JEE Main 22 Jan 2026, Shift 1

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

Physics

Q1 · MCQ · Rotational MotionOpen
A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is $\mathrm{kg.m^2}$ .
1. (1)0.36
2. (2)0.72
3. (3)0.18
4. (4)0.63
Q2 · MCQ · AtomsOpen
7.9 MeV $\alpha$ –particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) m. $\left[\dfrac{1}{4\pi\epsilon_0} = 9\times10^{9}\ \mathrm{Nm^2/C^2}\ \text{and electron charge} = 1.6\times10^{-19}\ \mathrm{C}\right]$
1. (1) $5.76\times10^{-14}$
2. (2) $1.44\times10^{-13}$
3. (3) $2.88\times10^{-14}$
4. (4) $1.69\times10^{-12}$
Q3 · MCQ · Electric Charges and FieldsOpen
Six point charges are kept $60^\circ$ apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the centre of the circle is . ( $\epsilon_0$ is permittivity of free space)
1. (1) $-\dfrac{5Q}{8\pi\epsilon_0R^2}(\hat i + \sqrt3\,\hat j)$
2. (2) $-\dfrac{Q}{4\pi\epsilon_0R^2}\left(\sqrt3\,\hat i - \hat j\right)$
3. (3) $-\left(\dfrac{5Q}{8\pi\epsilon_0R^2}\right)\left(\hat i - 3\hat j\right)$
4. (4) $\dfrac{Q}{4\pi\epsilon_0R^2}\left(\sqrt3\,\hat i - \hat j\right)$
Q4 · MCQ · Electromagnetic InductionOpen
XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and separation between them is $l$ . A constant magnetic field B perpendicular to the plane of the loop exists in the entire space. A rod CD of length L ( $L > l$ ) and mass m is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is m/s. ( $g$ = acceleration due to gravity)
1. (1) $\dfrac{2mgR}{B^2l^2}$
2. (2) $\dfrac{8mgR}{B^2l^2}$
3. (3) $\dfrac{2mgR}{B^2L^2}$
4. (4) $\dfrac{mgR}{B^2l^2}$
Q5 · MCQ · GravitationOpen
The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is m/s.
1. (1)1000
2. (2) $200\sqrt5$
3. (3) $100\sqrt{10}$
4. (4) $1000\sqrt2$
Q6 · MCQ · Current ElectricityOpen
A meter bridge with two resistances $R_1$ and $R_2$ as shown in figure was balanced (null point) at 40 cm from the point P. The null point changed to 50 cm from the point P, when $16\ \Omega$ resistance is connected in parallel to $R_2$ . The values of resistances $R_1$ and $R_2$ are .
1. (1) $R_2 = 16\ \Omega,\ R_1 = \dfrac{16}{3}\ \Omega$
2. (2) $R_2 = 4\ \Omega,\ R_1 = \dfrac{4}{3}\ \Omega$
3. (3) $R_2 = 8\ \Omega,\ R_1 = \dfrac{16}{3}\ \Omega$
4. (4) $R_2 = 12\ \Omega,\ R_1 = \dfrac{12}{3}\ \Omega$
Q7 · MCQ · Motion in a PlaneOpen
A projectile is thrown upward at an angle $60^\circ$ with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is $45^\circ$ with the horizontal. The initial speed of the projectile is m/s.
1. (1) $40\sqrt2$
2. (2)40
3. (3) $20\sqrt3$
4. (4) $20\sqrt2$
Q8 · MCQ · Mechanical Properties of FluidsOpen
Given below are two statements:
Statement I: Pressure of fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.
Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension.
In the light of the above statements, choose the correct answer from the options given below.
1. (1)Statement I is true but Statement II is false
2. (2)Both Statement I and Statement II are false
3. (3)Both Statement I and Statement II are true
4. (4)Statement I is false but Statement II is true
Q9 · MCQ · Semiconductor ElectronicsOpen
Find the correct combination of A, B, C and D inputs which can cause the LED to glow.
1. (1)0100
2. (2)0011
3. (3)1000
4. (4)1101
Q10 · MCQ · GravitationOpen
Net gravitational force at the centre of a square is found to be $F_1$ when four particles having mass $M$ , $2M$ , $3M$ and $4M$ are placed at the four corners of the square as shown in figure and it is $F_2$ when the positions of $3M$ and $4M$ are interchanged. The ratio $\dfrac{F_1}{F_2}$ is $\dfrac{\alpha}{\sqrt5}$ . The value of $\alpha$ is .
1. (1)2
2. (2)3
3. (3)1
4. (4) $2\sqrt5$
Q11 · MCQ · NucleiOpen
The minimum frequency of photon required to break a particle of mass 15.348 amu into $4\alpha$ particles is kHz. [mass of He nucleus $= 4.002$ amu, 1 amu $= 1.66\times10^{-27}$ kg, $h = 6.6\times10^{-34}$ J.s and $c = 3\times10^{8}$ m/s]
1. (1) $9\times10^{19}$
2. (2) $9\times10^{20}$
3. (3) $14.94\times10^{20}$
4. (4) $14.94\times10^{19}$
Q12 · MCQ · Mechanical Properties of FluidsOpen
A cylindrical tube $AB$ of length $l$ , closed at both ends contains an ideal gas of 1 mol having molecular weight $M$ . The tube is rotated in a horizontal plane with constant angular velocity $\omega$ about an axis perpendicular to $AB$ and passing through the edge at end A, as shown in the figure. If $P_A$ and $P_B$ are the pressures at $A$ and $B$ respectively, then (Consider the temperature is same at all points in the tube)
1. (1) $P_B = P_A\exp\left(M\omega^2l^2/2RT\right)$
2. (2) $P_B = P_A$
3. (3) $P_B = P_A\exp\left(M\omega^2l^2/3RT\right)$
4. (4) $P_B = P_A\exp\left(M\omega^2l^2/RT\right)$
Q13 · MCQ · Thermal Properties of MatterOpen
Rods x and y of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ are maintained at $100\ ^\circ$ C and $40\ ^\circ$ C respectively. Given the thermal conductivity of rod x is three times of that of rod y, the temperatures at junction points $B$ and $E$ are (close to):
1. (1) $89\ ^\circ$ C and $73\ ^\circ$ C respectively
2. (2) $80\ ^\circ$ C and $60\ ^\circ$ C respectively
3. (3) $80\ ^\circ$ C and $70\ ^\circ$ C respectively
4. (4) $60\ ^\circ$ C and $45\ ^\circ$ C respectively
We corrected a printing error in the original paper
Source printed “the temperature at junction points $B$ and $E$ are”.
Q14 · MCQ · Ray OpticsOpen
A thin convex lens of focal length 5 cm and a thin concave lens of focal length 4 cm are combined together (without any gap) and this combination has magnification $m_1$ when an object is placed 10 cm before the convex lens. Keeping the positions of convex lens and object undisturbed a gap of 1 cm is introduced between the lenses by moving the concave lens away, which lead to a change in magnification of total lens system to $m_2$ . The value of $\left|\dfrac{m_1}{m_2}\right|$ is .
1. (1) $\dfrac59$
2. (2) $\dfrac{5}{27}$
3. (3) $\dfrac32$
4. (4) $\dfrac{25}{27}$
Flawed question. No option is correct as printed ( $|m_1/m_2| = 5/6$ ) and no single evident misprint leads to one of the options; dropped in the source key. It is shown for completeness and is left out of practice tests.
Q15 · MCQ · Ray OpticsOpen
Consider an equilateral prism (refractive index $\sqrt2$ ). A ray of light is incident on its one surface at a certain angle $i$ . If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to .
1. (1) $15^\circ$
2. (2) $20^\circ$
3. (3) $40^\circ$
4. (4) $30^\circ$
Q16 · MCQ · ThermodynamicsOpen
The volume of an ideal gas increases 8 times and temperature becomes $\left(\frac14\right)^{\text{th}}$ of initial temperature during a reversible change. If there is no exchange of heat in this process ( $\Delta Q = 0$ ) then identify the gas from the following options (Assuming the gases given in the options are ideal gases):
1. (1) $\ce{CO2}$
2. (2) $\ce{O2}$
3. (3) $\ce{NH3}$
4. (4)He
Q17 · MCQ · Electric Potential and CapacitanceOpen
Electric field in a region is given by $\vec E = Ax\hat i + By\hat j$ , where $A = 10\ \mathrm{V/m^2}$ and $B = 5\ \mathrm{V/m^2}$ . If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is V.
1. (1)1000
2. (2)500
3. (3)2000
4. (4)0
Q18 · MCQ · Newton's Laws of MotionOpen
A simple pendulum has a bob with mass $m$ and charge $q$ . The pendulum string has negligible mass. When a uniform and horizontal electric field $\vec E$ is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is . ( $g$ : acceleration due to gravity)
1. (1) $mg - qE$
2. (2) $mg + qE$
3. (3) $\sqrt{m^2g^2 + q^2E^2}$
4. (4) $\sqrt{m^2g^2 - q^2E^2}$

Match the LIST-I with LIST-II

	List-I		List-II
A.	Spring constant	I.	$\mathrm{ML^2T^{-2}K^{-1}}$
B.	Thermal conductivity	II.	$\mathrm{ML^0T^{-2}}$
C.	Boltzmann constant	III.	$\mathrm{ML^2T^{-3}A^{-2}}$
D.	Inductive reactance	IV.	$\mathrm{MLT^{-3}K^{-1}}$

Choose the correct answer from the options given below:

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

Q20 · MCQ · Electromagnetic InductionOpen
Three identical coils $C_1$ , $C_2$ and $C_3$ are closely placed such that they share a common axis. $C_2$ is exactly midway. $C_1$ carries current $I$ in anti-clockwise direction while $C_3$ carries current $I$ in clockwise direction. An induced current flowing through $C_2$ will be in clockwise direction when
1. (1) $C_1$ and $C_3$ move with equal speeds away from $C_2$
2. (2) $C_1$ moves towards $C_2$ and $C_3$ moves away from $C_2$
3. (3) $C_1$ moves away from $C_2$ and $C_3$ moves towards $C_2$
4. (4) $C_1$ and $C_3$ move with equal speeds towards $C_2$
We corrected a printing error in the original paper
Source printed “An induced current flows through $C_2$ will be”.
Q21 · Numerical · WavesOpen
Two loudspeakers ( $L_1$ and $L_2$ ) are placed with a separation of 10 m, as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point $A$ , at equidistance to both loud speakers, is moved by 25 m along the line $AB$ while monitoring the audio signal. The measured signal was found to undergo 10 cycles of minima and maxima during the movement. The frequency of the input signal is Hz (Speed of sound in air is 324 m/s and $\sqrt5 = 2.23$ )
Q22 · Numerical · Electromagnetic WavesOpen
The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by, $E_y = 20\sin\left(3\times10^{6}x - 4.5\times10^{14}t\right)\ \mathrm{V/m}$ (where x, t and other values have S.I. units). The dielectric constant of the medium is . (speed of light in free space is $3\times10^{8}$ m/s)
Q23 · Numerical · Ray OpticsOpen
A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm. Refractive index of glass is 1.5. The rays converge to a point at a distance x cm from the centre of the curvature of the spherical surface. The value of x is cm.
Q24 · Numerical · Rotational MotionOpen
A circular disc has radius $R_1$ and thickness $T_1$ . Another circular disc made of the same material has radius $R_2$ and thickness $T_2$ . If the moments of inertia of both discs are same and $\dfrac{R_1}{R_2} = 2$ then $\dfrac{T_1}{T_2} = \dfrac{1}{\alpha}$ . The value of $\alpha$ is .
We corrected a printing error in the original paper
Source printed “the moment of inertia of both discs are same”.
Q25 · Numerical · Electromagnetic InductionOpen
Inductance of a coil with $10^{4}$ turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of $10\ \Omega$ . The energy density in the inductor when the current reaches $\left(\dfrac{1}{e}\right)$ of its maximum value is $\alpha\pi\times\dfrac{1}{e^2}\ \mathrm{J/m^3}$ . The value of $\alpha$ is . ( $\mu_0 = 4\pi\times10^{-7}$ Tm/A). (Take the length of the coil as 1 m)
We corrected a printing error in the original paper
Assumption “Take the length of the coil as 1 m” added; the source gives neither the length nor the turns per unit length, and the key 20 needs $n = 10^4$ turns/m (consistent with $L = 10$ mH for a long solenoid).

Chemistry

Q1 · MCQ · Coordination CompoundsOpen
Consider the transition metal ions $\ce{Mn^{3+}}$ , $\ce{Cr^{3+}}$ , $\ce{Fe^{3+}}$ and $\ce{Co^{3+}}$ and all form low spin octahedral complexes. The correct decreasing order of unpaired electrons in their respective d-orbitals of the complexes is
1. (1) $\ce{Cr^{3+}}$ $>$ $\ce{Fe^{3+}}$ $>$ $\ce{Co^{3+}}$ $>$ $\ce{Mn^{3+}}$
2. (2) $\ce{Mn^{3+}}$ $>$ $\ce{Fe^{3+}}$ $>$ $\ce{Co^{3+}}$ $>$ $\ce{Cr^{3+}}$
3. (3) $\ce{Fe^{3+}}$ $>$ $\ce{Co^{3+}}$ $>$ $\ce{Mn^{3+}}$ $>$ $\ce{Cr^{3+}}$
4. (4) $\ce{Cr^{3+}}$ $>$ $\ce{Mn^{3+}}$ $>$ $\ce{Fe^{3+}}$ $>$ $\ce{Co^{3+}}$
Q2 · MCQ · Chemical BondingOpen
The formal charges on the atoms marked as (1) to (4) in the Lewis representation of $\ce{HNO3}$ molecule respectively are
1. (1) $+1$ , 0, 0, $-1$
2. (2)0, $-1$ , 0, $+1$
3. (3)0, $+1$ , 0, $-1$
4. (4)0, 0, $-1$ , $+1$
We corrected a printing error in the original paper
Source printed “The formal changes” and “HnO $_3$ ”.
Q3 · MCQ · Alcohols, Phenols & EthersOpen
Given below are two statements :
Statement I : Phenol on treatment with $\ce{CHCl3}$ /aq. KOH under refluxing condition, followed by acidification produces p-hydroxy benzaldehyde as the major product and o-hydroxy benzaldehyde as the minor product.
Statement II : The mixture of p-hydroxybenzaldehyde and o-hydroxybenzaldehyde can be easily separated through steam distillation.
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 “p-hydroxy benzladehyde”.
Q4 · MCQ · Structure of AtomOpen
The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is J mol $^{-1}$ .
Given : $R_\mathrm{H} = 2.18\times10^{-11}$ ergs.
1. (1) $1.635\times10^{-18}$
2. (2) $9.835\times10^{5}$
3. (3) $9.835\times10^{12}$
4. (4) $1.635\times10^{-11}$
Q5 · MCQ · Classification & PeriodicityOpen
A ‘p'-block element (E) and hydrogen form a binary cation $\ce{(EH_x)^+}$ , while $\ce{EH3}$ on treatment with $\ce{K2HgI4}$ in alkaline medium gives a precipitate of basic mercury(II)amido-iodine. Given below are first ionisation enthalpy values (kJ mol $^{-1}$ ) for first element each from group 13, 14, 15 and 16. Identify the correct first ionisation enthalpy value for element E.
1. (1)1312
2. (2)1086
3. (3)1402
4. (4)801
Q6 · MCQ · Some Basic ConceptsOpen
In the reaction,
$\ce{2Al(s) + 6HCl(aq) -> 2Al^{3+}(aq) + 6Cl^{-}(aq) + 3H2(g)}$
which of the following statements is correct ?
1. (1)11.2 L $\ce{H2(g)}$ at STP is produced for every mole of HCl consumed.
2. (2)67.2 L $\ce{H2(g)}$ at STP is produced for every mole of Al that reacts.
3. (3)12 L HCl(aq) is consumed for every 6L $\ce{H2(g)}$ produced.
4. (4)33.6 L $\ce{H2(g)}$ is produced regardless of temperature and pressure for every mole of Al that reacts.
We corrected a printing error in the original paper
The source prints no question after the equation; “which of the following statements is correct ?” added.
Q7 · MCQ · SolutionsOpen
Consider a solution of $\ce{CO2(g)}$ dissolved in water in a closed container.
Which one of the following plots correctly represents variation of log (partial pressure of $\ce{CO2}$ in vapour phase above water) [y-axis] with log (mole fraction of $\ce{CO2}$ in water) [x-axis] at 25 $^\circ$ C ?
1. (1)
2. (2)
3. (3)
4. (4)
Q8 · MCQ · Coordination CompoundsOpen
A first row transition metal (M) does not liberate $\ce{H2}$ gas from dilute HCl. 1 mol of aqueous solution of $\ce{MSO4}$ is treated with excess of aqueous KCN and then $\ce{H2S(g)}$ is passed through the solution. The amount of MS (metal sulphide) formed from the above reaction is mol.
1. (1)2
2. (2)1
3. (3)3
4. (4)0
We corrected a printing error in the original paper
Source printed “A first row transition metla (M)”.
Q9 · MCQ · Haloalkanes & HaloarenesOpen
The correct order of reactivity of $\ce{CH3Br}$ in methanol with the following nucleophiles is
$\ce{F-}$ , $\ce{I-}$ , $\ce{C2H5O-}$ and $\ce{C6H5O-}$
1. (1) $\ce{I-}$ $>$ $\ce{C6H5O-}$ $>$ $\ce{F-}$ $>$ $\ce{C2H5O-}$
2. (2) $\ce{I-}$ $>$ $\ce{C2H5O-}$ $>$ $\ce{C6H5O-}$ $>$ $\ce{F-}$
3. (3) $\ce{I-}$ $>$ $\ce{C2H5O-}$ $>$ $\ce{F-}$ $>$ $\ce{C6H5O-}$
4. (4) $\ce{I-}$ $>$ $\ce{F-}$ $>$ $\ce{C6H5O-}$ $>$ $\ce{C2H5O-}$

Q10 · MCQ · ThermodynamicsOpen

Match the LIST-I with LIST-II

List-I: Thermodynamic Process		List-II: Magnitude in kJ
A.	Work done in reversible, isothermal expansion of 2 mol of ideal gas from 2 dm $^3$ to 20 dm $^3$ at 300 K.	I.	4
B.	Work done in irreversible isothermal expansion of 1 mol ideal gas from 1 m $^3$ to 3 m $^3$ at 300 K against A constant pressure of 3kPa.	II.	11.5
C.	Change in internal energy for adiabatic expansion of a 1 mol ideal gas with change of temperature = 320 K and $\bar{C}_\mathrm{V} = \dfrac{3}{2}R$ .	III.	6
D.	Change in enthalpy at constant pressure of 1 mole ideal gas with change of temperature = 337 K and $\bar{C}_\mathrm{P} = \dfrac{5}{2}R$ .	IV.	7

Choose the correct answer from the option given below :

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

Q11 · MCQ · HydrocarbonsOpen
Given below are two statements :
Statement I : Benzene is nitrated to give nitrobenzene, which on further treatment with $\ce{CH3COCl}$ / $\ce{AlCl3}$ will give
Statement II : $\ce{NO2}$ group is a m-directing, and deactivating group.
In the light of the above statements, choose the most appropriate answer from the options given below.
1. (1)Statement I is correct but Statement II is incorrect.
2. (2)Both Statement I and Statement II are correct.
3. (3)Statement I is incorrect but Statement II is correct.
4. (4)Both Statement I and Statement II are incorrect.
We corrected a printing error in the original paper
Option (4): source printed “Both Statement I and Statement II is are incorrect”.
Q12 · MCQ · Chemical KineticsOpen
$\ce{A -> products}$ (First order reaction).
Three sets of experiment were performed for a reaction under similar experimental conditions.
Run 1 $\Rightarrow$ 100 mL of 10 M solution of reactant A
Run 2 $\Rightarrow$ 200 mL of 10 M solution of reactant A
Run 3 $\Rightarrow$ 100 mL of 10 M solution of reactant A + 100 mL of $\ce{H2O}$ added.
The correct variation of rate of reaction is
1. (1)Run 1 = Run 2 = Run 3
2. (2)Run 3 $<$ Run 1 = Run 2
3. (3)Run 3 $<$ Run 1 $<$ Run 2
4. (4)Run 1 $<$ Run 2 $<$ Run 3

Q13 · MCQ · Aldehydes, Ketones & AcidsOpen

Match the LIST-I with LIST-II

List-I		List-II
Reagents		Name of Reaction involving carbonyl compound
A.	$\ce{NH2-NH2}$ , KOH	I.	Tollen's Test
B.	$\ce{Ag(NH3)2OH}$	II.	Clemmensen Reduction
C.	Aq. $\ce{CuSO4}$ , Sodium Potassium tartrate, KOH	III.	Wolff-Kishner Reduction
D.	Zn – Hg, HCl	IV.	Fehling's Test

Choose the correct answer from the options given below

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

We corrected a printing error in the original paper

Source printed “Sodium Potassium tartarate”.

Q14 · MCQ · p-Block (15–18)Open
Given below are two statements :
Statement I : The halogen that makes longest bond with hydrogen in HX, has the smallest covalent radius in its group.
Statement II : A group 15 element's hydride $\ce{EH3}$ has the lowest boiling point among corresponding hydrides of other group 15 elements. The maximum covalency of that element E is 4.
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)Both Statement I and Statement II are false.
4. (4)Statement I is true but Statement II is false.
Q15 · MCQ · BiomoleculesOpen
Given below are two statements:
Statement I : Sucrose is dextrorotatory. However sucrose upon hydrolysis gives a solution having mixture of products. This solution shows laevorotation.
Statement II : Hydrolysis of sucrose gives glucose and fructose. Since the laevorotation of glucose is more than the dextrorotation of fructose the resulting solution becomes laevorotatory.
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 false.
3. (3)Both Statement I and Statement II are true.
4. (4)Statement I is true but Statement II is false.
Q16 · MCQ · AminesOpen
‘A' is a neutral organic compound (M. F : $\ce{C8H9ON}$ ). On treatment with aqueous $\ce{Br2}$ / $\ce{HO^{(-)}}$ , ‘A' forms a compound ‘B' which is soluble in dilute acid. ‘B' on treatment with aqueous $\ce{NaNO2}$ /HCl(0–5 $^\circ$ C) produces a compound ‘C' which on treatment with CuCN/NaCN produces ‘D' Hydrolysis of ‘D' produces ‘E' which is also obtainable from the hydrolysis of ‘A'. ‘E' on treatment with acidified $\ce{KMnO4}$ produces ‘F'. ‘F' contains two different types of hydrogen atoms. The structure of ‘A' is
1. (1)
2. (2)
3. (3)
4. (4)
Q17 · MCQ · Haloalkanes & HaloarenesOpen
The correct order of the rate of reaction of the following reactants with nucleophile by $\mathrm{S_N1}$ mechanism is :
(Given : Structure I and II are rigid)
1. (1)IV $<$ III $<$ II $<$ I
2. (2)III $<$ I $<$ II $<$ IV
3. (3)II $<$ I $<$ III $<$ IV
4. (4)I $<$ II $<$ III $<$ IV
Q18 · MCQ · Chemical BondingOpen
Two p-block elements X and Y form fluorides of the type $\ce{EF3}$ . The fluoride compound $\ce{XF3}$ is a Lewis acid and $\ce{YF3}$ is a Lewis base. The hybridization of the central atoms of $\ce{XF3}$ and $\ce{YF3}$ respectively are
1. (1)Both sp $^3$
2. (2)sp $^2$ and sp $^3$
3. (3)sp $^3$ and sp $^2$
4. (4)Both sp $^2$
We corrected a printing error in the original paper
Source printed “form fluroides of the type”.
Q19 · MCQ · Haloalkanes & HaloarenesOpen
As compared with chlorocyclohexane, which of the following statements correctly apply to chlorobenzene ?
- (A)The magnitude of negative charge is more on chlorine atoms
- (B)The C – Cl bond has partial double bond character
- (C)C – Cl bond is less polar
- (D)C – Cl bond is longer due to repulsion between delocalised electrons of the aromatic ring and lone pairs of electrons of chlorine.
- (E)The C–Cl bond is formed using sp $^2$ hybridised orbital of carbon.
Choose the correct answer from the options given below :
1. (1)A, C and E only
2. (2)B, C and D only
3. (3)A, D and E only
4. (4)B, C and E only
Q20 · MCQ · SolutionsOpen
Given below are two statements:
Statement I : The Henry's law constant $K_\mathrm{H}$ is constant with respect to variations in solution's concentration over the range for which the solution is ideally dilute.
Statement II : $K_\mathrm{H}$ does not differ for the same solute in different solvents.
In the light of the above statements, choose the correct answer from the options.
1. (1)Statement I is false but Statement II is true.
2. (2)Statement I is true but Statement II is false.
3. (3)Both Statement I and Statement II are true.
4. (4)Both Statement I and Statement II are false.
We corrected a printing error in the original paper
Source printed “over the range for which the solutions is ideally dilute”.
Q21 · Numerical · HydrocarbonsOpen
The cycloalkane (X) on bromination consumes one mole of bromine per mole of (X) and gives the product (Y) in which C:Br ratio is 3 : 1. The percentage of bromine in the product (Y) is %. (Nearest integer)
(Given : Molar mass in g mol $^{-1}$ H : 1, C : 12, O : 16, Br : 80 )
Q22 · Numerical · ElectrochemistryOpen
Consider the following electrochemical cell at 298K
$\mathrm{Pt}\,|\,\ce{HSnO2^-}(\mathrm{aq})\,|\,\ce{Sn(OH)6^{2-}}(\mathrm{aq})\,|\,\ce{Bi2O3}(\mathrm{s})\,|\,\mathrm{Bi}(\mathrm{s})$ .
If the reaction quotient at a given time is $10^{6}$ , then the cell EMF ( $E_\mathrm{cell}$ ) is $\times\,10^{-1}$ V (Nearest integer).
Given the standard half-cell reduction potential as
$E^{0}_{\ce{Bi2O3}/\mathrm{Bi},\,\ce{OH-}} = -0.44$ V and
$E^{0}_{\ce{Sn(OH)6^{2-}}/\ce{HSnO2^-},\,\ce{OH-}} = -0.90$ V
We corrected a printing error in the original paper
Source printed the second electrode as “Sn(OH) $_6^{2-}$ /HSnO $_2^-$ , OH” (charge of $\ce{OH-}$ missing).
Q23 · Numerical · Chemical KineticsOpen
The temperature at which the rate constants of the given below two gaseous reactions become equal is K. (Nearest integer).
$\ce{X -> Y}$ $k_1 = 10^{6}\,e^{\frac{-30000}{T}}$
$\ce{P -> Q}$ $k_2 = 10^{4}\,e^{\frac{-24000}{T}}$
Given : $\ln 10 = 2.303$
Q24 · Numerical · Purification & CharacterisationOpen
Sodium fusion extract of an organic compound (Y) with $\ce{CHCl3}$ and chlorine water gives violet color to the $\ce{CHCl3}$ layer. 0.15g of (Y) gave 0.12 g of the silver halide precipitate in Carius method. Percentage of halogen in the compound (Y) is . (Nearest integer).
(Given : molar mass g mol $^{-1}$ C : 12, H : 1, Cl : 35.5, Br : 80, I : 127)
Q25 · Numerical · ThermodynamicsOpen
Dissociation of a gas $\ce{A2}$ takes place according to the following chemical reactions. At equilibrium, the total pressure is 1 bar at 300K.
$\ce{A2(g) <=> 2A(g)}$
The standard Gibbs energy of formation of the involved substances has been provided below:
Substance $\Delta G_\mathrm{f}^\circ$ / kJ mol $^{-1}$
$\ce{A2}$ $-100.00$
A $-50.832$
The degree of dissociation of $\ce{A2(g)}$ is given by $(x\times10^{-2})^{1/2}$ where $x$ = . (Nearest integer).
[Given : $R = 8$ J mol $^{-1}$ K $^{-1}$ , $\log 2 = 0.3010$ , $\log 3 = 0.48$ ]
We corrected a printing error in the original paper
Source printed the table heading as “ $\Delta G_\mathrm{t}^\circ$ ” (subscript t for f, formation).

Maths

Q1 · MCQ · VectorsOpen
Let $\overrightarrow{AB} = 2\hat i + 4\hat j - 5\hat k$ and $\overrightarrow{AD} = \hat i + 2\hat j + \lambda\hat k$ , $\lambda \in \mathbb{R}$ . Let the projection of the vector $\vec v = \hat i + \hat j + \hat k$ on the diagonal $\overrightarrow{AC}$ of the parallelogram $ABCD$ be of length one unit. If $\alpha, \beta$ , where $\alpha > \beta$ , be the roots of the equation $\lambda^2x^2 - 6\lambda x + 5 = 0$ , then $2\alpha - \beta$ is equal to
1. (1)1
2. (2)4
3. (3)3
4. (4)6
We corrected a printing error in the original paper
Source printed “ $2\hat i + 4\hat j - 5k$ ” and “ $\hat i + 2\hat j + \lambda k$ ” (unit vector $\hat k$ printed without its hat).
Q2 · MCQ · Sets, Relations & FunctionsOpen
Let the relation $R$ on the set $M = \{1, 2, 3, \ldots, 16\}$ be given by $R = \{(x, y) : 4y = 5x - 3,\ x, y \in M\}.$ Then the minimum number of elements required to be added in $R$ , in order to make the relation symmetric, is equal to
1. (1)1
2. (2)2
3. (3)4
4. (4)3
Q3 · MCQ · Area under CurvesOpen
Let the line $x = -1$ divide the area of the region $\{(x, y) : 1 + x^2 \le y \le 3 - x\}$ in the ratio $m : n$ , $\gcd(m, n) = 1$ . Then $m + n$ is equal to
1. (1)25
2. (2)28
3. (3)26
4. (4)27
Q4 · MCQ · ProbabilityOpen
Two distinct numbers $a$ and $b$ are selected at random from $1, 2, 3, \ldots, 50$ . The probability, that their product $ab$ is divisible by 3, is
1. (1) $\dfrac{561}{1225}$
2. (2) $\dfrac{664}{1225}$
3. (3) $\dfrac{272}{1225}$
4. (4) $\dfrac{8}{25}$
Q5 · MCQ · Applications of DerivativesOpen
Let $f(x) = x^{2025} - x^{2000}$ , $x \in [0, 1]$ and the minimum value of the function $f(x)$ in the interval $[0, 1]$ be $(80)^{80}(n)^{-81}$ . Then $n$ is equal to
1. (1) $-81$
2. (2) $-40$
3. (3) $-41$
4. (4) $-80$
Q6 · MCQ · 3D GeometryOpen
Let $P(\alpha, \beta, \gamma)$ be the point on the line $\dfrac{x-1}{2} = \dfrac{y+1}{-3} = z$ at a distance $4\sqrt{14}$ from the point $(1, -1, 0)$ and nearer to the origin. Then the shortest distance, between the lines $\frac{x-\alpha}{1} = \frac{y-\beta}{2} = \frac{z-\gamma}{3} \quad\text{and}\quad \frac{x+5}{2} = \frac{y-10}{1} = \frac{z-3}{1},$ is equal to
1. (1) $7\sqrt{\dfrac54}$
2. (2) $4\sqrt{\dfrac75}$
3. (3) $4\sqrt{\dfrac57}$
4. (4) $2\sqrt{\dfrac74}$
Q7 · MCQ · ProbabilityOpen
If a random variable $x$ has the probability distribution
$x$ 0 1 2 3 4 5 6 7
$p(x)$ 0 $2k$ $k$ $3k$ $2k^2$ $2k$ $k^2+k$ $7k^2$
then $P(3 < x \le 6)$ is equal to
1. (1)0.34
2. (2)0.22
3. (3)0.64
4. (4)0.33
Q8 · MCQ · Quadratic EquationsOpen
The number of distinct real solutions of the equation $x\lvert x + 4\rvert + 3\lvert x + 2\rvert + 10 = 0$ is
1. (1)3
2. (2)1
3. (3)0
4. (4)2
Q9 · MCQ · Differential EquationsOpen
Let $f : [1, \infty) \to \mathbb{R}$ be a differentiable function, If $6\int_1^x f(t)\,dt = 3xf(x) + x^3 - 4$ for all $x \ge 1$ , then the value of $f(2) - f(3)$ is
1. (1) $-4$
2. (2) $-3$
3. (3)4
4. (4)3
Q10 · MCQ · Conic SectionsOpen
If the line $\alpha x + 2y = 1$ , where $\alpha \in \mathbb{R}$ , does not meet the hyperbola $x^2 - 9y^2 = 9$ , then a possible value of $\alpha$ is:
1. (1)0.6
2. (2)0.8
3. (3)0.5
4. (4)0.7
Q11 · MCQ · 3D GeometryOpen
If the image of the point $P(1, 2, a)$ in the line $\dfrac{x-6}{3} = \dfrac{y-7}{2} = \dfrac{7-z}{2}$ is $Q(5, b, c)$ , then $a^2 + b^2 + c^2$ is equal to
1. (1)293
2. (2)264
3. (3)298
4. (4)283
Q12 · MCQ · CirclesOpen
Let the set of all values of $r$ , for which the circles $(x + 1)^2 + (y + 4)^2 = r^2$ and $x^2 + y^2 - 4x - 2y - 4 = 0$ intersect at two distinct points be the interval $(\alpha, \beta)$ . Then $\alpha\beta$ is equal to
1. (1)25
2. (2)20
3. (3)21
4. (4)24
Q13 · MCQ · Matrices & DeterminantsOpen
If $A = \begin{bmatrix} 2 & 3\\ 3 & 5\end{bmatrix}$ , then the determinant of the matrix $(A^{2025} - 3A^{2024} + A^{2023})$ is
1. (1)28
2. (2)12
3. (3)24
4. (4)16
Q14 · MCQ · Inverse TrigonometryOpen
If the domain of the function $f(x) = \sin^{-1}\left(\frac{5-x}{3+2x}\right) + \frac{1}{\log_e(10-x)}$ is $(-\infty, \alpha] \cup [\beta, \gamma) - \{\delta\}$ , then $6(\alpha + \beta + \gamma + \delta)$ is equal to
1. (1)70
2. (2)66
3. (3)67
4. (4)68
We corrected a printing error in the original paper
Source printed the second term garbled as “ $\dfrac{1}{\log_e(1\text{-}0}$ ” (a stroke through the 1, the closing “ $x)$ ” missing); corrected to the intended “ $\dfrac{1}{\log_e(10-x)}$ ” (the source solution uses $10 - x > 0$ , $10 - x \neq 1$ , and the printed key needs $\gamma = 10$ , $\delta = 9$ ).
Q15 · MCQ · Definite IntegrationOpen
The value of $\displaystyle\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{1}{[x] + 4}\right)dx$ , where $[\bullet]$ denotes the greatest integer function, is
1. (1) $\dfrac{1}{60}(21\pi - 1)$
2. (2) $\dfrac{1}{60}(\pi - 7)$
3. (3) $\dfrac{7}{60}(3\pi - 1)$
4. (4) $\dfrac{7}{60}(\pi - 3)$
Q16 · MCQ · Binomial TheoremOpen
The coefficient of $x^{48}$ in $(1 + x) + 2(1 + x)^2 + 3(1 + x)^3 + \ldots + 100(1 + x)^{100}$ is equal to:
1. (1) $100\cdot{}^{100}C_{49} - {}^{100}C_{50}$
2. (2) ${}^{100}C_{50} + {}^{101}C_{49}$
3. (3) $100\cdot{}^{100}C_{49} - {}^{100}C_{48}$
4. (4) $100\cdot{}^{101}C_{49} - {}^{101}C_{50}$
We corrected a printing error in the original paper
Source printed option (4) as “ $100\cdot{}^{101}C_{49} - {}^{100}C_{50}$ ” (then no option is correct); corrected to the intended “ $100\cdot{}^{101}C_{49} - {}^{101}C_{50}$ ” (the correct coefficient and the source solution's result; printed key (4)).
Q17 · MCQ · Conic SectionsOpen
If the chord joining the points $P_1(x_1, y_1)$ and $P_2(x_2, y_2)$ on the parabola $y^2 = 12x$ subtends a right angle at the vertex of the parabola, then $x_1x_2 - y_1y_2$ is equal to
1. (1)288
2. (2)280
3. (3)284
4. (4)292
Q18 · MCQ · Inverse TrigonometryOpen
The number of solutions of $\tan^{-1}4x + \tan^{-1}6x = \dfrac{\pi}{6}$ , where $-\dfrac{1}{2\sqrt6} < x < \dfrac{1}{2\sqrt6}$ is equal to
1. (1)3
2. (2)0
3. (3)1
4. (4)2
Q19 · MCQ · Differential EquationsOpen
Let the solution curve of the differential equation $x\,dy - y\,dx = \sqrt{x^2 + y^2}\,dx$ , $x > 0$ , $y(1) = 0$ , be $y = y(x)$ . Then $y(3)$ is equal to
1. (1)4
2. (2)6
3. (3)1
4. (4)2
Q20 · MCQ · Sequences & SeriesOpen
If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4, then the sum of its first twelve terms is
1. (1) $-20$
2. (2) $-24$
3. (3) $-26$
4. (4) $-22$
Q21 · Numerical · Complex NumbersOpen
Let $\alpha = \dfrac{-1 + i\sqrt3}{2}$ and $\beta = \dfrac{-1 - i\sqrt3}{2}$ , $i = \sqrt{-1}$ . If $(7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10},$ then $m$ is .
Q22 · Numerical · Matrices & DeterminantsOpen
Let $A$ be a $3 \times 3$ matrix such that $A + A^T = O$ . If $A\begin{bmatrix} 1\\ -1\\ 0\end{bmatrix} = \begin{bmatrix} 3\\ 3\\ 2\end{bmatrix},\quad A^2\begin{bmatrix} 1\\ -1\\ 0\end{bmatrix} = \begin{bmatrix} -3\\ 19\\ -24\end{bmatrix}$ and $\det(\operatorname{adj}(2\operatorname{adj}(A + I))) = (2)^{\alpha}\cdot(3)^{\beta}\cdot(11)^{\gamma}$ , $\alpha, \beta, \gamma$ are non-negative integers, then $\alpha + \beta + \gamma$ is equal to .
Q23 · Numerical · Indefinite IntegrationOpen
If $\int(\sin x)^{\frac{-11}{2}}(\cos x)^{\frac{-5}{2}}\,dx = -\frac{p_1}{q_1}(\cot x)^{\frac92} - \frac{p_2}{q_2}(\cot x)^{\frac52} - \frac{p_3}{q_3}(\cot x)^{\frac12} + \frac{p_4}{q_4}(\cot x)^{\frac{-3}{2}} + C,$ where $p_i$ and $q_i$ are positive integers with $\gcd(p_i, q_i) = 1$ for $i = 1, 2, 3, 4$ and $C$ is the constant of integration, then $\dfrac{15p_1p_2p_3p_4}{q_1q_2q_3q_4}$ is equal to .
Q24 · Numerical · TrigonometryOpen
If $\dfrac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ} = \dfrac{\alpha + \beta\sqrt5}{2}$ , where $\alpha, \beta \in \mathbb{N}$ , then $\alpha + \beta$ is equal to .
Q25 · Numerical · Permutations & CombinationsOpen
Let $ABC$ be a triangle. Consider four points $p_1$ , $p_2$ , $p_3$ , $p_4$ on the side $AB$ , five points $p_5$ , $p_6$ , $p_7$ , $p_8$ , $p_9$ on the side $BC$ and four points $p_{10}$ , $p_{11}$ , $p_{12}$ , $p_{13}$ on the side $AC$ . None of these points is a vertex of the triangle $ABC$ . Then the total number of pentagons, that can be formed by taking all the vertices from the points $p_1$ , $p_2$ , $\ldots$ , $p_{13}$ , is .

Substance	$\Delta G_\mathrm{f}^\circ$ / kJ mol $^{-1}$
$\ce{A2}$	$-100.00$
A	$-50.832$

$x$	0	1	2	3	4	5	6	7
$p(x)$	0	$2k$	$k$	$3k$	$2k^2$	$2k$	$k^2+k$	$7k^2$