination CompoundsOpen
Which of the following sequence of hybridisation, geometry and magnetic nature are correct for the given coordination compounds ?
- (A) $\ce{[NiCl4]^{2-}}$ – sp $^3$ , tetrahedral, paramagnetic
- (B) $\ce{[Ni(NH3)6]^{2+}}$ – sp $^3$ d $^2$ , octahedral, paramagnetic
- (C) $\ce{[Ni(CO)4]}$ – sp $^3$ , tetrahedral, paramagnetic
- (D) $\ce{[Ni(CN)4]^{2-}}$ – dsp $^2$ , square planar diamagnetic
Choose the correct answer from the options given below :
1. (1)A, B, C and D
2. (2)B, C and D only
3. (3)A, C and D only
4. (4)A, B and D only
Q12 · MCQ · Purification & CharacterisationOpen
Given below are two statements :
Statement I : A mixture of $\ce{C12H22O11}$ (sugar) and NaCl can be separated by dissolving sugar in alcohol, due to differential solubility
Statement II : Rose essence from rose petals is separated by steam distillation due to its high volatility and insolubility in $\ce{H2O}$ .
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
We corrected a printing error in the original paper
Source printed options (3) and (4) as “Statement I is true Statement II is false” and “Statement I is false Statement II is true”.
Q13 · MCQ · Organic Basics (GOC)Open
Shown below is the structure of methyl acetate with three different $\alpha$ , $\beta$ and $\gamma$ carbon-oxygen bonds.
The correct order of bond length of these bonds is :
1. (1) $\alpha > \beta > \gamma$
2. (2) $\alpha < \beta < \gamma$
3. (3) $\alpha = \beta = \gamma$
4. (4) $\alpha < \beta = \gamma$
Q14 · MCQ · Aldehydes, Ketones & AcidsOpen
‘x' is the product which is obtained by the hydrolysis of prop-1-yne in the presence of mercuric sulphate under dilute acidic medium at 333 K. ‘y' is the product which is obtained by the reaction of ethane nitrile with methyl magnesium bromide in dry ether followed by hydrolysis. IUPAC name of product obtained from ‘x' and ‘y' in the presence of barium hydroxide followed by heating is:
1. (1)2-Methylpent-4-en-3-one
2. (2)4-Methylpent-3-en-2-one
3. (3)4-Methylpent-1-ene
4. (4)2-Methylpent-3-one
Q15 · MCQ · HydrocarbonsOpen
An optically active alkyl bromide $\ce{C4H9Br}$ , reacts with ethanolic KOH to form major compound [A] which reacts with bromine to give compound [B]. Compound [B] reacts with ethanolic KOH and sodamide to give compound [C]. One molecule of water adds to compound [C] on warming with mercuric sulphate and dilute sulphuric acid at 333 K to form compound [D]. The functional group in compound D will be confirmed by:
1. (1)Haloform test
2. (2)Lucas test
3. (3)Silver mirror test
4. (4)Benedict test
Q16 · MCQ · Alcohols, Phenols & EthersOpen
Consider the following reaction.
Statement I : In the above reaction, product formed will be a mixture of benzyl alcohol and iodobenzene.
Statement II : In the above reaction, the $\ce{-O-CH2-}$ bond is cleaved to give the product.
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
Q17 · MCQ · AminesOpen
Consider the following organic reaction sequence. Choose the final product (X) from the following (consider the major product in all intermediate reactions)
1. (1)Benzene
2. (2)Phenol
3. (3)Propanol
4. (4)Chlorobenzene
Q18 · MCQ · AminesOpen
The number of compounds from the following which can undergo reaction with $\ce{Br2}$ /KOH/(alcoholic) to give respective products and these respective products can also be obtained separately by Gabriel phthalimide reaction is:
1. (1)5
2. (2)4
3. (3)3
4. (4)6
Q19 · MCQ · HydrocarbonsOpen
Consider the following reactions. Total number of electrons in the $\pi$ bonds and lone pair of electrons in the product (X) is:
1. (1)12
2. (2)16
3. (3)14
4. (4)18
Q20 · MCQ · Practical / Qualitative AnalysisOpen
Treatment of a gas ‘X' with a freshly prepared ferrous sulphate solution gives a compound ‘Y' as a brown ring. The compounds X and Y are.
1. (1) $\ce{NO}$ and $\ce{[Fe(NO)]SO4}$
2. (2) $\ce{NO2}$ and $\ce{[Fe(NO2)]SO4}$
3. (3) $\ce{N2O}$ and $\ce{[Fe(N2O)]SO4}$
4. (4) $\ce{N2O4}$ and $\ce{[Fe(N2O4)]SO4}$
Q21 · Numerical · Coordination CompoundsOpen
An excess of $\ce{AgNO3}$ is added to 100 mL of a 0.05 M solution of tetraaquadichloridochromium (III) chloride. The number of moles of AgCl precipitated will be $\times\,10^{-3}$ . (Nearest integer)
Q22 · Numerical · HydrocarbonsOpen
An alkane (Y) requires 8 moles of oxygen for complete combustion and on chlorination with $\ce{Cl2}$ /h $\nu$ , (Y) gives only one monochlorinated product (Z). The total number of primary carbon atoms in (Y) is .
We corrected a printing error in the original paper
Source printed “ $\ce{Cl2}$ /hv” (Latin v for $\nu$ ).
Q23 · Numerical · Redox ReactionsOpen
500 mL of 0.2 M $\ce{MnO4-}$ solution in basic medium when mixed with 500 mL of 1.5 M KI solution, oxidises iodide ions to liberate molecular iodine. This liberated iodine is then titrated with a standard $x$ M thiosulphate solution in presence of starch till the end point. If 300 mL of thiosulphate was consumed, then the value of $x$ is .
Q24 · Numerical · ThermodynamicsOpen
In a closed flask at 600 K, one mole of $\ce{X2Y4(g)}$ attains equilibrium as given below:
$\ce{X2Y4(g) <=> 2XY2(g)}$
At equilibrium, 75% $\ce{X2Y4(g)}$ was dissociated and the total pressure is 1 atm. The magnitude of $\Delta_\mathrm{r}G^\ominus$ (in kJ mol $^{-1}$ ) at this temperature is . (Nearest Integer)
(Given: $R = 8.3$ J mol $^{-1}$ K $^{-1}$ ; $\ln 10 = 2.3$ , $\log 2 = 0.3$ , $\log 3 = 0.48$ , $\log 5 = 0.69$ , $\log 7 = 0.84$ )
Q25 · Numerical · Chemical KineticsOpen
Decomposition of a hydrocarbon follows the equation $k = (5.5\times10^{11}\ \mathrm{s^{-1}})\ e^{\frac{-28000\,\mathrm{K}}{T}}$ . The activation energy of reaction is kJ mol $^{-1}$ . (Nearest Integer)
Given : $R = 8.3$ J K $^{-1}$ mol $^{-1}$

Maths

Q1 · MCQ · Sets, Relations & FunctionsOpen
Let $f : \mathbb{R} \to \mathbb{R}$ be defined as $f(x) = \dfrac{2x^2 - 3x + 2}{3x^2 + x + 3}$ . Then $f$ is:
1. (1)both one-one and onto
2. (2)one-one but not onto
3. (3)onto but not one-one
4. (4)neither one-one nor onto
Q2 · MCQ · Sequences & SeriesOpen
Consider the quadratic equation $(n^2 - 2n + 2)x^2 - 3x + (n^2 - 2n + 2)^2 = 0$ , $n \in \mathbb{R}$ . Let $\alpha$ be the minimum value of the product of its roots and $\beta$ be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is $\alpha$ and the common ratio is $\dfrac{\alpha}{\beta}$ , is:
1. (1) $\dfrac{61}{37}$
2. (2) $\dfrac{121}{81}$
3. (3) $\dfrac{364}{243}$
4. (4) $\dfrac{1093}{729}$
Q3 · MCQ · Complex NumbersOpen
Let $S = \left\{z \in \mathbb{C} : z^2 + \sqrt6\,iz - 3 = 0\right\}$ . Then $\displaystyle\sum_{z\in S} z^8$ is equal to:
1. (1)162
2. (2)184
3. (3)262
4. (4)324
Q4 · MCQ · Matrices & DeterminantsOpen
The sum of all possible values of $\theta \in [0, 2\pi]$ , for which the system of equations:
$\begin{align*} x\cos3\theta - 8y - 12z &= 0\\ x\cos2\theta + 3y + 3z &= 0\\ x + y + 3z &= 0 \end{align*}$
has a non-trivial solution, is equal to:
1. (1) $\pi$
2. (2) $2\pi$
3. (3) $3\pi$
4. (4) $4\pi$
Q5 · MCQ · Matrices & DeterminantsOpen
Let $A = \begin{bmatrix} 1 & 0 & 0\\ 3 & 1 & 0\\ 9 & 3 & 1\end{bmatrix} \quad\text{and}\quad B = [b_{ij}],\ 1 \le i, j \le 3.$ If $B = A^{99} - I$ , then the value of $\dfrac{b_{31} - b_{21}}{b_{32}}$ is:
1. (1)99
2. (2)199
3. (3)149
4. (4)159
We corrected a printing error in the original paper
Source printed “ $B = [b_{ij}]$ , $l \le i, j \le 3$ ” (letter l for the digit 1).
Q6 · MCQ · Sequences & SeriesOpen
The sum $1 + \dfrac12\left(1^2 + 2^2\right) + \dfrac13\left(1^2 + 2^2 + 3^2\right) + \ldots$ upto 10 terms is equal to:
1. (1)130
2. (2)155
3. (3) $\dfrac{315}{2}$
4. (4) $\dfrac{325}{2}$
Q7 · MCQ · Permutations & CombinationsOpen
A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the $10^{\text{th}}$ floor. The number of ways, in which any 4 persons exit at a floor and the remaining 5 persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to:
1. (1)2184
2. (2)3064
3. (3)7056
4. (4)11340
Q8 · MCQ · StatisticsOpen
Let the mean and the variance of seven observations 2, 4, $\alpha$ , 8, $\beta$ , 12, 14, $\alpha < \beta$ , be 8 and 16 respectively. Then the quadratic equation whose roots are $3\alpha + 2$ and $2\beta + 1$ is:
1. (1) $x^2 - 35x + 306 = 0$
2. (2) $x^2 - 41x + 420 = 0$
3. (3) $x^2 - 45x + 506 = 0$
4. (4) $x^2 - 37x + 342 = 0$
Q9 · MCQ · ProbabilityOpen
A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is:
1. (1) $\dfrac{63}{925}$
2. (2) $\dfrac{17}{231}$
3. (3) $\dfrac{16}{231}$
4. (4) $\dfrac{64}{925}$
Q10 · MCQ · CirclesOpen
Let $C$ be a circle having centre in the first quadrant and touching the $x$ -axis at a distance 3 units from the origin. If the circle $C$ has an intercept of length $6\sqrt3$ on $y$ -axis, then the length of the chord of the circle $C$ on the line $x - y = 3$ is:
1. (1)8
2. (2)6
3. (3) $6\sqrt2$
4. (4) $8\sqrt2$
Q11 · MCQ · Conic SectionsOpen
The eccentricity of an ellipse $E$ with centre at the origin $O$ is $\dfrac{\sqrt3}{2}$ and its directrices are $x = \pm\dfrac{4\sqrt6}{3}$ . Let $H : \dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ be a hyperbola whose eccentricity is equal to the length of semi-major axis of $E$ , and whose length of latus rectum is equal to the length of minor axis of $E$ . Then the distance between the foci of $H$ is:
1. (1) $\dfrac{4\sqrt2}{\sqrt7}$
2. (2) $\dfrac{4\sqrt2}{7}$
3. (3) $\dfrac{4}{\sqrt7}$
4. (4) $\dfrac{8}{7}$
Q12 · MCQ · Conic SectionsOpen
Let $x = 9$ be a directrix of an ellipse $E$ , whose centre is at the origin and eccentricity is $\dfrac13$ . Let $P(\alpha, 0)$ , $\alpha > 0$ , be a focus of $E$ and $AB$ be a chord passing through $P$ . Then the locus of the mid point of $AB$ is:
1. (1) $9y^2 = 8x(1 - x)$
2. (2) $3y^2 = 4x(1 - x)$
3. (3) $9y^2 = 8x(x - 1)$
4. (4) $3y^2 = 4x(x - 1)$
Q13 · MCQ · Inverse TrigonometryOpen
If $\sin\left(\tan^{-1}(x\sqrt2)\right) = \cot\left(\sin^{-1}\sqrt{1 - x^2}\right)$ , $x \in (0, 1)$ , then the value of $x$ is:
1. (1) $\dfrac12$
2. (2) $\dfrac13$
3. (3) $\dfrac23$
4. (4) $\dfrac58$
Q14 · MCQ · 3D GeometryOpen
The shortest distance between the lines $\dfrac{x-4}{1} = \dfrac{y-3}{2} = \dfrac{z-2}{-3}$ and $\dfrac{x+2}{2} = \dfrac{y-6}{4} = \dfrac{z-5}{-5}$ is:
1. (1) $\dfrac{5\sqrt6}{6}$
2. (2) $2\sqrt5$
3. (3) $3\sqrt5$
4. (4) $4\sqrt5$
Q15 · MCQ · VectorsOpen
Let $\vec a = 2\hat i + 3\hat j + 3\hat k$ and $\vec b = 6\hat i + 3\hat j + 3\hat k$ . Then the square of the area of the triangle with adjacent sides determined by the vectors $\left(2\vec a + 3\vec b\right)$ and $\left(\vec a - \vec b\right)$ is:
1. (1)450
2. (2)900
3. (3)1800
4. (4)2400
Q16 · MCQ · Limits, Continuity & DifferentiabilityOpen
Let $\lim_{x\to2}\dfrac{\left(\tan(x-2)\right)\left(rx^2 + (p-2)x - 2p\right)}{(x-2)^2} = 5$ for some $r, p \in \mathbb{R}$ . If the set of all possible values of $q$ , such that the roots of the equation $rx^2 - px + q = 0$ lie in $(0, 2)$ , be the interval $(\alpha, \beta]$ , then $4(\alpha + \beta)$ equals.
1. (1)11
2. (2)13
3. (3)17
4. (4)21
Q17 · MCQ · Applications of DerivativesOpen
Let $A = \begin{bmatrix} 1 & 3 & -1\\ 2 & 1 & \alpha\\ 0 & 1 & -1\end{bmatrix}$ be a singular matrix. Let $f(x) = \displaystyle\int_0^x \left(t^2 + 2t + 3\right)dt$ , $x \in [1, \alpha]$ . If $M$ and $m$ are respectively the maximum and the minimum values of $f$ in $[1, \alpha]$ then $3(M - m)$ is equal to:
1. (1)64
2. (2)68
3. (3)72
4. (4)76
We corrected a printing error in the original paper
Source printed the matrix $A$ between determinant bars (“ $A = \lvert\ldots\rvert$ be a singular matrix”).
Q18 · MCQ · Differential EquationsOpen
Let $f : \mathbb{R} \to \mathbb{R}$ be such that $f(xy) = f(x)f(y)$ , for all $x, y \in \mathbb{R}$ and $f(0) \neq 0$ . Let $g : [1, \infty) \to \mathbb{R}$ be a differentiable function such that $x^2g(x) = \int_1^x \left(t^2f(t) - tg(t)\right)dt$ Then $g(2)$ is equal to:
1. (1) $\dfrac{13}{8}$
2. (2) $\dfrac{11}{16}$
3. (3) $\dfrac{15}{32}$
4. (4) $\dfrac{17}{64}$
Q19 · MCQ · Area under CurvesOpen
The area of the region $\{(x, y) : x^2 - 8x \le y \le -x\}$ is:
1. (1) $\dfrac{343}{6}$
2. (2) $\dfrac{637}{6}$
3. (3) $\dfrac{437}{6}$
4. (4) $\dfrac{523}{6}$
Q20 · MCQ · Definite IntegrationOpen
The value of the integral $\displaystyle\int_{-1}^{1}\left(\frac{x^3 + \lvert x\rvert + 1}{x^2 + 2\lvert x\rvert + 1}\right)dx$ is equal to
1. (1) $3\log_e2$
2. (2) $2\log_e2$
3. (3) $5\log_e3$
4. (4) $3\log_e3$
Q21 · Numerical · Sets, Relations & FunctionsOpen
Let $R = \{(x, y) \in \mathbb{N} \times \mathbb{N} : \log_e(x + y) \le 2\}$ . Then the minimum number of elements, required to be added in $R$ to make it a transitive relation, is .
Q22 · Numerical · Binomial TheoremOpen
If $\left(1 - x^3\right)^{10} = \displaystyle\sum_{r=0}^{10} a_r x^r (1 - x)^{30-2r}$ , then $\dfrac{9a_9}{a_{10}}$ is equal to .
Q23 · Numerical · CirclesOpen
Let the line $x - y = 4$ intersect the circle $C : (x - 4)^2 + (y + 3)^2 = 9$ at the points $Q$ and $R$ . If $P(\alpha, \beta)$ is a point on $C$ such that $PQ = PR$ , then $(6\alpha + 8\beta)^2$ is equal to .
Q24 · Numerical · 3D GeometryOpen
Let the image of the point $P(0, -5, 0)$ in the line $\dfrac{x-1}{2} = \dfrac{y}{1} = \dfrac{z+1}{-2}$ be the point $R$ and the image of the point $Q\left(0, \dfrac{-1}{2}, 0\right)$ in the line $\dfrac{x-1}{-1} = \dfrac{y+9}{4} = \dfrac{z+1}{1}$ be the point $S$ . Then the square of the area of the parallelogram $PQRS$ is .
Q25 · Numerical · Limits, Continuity & DifferentiabilityOpen
Let $f(x) = \begin{cases} x^3 + 8 & x < 0\\ x^2 - 4 & x \ge 0\end{cases} \quad\text{and}\quad g(x) = \begin{cases} (x - 8)^{1/3}; & x < 0\\ (x + 4)^{1/2}; & x \ge 0\end{cases}$ Then the number of points, where the function $g\mathrm{o}f$ is discontinuous, is .

Chamber 1		Chamber 2
18 g glucose in 100 mL aqueous solution	Semi-permeable membrane	30 g glucose in 250 mL aqueous solution