JEE Main 24 Jan 2026, Shift 1

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

Physics

Match the List-I with List-II

List-I		List-II
A.	Magnetic induction	I.	$\mathrm{M\,L\,T^{-2}A^{-2}}$
B.	Magnetic flux	II.	$\mathrm{M\,L^{2}\,T^{-2}A^{-2}}$
C.	Magnetic permeability	III.	$\mathrm{M\,L^{0}\,T^{-2}A^{-1}}$
D.	Self inductance	IV.	$\mathrm{M\,L^{2}\,T^{-2}A^{-1}}$

Choose the correct answer from the options given below:

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

Q2 · MCQ · Electric Charges and FieldsOpen
Three charges $+2q$ , $+3q$ and $-4q$ are situated at $(0, -3a)$ , $(2a, 0)$ and $(-2a, 0)$ respectively in the $xy$ plane. The resultant dipole moment about origin is
1. (1) $2qa\left(3\hat j - \hat i\right)$
2. (2) $2qa\left(3\hat i - 7\hat j\right)$
3. (3) $2qa\left(7\hat i - 3\hat j\right)$
4. (4) $2qa\left(3\hat j - 7\hat i\right)$
We corrected a printing error in the original paper
Source printed “ $+2q$ . $+3q$ ” (full stop for the comma).
Q3 · MCQ · OscillationsOpen
A cylindrical block of mass $M$ and area of cross section $A$ is floating in a liquid of density $\rho$ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is .
1. (1) $2\pi\sqrt{\dfrac{M}{\rho A g}}$
2. (2) $\pi\sqrt{\dfrac{2M}{\rho A g}}$
3. (3) $\pi\sqrt{\dfrac{\rho A}{M g}}$
4. (4) $2\pi\sqrt{\dfrac{\rho A}{M g}}$
Q4 · MCQ · ThermodynamicsOpen
Density of water at $4^\circ$ C and $20^\circ$ C are $1000\ \mathrm{kg/m^3}$ and $998\ \mathrm{kg/m^3}$ respectively. The increase in internal energy of 4 kg water when it is heated from $4^\circ$ C to $20^\circ$ C is J.
(Specific heat capacity of water $= 4.2\ \mathrm{kJ\,kg^{-1}\,{}^\circ C^{-1}}$ and 1 atmospheric pressure $= 10^{5}$ Pa)
1. (1)315826.2
2. (2)234699.2
3. (3)258700.8
4. (4)268799.2
We corrected a printing error in the original paper
Source printed “1000 kg/m $^3$ and respectively” and “4.2 J/kg.”; corrected to the intended “1000 kg/m $^3$ and 998 kg/m $^3$ respectively” and “4.2 kJ kg $^{-1}$ $^\circ$ C $^{-1}$ ” (the values the key uses).
Q5 · MCQ · Current ElectricityOpen
Two resistors of $100\ \Omega$ each are connected in series with a 9 V battery. A voltmeter of $400\ \Omega$ resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is V.
1. (1)3
2. (2)4.5
3. (3)4
4. (4)2
Q6 · MCQ · Ray OpticsOpen
The exit surface of a prism with refractive index $n$ is coated with a material having refractive index $\dfrac{n}{2}$ . When this prism is set for minimum angle of deviation it exactly meets the condition of critical angle. The prism angle is
1. (1) $60^\circ$
2. (2) $15^\circ$
3. (3) $30^\circ$
4. (4) $45^\circ$
Q7 · MCQ · AtomsOpen
Two electrons are moving in orbits of two hydrogen like atoms with speeds $3\times10^{5}$ m/s and $2.5\times10^{5}$ m/s respectively. If the radii of these orbits are nearly same then the possible orders of energy states are respectively.
1. (1)6 and 5
2. (2)9 and 8
3. (3)8 and 10
4. (4)10 and 12
We corrected a printing error in the original paper
Source printed “the possible order of energy states are”.
Q8 · MCQ · Ray OpticsOpen
In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and 5 cm. Total magnification obtained with this system for normal adjustment is $(5)^{k}$ . The value of $k$ is
1. (1)2
2. (2)5
3. (3)3.5
4. (4)4
Q9 · MCQ · Alternating CurrentOpen
For the series LCR circuit connected with 220 V, 50 Hz a.c source as shown in the figure, the power factor is $\dfrac{\alpha}{10}$ . The value of $\alpha$ is
1. (1)4
2. (2)10
3. (3)6
4. (4)8

Q10 · MCQ · Electromagnetic WavesOpen

Match the List-I with List-II

List-I		List-II
A	Radio-wave	I	is produced by Magnetron valve
B	Micro-wave	II	Due to change in the vibrational modes of atoms
C	Infrared-wave	III	Due to inner shell electrons moving from higher energy level to lower energy level
D	X-ray	IV	Due to rapid acceleration of electrons

Choose the correct answer from the options given below:

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

We corrected a printing error in the original paper

Source printed “Magnetron value”.

Q11 · MCQ · OscillationsOpen
A spring of force constant 15 N/m is cut into two pieces. If the ratio of their length is $1:3$ , then the force constant of smaller piece is N/m
1. (1)15
2. (2)20
3. (3)60
4. (4)45
Q12 · MCQ · Current ElectricityOpen
Two resistors $2\ \Omega$ and $3\ \Omega$ are connected in the gaps of bridge as shown in figure. The null point is obtained with the contact of jockey at some point on wire XY. When an unknown resistor is connected in parallel with $3\ \Omega$ resistor, the null point is shifted by 22.5 cm toward Y. The resistance of unknown resistor is $\Omega$ . (Take the length of the wire XY as 100 cm)
1. (1)3
2. (2)2
3. (3)4
4. (4)1
We corrected a printing error in the original paper
Assumption “(Take the length of the wire XY as 100 cm)” added; the source leaves it unstated.
Q13 · MCQ · NucleiOpen
Given below are two statements:
Statement I : For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon.
Statement II : For all elements, nuclei with less binding energy per nucleon transform to nuclei with greater binding energy per nucleon.
In the light of the above statements, choose the correct answer from the options given below:
1. (1)Both Statement I and Statement II are true
2. (2)Statement I is true but Statement II is false
3. (3)Both Statement I and Statement II are false
4. (4)Statement I is false but Statement II is true
We corrected a printing error in the original paper
Source printed “nuclei with less binding energy per nucleon transforms”.
Q14 · MCQ · Thermal Properties of MatterOpen
A brass wire of length 2 m and radius 1 mm at $27^\circ$ C is held taut between two rigid supports. Initially it was cooled to a temperature of $-43^\circ$ C creating a tension $T$ in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to $1.4T$ , is $^\circ$ C
1. (1) $-86$
2. (2) $-71$
3. (3) $-65$
4. (4) $-80$
Q15 · MCQ · Electric Potential and CapacitanceOpen
The electrostatic potential in a charged spherical region of radius $r$ varies as $V = ar^{3} + b$ , where $a$ and $b$ are constants. The total charge in the sphere of unit radius is $\alpha\times\pi a\epsilon_0$ . The value of $\alpha$ is .
(permittivity of vacuum is $\epsilon_0$ )
1. (1) $-12$
2. (2) $-6$
3. (3) $-9$
4. (4) $-8$
Q16 · MCQ · Rotational MotionOpen
Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from rest the heavier mass is observed to fall 81 cm in 9 s. The rotational inertia of the pulley is $\mathrm{kg.m^2}$ .
( $g = 9.8\ \mathrm{m/s^2}$ )
1. (1) $9.5\times10^{-3}$
2. (2) $4.75\times10^{-3}$
3. (3) $1.86\times10^{-2}$
4. (4) $8.3\times10^{-3}$
Q17 · MCQ · Wave OpticsOpen
An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and $2\sqrt3$ (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is .
1. (1) $60^\circ$
2. (2) $10^\circ$
3. (3) $30^\circ$
4. (4) $45^\circ$
Q18 · MCQ · Motion in a PlaneOpen
A boy throws a ball into air at $45^\circ$ from the horizontal to land it on a roof of a building of height $H$ . If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of $H$ is m.
( $g = 10\ \mathrm{m/s^2}$ )
1. (1)20
2. (2)10
3. (3)25
4. (4)15
We corrected a printing error in the original paper
Source printed “A boy thrown a ball”.
Q19 · MCQ · Electric Potential and CapacitanceOpen
There are three concentric conducting spherical shells A, B and C of radii $a$ , $b$ and $c$ carrying charges $q_1$ , $q_2$ and $q_3$ respectively. The potential of the spheres A, B and C respectively, are :
1. (1) $\dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2+q_3}{a}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2+q_3}{b}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2+q_3}{c}\right)$
2. (2) $\dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2+q_3}{a}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2}{b}+\dfrac{q_3}{c}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1}{a}+\dfrac{q_2}{b}+\dfrac{q_3}{c}\right)$
3. (3) $\dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1}{a}+\dfrac{q_2}{b}+\dfrac{q_3}{c}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2}{b}+\dfrac{q_3}{c}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2+q_3}{c}\right)$
4. (4) $\dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1}{a}+\dfrac{q_2}{b}+\dfrac{q_3}{c}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2+q_3}{b}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2+q_3}{c}\right)$
We corrected a printing error in the original paper
Source printed “three co-centric conducting spherical shells A, B and C of radii $a$ , $b$ and $c$ respectively” (the charges used in the options are never stated); corrected to the intended “three concentric conducting spherical shells A, B and C of radii $a$ , $b$ and $c$ carrying charges $q_1$ , $q_2$ and $q_3$ respectively”.
Q20 · MCQ · GravitationOpen
Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process is J.
(Gravitational constant $G = 6.7\times10^{-11}\ \mathrm{N\,m^2/kg^2}$ )
1. (1) $9.86\times10^{-6}$
2. (2) $2.85\times10^{-7}$
3. (3) $1.74\times10^{-7}$
4. (4) $4.77\times10^{-7}$
We corrected a printing error in the original paper
Source printed “The work done in this process ___ J” (“is” missing).
Q21 · Numerical · Magnetism and MatterOpen
A short bar magnet placed with its axis at $30^\circ$ with an external field of 800 Gauss, experiences a torque of 0.016 N.m. The work done in moving it from most stable to most unstable position is $\alpha\times10^{-3}$ J. The value of $\alpha$ is .
Q22 · Numerical · Kinetic Theory of GasesOpen
A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature $50^\circ$ C. The gas is now heated to $100^\circ$ C. The modified pressure is Pa.
We corrected a printing error in the original paper
Source printed “heated to double its temperature”; reworded to “heated to $100^\circ$ C”, the reading behind the NTA key 3730 (doubling the absolute temperature would give 6460 Pa).
Q23 · Numerical · Semiconductor ElectronicsOpen
A voltage regulating circuit consisting of Zener diode, having break-down voltage of 10 V and maximum power dissipation of 0.4 W, is operated at 15 V. The approximate value of protective resistance in this circuit is $\Omega$ .
Q24 · Numerical · Newton's Laws of MotionOpen
In the given figure the blocks A, B and C weigh 4 kg, 6 kg and 8 kg respectively. The co-efficient of sliding friction between any two surfaces is 0.5. The force $\vec F$ required to slide the block C with constant speed is N. (Use $g = 10\ \mathrm{m/s^2}$ )
We corrected a printing error in the original paper
Answer corrected; the source key is (210) — it holds A fixed (friction 20 N on A), but in the figure A rests free on B and moves with it: $T = 50$ N, $F = 90 + 50 + 50 = 190$ N; source printed “(Used $g = 10\ \mathrm{m/s^2}$ )”.
Q25 · Numerical · Mechanical Properties of FluidsOpen
Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 cm/s coalesce to form a bigger drop. The terminal velocity of bigger drop is cm/s.

Chemistry

Q1 · MCQ · Coordination CompoundsOpen
Given below are two statements :
Statement-I Hybridisation, shape and spin only magnetic moment of $\ce{K3[Co(CO3)3]}$ are sp $^3$ d $^2$ , octahedral and 4.9 BM respectively.
Statement-II Geometry, hybridisation and spin only magnetic moment values (BM) of the ions $\ce{[Ni(CN)4]^{2-}}$ , $\ce{[MnBr4]^{2-}}$ and $\ce{[CoF6]^{3-}}$ respectively are square planar, tetrahedral, octahedral : dsp $^2$ , sp $^3$ , sp $^3$ d $^2$ and 0, 5.9, 4.9.
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 false but statement-II is true
3. (3)Both statement-I and statement-II are true
4. (4)Statement-I is true but statement-II is false
We corrected a printing error in the original paper
Answer corrected; the source key is (3) — $\ce{[Co(CO3)3]^{3-}}$ is a low-spin Co(III) (d $^6$ ) complex like $\ce{[Co(C2O4)3]^{3-}}$ : d $^2$ sp $^3$ , diamagnetic (0 BM), so Statement-I is false and Statement-II is true; also source printed “spin only magnetic moment of $\ce{K3[Co(CO3)3]}$ is”.
Q2 · MCQ · Chemical KineticsOpen
$\ce{A -> D}$ is an endothermic reaction occurring in three steps (elementary).
(i) $\ce{A -> B}$ $\Delta H_\mathrm{i} = +$ ve
(ii) $\ce{B -> C}$ $\Delta H_\mathrm{ii} = -$ ve
(iii) $\ce{C -> D}$ $\Delta H_\mathrm{iii} = -$ ve
Which of the following graphs between potential energy (y-axis) vs reaction coordinate (x-axis) correctly represents the reaction profile of $\ce{A -> D}$ ?
1. (1)
2. (2)
3. (3)
4. (4)
Q3 · MCQ · HydrocarbonsOpen
Arrange the following alkenes in decreasing order of stability.
Choose the correct answer from the options given below :
1. (1)III $>$ I $>$ II $>$ IV
2. (2)III $>$ II $>$ I $>$ IV
3. (3)I $>$ III $>$ II $>$ IV
4. (4)I $>$ III $>$ IV $>$ II
Q4 · MCQ · Chemical BondingOpen
Given below are statements about some molecules/ions.
Identify the CORRECT statements.
- (A)The dipole moment value of $\ce{NF3}$ is higher than that of $\ce{NH3}$ .
- (B)The dipole moment value of $\ce{BeH2}$ is zero.
- (C)The bond order of $\ce{O2^{2-}}$ and $\ce{F2}$ is same.
- (D)The formal charge on the central oxygen atom of ozone is $-1$ .
- (E)In $\ce{NO2}$ , all the three atoms satisfy the octet rule, hence it is very stable.
Choose the correct answer from the options given below :
1. (1)A, B, C, D & E
2. (2)B & C only
3. (3)B, C & D only
4. (4)A, C & D only
Q5 · MCQ · SolutionsOpen
A solution is prepared by dissolving 0.3 g of a non-volatile non-electrolyte solute ‘A' of molar mass 60 g mol $^{-1}$ and 0.9 g of a non-volatile non-electrolyte solute ‘B' of molar mass 180 g mol $^{-1}$ in 100 mL $\ce{H2O}$ at 27 $^\circ$ C. Osmotic pressure of the solution will be
[Given : $R = 0.082$ L atm K $^{-1}$ mol $^{-1}$ ]
1. (1)1.23 atm
2. (2)2.46 atm
3. (3)0.82 atm
4. (4)1.47 atm
Q6 · MCQ · Chemical BondingOpen
Among the following, the CORRECT combinations are :
- (A) $\ce{IF3}$ $\rightarrow$ T-shaped (sp $^3$ d)
- (B) $\ce{IF5}$ $\rightarrow$ Square pyramidal (sp $^3$ d $^2$ )
- (C) $\ce{IF7}$ $\rightarrow$ Pentagonal bipyramidal (sp $^3$ d $^3$ )
- (D) $\ce{ClO4^-}$ $\rightarrow$ Square planar (sp $^2$ d)
Choose the correct answer from the options given below :
1. (1)A, B and C only
2. (2)A and B only
3. (3)A, B, C and D
4. (4)B, C and D Only
Q7 · MCQ · AminesOpen
The correct stability order of the following diazonium salts is
1. (1)A $>$ B $>$ C $>$ D
2. (2)C $>$ D $>$ B $>$ A
3. (3)A $>$ C $>$ D $>$ B
4. (4)C $>$ A $>$ D $>$ B
Q8 · MCQ · Coordination CompoundsOpen
Consider a mixture ‘X' which is made by dissolving 0.4 mol of $\ce{[Co(NH3)5SO4]Br}$ and 0.4 mol of $\ce{[Co(NH3)5Br]SO4}$ in water to make 4 L of solution. When 2 L of mixture ‘X' is allowed to react with excess of $\ce{AgNO3}$ , it forms precipitate ‘Y'. The rest 2 L of mixture ‘X' reacts with excess $\ce{BaCl2}$ to form precipitate ‘Z'. Which of the following statements is CORRECT.
1. (1)0.2 mol of ‘Z' is formed
2. (2)‘Y' is $\ce{BaSO4}$ and ‘Z' is AgBr
3. (3)0.4 mol of ‘Z' is formed
4. (4)0.1 mol of ‘Y' is formed
Q9 · MCQ · Coordination CompoundsOpen
Given below are two statements
Statement-I : The number of paramagnetic species among $\ce{[CoF6]^{3-}}$ , $\ce{[TiF6]^{3-}}$ , $\ce{V2O5}$ and $\ce{[Fe(CN)6]^{3-}}$ is 3.
Statement-II : $\ce{K4[Fe(CN)6]}$ $<$ $\ce{K3[Fe(CN)6]}$ $<$ $\ce{[Fe(H2O)6]SO4.H2O}$ $<$ $\ce{[Fe(H2O)6]Cl3}$ is the correct order in terms of number of unpaired electron(s) in the complexes.
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 “Statements-I :”.
Q10 · MCQ · Practical / Qualitative AnalysisOpen
Consider three metal chlorides x, y and z, where x is water soluble at room temperature, y is sparingly soluble in water at room temperature and z is soluble in hot water. x, y and z are respectively
1. (1) $\ce{MgCl2}$ , AgCl and $\ce{AlCl3}$
2. (2)AgCl, $\ce{Hg2Cl2}$ and $\ce{PbCl2}$
3. (3) $\ce{AlCl3}$ , $\ce{PbCl2}$ and $\ce{BaCl2}$
4. (4) $\ce{CuCl2}$ , AgCl and $\ce{PbCl2}$

Q11 · MCQ · Haloalkanes & HaloarenesOpen

Match the List-I with List-II

List-I		List-II
(Chloro derivative)		(Example)
A.	Vinyl Chloride	I.	$\ce{CH2=CH-CH2Cl}$
B.	Benzyl chloride	II.	$\ce{CH3-CH(Cl)CH3}$
C.	Alkyl chloride	III.	$\ce{CH2=CHCl}$
D.	Allyl chloride	IV.

Choose the correct answer from the options given below :

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

We corrected a printing error in the original paper

List-II entry II: source printed “CH $_3$ = CH(Cl)CH $_3$ ” (a double bond on a CH $_3$ carbon); corrected to the intended alkyl chloride “CH $_3$ –CH(Cl)CH $_3$ ” (2-chloropropane).

Q12 · MCQ · SolutionsOpen
‘W' g of a non-volatile electrolyte solid solute of molar mass ‘M' g mol $^{-1}$ when dissolved in 100 mL water, decreases vapour pressure of water from 640 mm Hg to 600 mm Hg. If aqueous solution of the electrolyte boils at 375 K and $K_\mathrm{b}$ for water is 0.52 K kg mol $^{-1}$ , then the mole fraction of the electrolyte solute ( $x_2$ ) in the solution can be expressed as
(Given : density of water = 1 g/mL and boiling point of water = 373 K)
1. (1) $\dfrac{1.3}{8}\times\dfrac{\mathrm{W}}{\mathrm{M}}$
2. (2) $\dfrac{16}{2.6}\times\dfrac{\mathrm{W}}{\mathrm{M}}$
3. (3) $\dfrac{2.6}{16}\times\dfrac{\mathrm{M}}{\mathrm{W}}$
4. (4) $\dfrac{1.3}{8}\times\dfrac{\mathrm{M}}{\mathrm{W}}$

Q13 · MCQ · ThermodynamicsOpen

Match the List-I with List-II

List-I		List-II
(Isothermal process		Work done ( $\boldsymbol{V_\mathrm{f} > V_\mathrm{i}}$ )
for ideal gas system)
A.	Reversible expansion	I.	$w = 0$
B.	Free expansion	II.	$w = -nRT\ln\dfrac{V_\mathrm{f}}{V_\mathrm{i}}$
C.	Irreversible expansion	III.	$w = -p_\mathrm{ex}\,(V_\mathrm{f} - V_\mathrm{i})$
D.	Irreversible compression	IV.	$w = -p_\mathrm{ex}\,(V_\mathrm{i} - V_\mathrm{f})$

Choose the correct answer from the options given below :

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

Q14 · MCQ · Aldehydes, Ketones & AcidsOpen
A student is given one compound among the following compounds that gives positive test with Tollen's reagent.
The compound is :
1. (1)D
2. (2)A
3. (3)B
4. (4)C
Q15 · MCQ · Alcohols, Phenols & EthersOpen
A hydroxy compound (X) with molar mass 122 g mol $^{-1}$ is acetylated with acetic anhydride, using a large excess of the reagent ensuring complete acetylation of all hydroxyl groups. The product obtained has a molar mass of 290 g mol $^{-1}$ . The number of hydroxyl groups present in compound (X) is :
1. (1)3
2. (2)5
3. (3)2
4. (4)4
Q16 · MCQ · Chemical KineticsOpen
At 27 $^\circ$ C in presence of a catalyst, activation energy of a reaction is lowered by 10 kJ mol $^{-1}$ . The logarithm ratio of $\dfrac{k(\text{catalysed})}{k(\text{uncatalysed})}$ is ….
(Consider that the frequency factor for both the reactions is same)
1. (1)17.41
2. (2)1.741
3. (3)3.482
4. (4)0.1741
Q17 · MCQ · Haloalkanes & HaloarenesOpen
Given below are two statements :
Statement I : ‘C–Cl' bond is stronger in $\ce{CH2=CH-Cl}$ than $\ce{CH3-CH2-Cl}$
Statement II : The given optically active molecule,
on hydrolysis gives a solution that can rotate the plane polarized light.
In the light of the above statements, choose the correct answer from the options given below
1. (1)Statement I is false but Statement II is true
2. (2)Both Statement I and Statement II are true
3. (3)Both Statement I and Statement II are false
4. (4)Statement I is true but Statement II is false
Q18 · MCQ · Alcohols, Phenols & EthersOpen
Consider the following two reactions A and B.
Numerical value of [molar mass of x $+$ molar mass of y] is .
1. (1)4
2. (2)88
3. (3)46
4. (4)160
Q19 · MCQ · Organic Basics (GOC)Open
Arrange the following carbanions in the decreasing order of stability
- (I) $p$ –Br– $\ce{C6H4}$ – $\overset{\ominus}{\ddot{\mathrm{C}}}\mathrm{H_2}$
- (II) $\ce{C6H5}$ – $\overset{\ominus}{\ddot{\mathrm{C}}}\mathrm{H_2}$
- (III) $p$ – $\ce{CH3O}$ – $\ce{C6H4}$ – $\overset{\ominus}{\ddot{\mathrm{C}}}\mathrm{H_2}$
- (IV) $p$ –CHO– $\ce{C6H4}$ – $\overset{\ominus}{\ddot{\mathrm{C}}}\mathrm{H_2}$
- (V) $p$ – $\ce{CH3}$ – $\ce{C6H4}$ – $\overset{\ominus}{\ddot{\mathrm{C}}}\mathrm{H_2}$
Choose the correct answer from the options given below :
1. (1)I $>$ II $>$ IV $>$ V $>$ III
2. (2)I $>$ IV $>$ II $>$ V $>$ III
3. (3)IV $>$ I $>$ II $>$ V $>$ III
4. (4)IV $>$ II $>$ I $>$ III $>$ V
Q20 · MCQ · Classification & PeriodicityOpen
Given below are two statements :
Statement I : K $>$ Mg $>$ Al $>$ B is the correct order in terms of metallic character.
Statement II : Atomic radius is always greater than the ionic radius for any element.
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 false but Statement II is true
4. (4)Statement I is true but Statement II is false
Q21 · Numerical · ElectrochemistryOpen
Electricity is passed through an acidic solution of $\ce{Cu^{2+}}$ till all the $\ce{Cu^{2+}}$ was exhausted, leading to the deposition of 300 mg of Cu metal. However, a current of 600 mA was continued to pass through the same solution for another 28 minutes by keeping the total volume of the solution fixed at 200 mL. The total volume of oxygen evolved at STP during the entire process is mL. (Nearest integer)
[Given :
$\ce{Cu^{2+}(aq) + 2e^- -> Cu(s)}$ $E^0_\mathrm{red} = +0.34$ V
$\ce{O2(g) + 4H^+ + 4e^- -> 2H2O}$ $E^0_\mathrm{red} = +1.23$ V
Molar mass of Cu = 63.54 g mol $^{-1}$
Molar mass of $\ce{O2}$ = 32 g mol $^{-1}$
Faraday Constant = 96500 C mol $^{-1}$
Molar volume at STP = 22.4 L ]
We corrected a printing error in the original paper
Source printed “till all the cu $^{2+}$ was exhausted”.
Q22 · Numerical · EquilibriumOpen
Consider two Group IV metal ions $\ce{X^{2+}}$ and $\ce{Y^{2+}}$ .
A solution containing 0.01 M $\ce{X^{2+}}$ and 0.01 M $\ce{Y^{2+}}$ is saturated with $\ce{H2S}$ . The pH at which the metal sulphide YS will form as a precipitate is (Nearest integer)
(Given :
$K_\mathrm{sp}(\mathrm{XS}) = 1\times10^{-22}$ at 25 $^\circ$ C, $K_\mathrm{sp}(\mathrm{YS}) = 4\times10^{-16}$ at 25 $^\circ$ C,
[ $\ce{H2S}$ ] = 0.1 M in solution, $K_\mathrm{a1}\times K_\mathrm{a2}$ ( $\ce{H2S}$ ) $= 1.0\times10^{-21}$ ,
$\log 2 = 0.30$ , $\log 3 = 0.48$ , $\log 5 = 0.70$ )
Q23 · Numerical · Structure of AtomOpen
The hydrogen spectrum consists of several spectral lines in Lyman series ( $L_1$ , $L_2$ , $L_3$ …; $L_1$ has lowest energy among Lyman series). Similarly it consists of several spectral lines in Balmer series ( $B_1$ , $B_2$ , $B_3$ …; $B_1$ has lowest energy among Balmer lines). The energy of $L_1$ is $x$ times the energy of $B_1$ . The value of $x$ is $\times\,10^{-1}$ (Nearest integer)
We corrected a printing error in the original paper
Source printed “(Nearest inteter)”.
Q24 · Numerical · Purification & CharacterisationOpen
In Dumas method for estimation of nitrogen, 0.50 g of an organic compound gave 70 mL of nitrogen collected at 300 K and 715 mm pressure. The percentage of nitrogen in the organic compound is %
(Aqueous tension at 300 K is 15 mm).
Q25 · Numerical · Redox ReactionsOpen
X and Y are the number of electrons involved, respectively during the oxidation of $\ce{I^-}$ to $\ce{I2}$ and $\ce{S^{2-}}$ to S by acidified $\ce{K2Cr2O7}$ . The value of X + Y is .
(Consider the electrons transferred per mole of $\ce{K2Cr2O7}$ reduced in each reaction)
We corrected a printing error in the original paper
Assumption “(Consider the electrons transferred per mole of $\ce{K2Cr2O7}$ reduced in each reaction)” added; the source leaves it unstated (per $\ce{I2}$ /S formed it would be 2 + 2 = 4).

Maths

Q1 · MCQ · Limits, Continuity & DifferentiabilityOpen
If the function $f(x) = \dfrac{e^x\left(e^{\tan x - x} - 1\right) + \log_e(\sec x + \tan x) - x}{\tan x - x}$ is Continuous at $x = 0$ , then the value of $f(0)$ is equal to
1. (1)2
2. (2) $\dfrac23$
3. (3) $\dfrac12$
4. (4) $\dfrac32$
Q2 · MCQ · CirclesOpen
Let a circle of radius 4 pass through the origin $O$ , the points $A\left(-\sqrt3\,a, 0\right)$ and $B\left(0, -\sqrt2\,b\right)$ , where $a$ and $b$ are real parameters and $ab \neq 0$ . Then the locus of the centroid of $\Delta OAB$ is a circle of radius
1. (1) $\dfrac53$
2. (2) $\dfrac73$
3. (3) $\dfrac83$
4. (4) $\dfrac{11}{3}$
Q3 · MCQ · 3D GeometryOpen
Let the lines $L_1 : \vec r = \hat i + 2\hat j + 3\hat k + \lambda\left(2\hat i + 3\hat j + 4\hat k\right)$ , $\lambda \in \mathbb{R}$ and $L_2 : \vec r = \left(4\hat i + \hat j\right) + \mu\left(5\hat i + 2\hat j + \hat k\right)$ , $\mu \in \mathbb{R}$ , intersect at the point $R$ . Let $P$ and $Q$ be the points lying on lines $L_1$ and $L_2$ , respectively, such that $\left\lvert\overrightarrow{PR}\right\rvert = \sqrt{29}$ and $\left\lvert\overrightarrow{PQ}\right\rvert = \sqrt{\dfrac{47}{3}}$ . If the point $P$ lies in the first octant, then $27(QR)^2$ is equal to
1. (1)340
2. (2)360
3. (3)320
4. (4)348
Q4 · MCQ · Sequences & SeriesOpen
Let $729, 81, 9, 1, \ldots$ be a sequence and $P_n$ denote the product of the first $n$ terms of this sequence. If $2\sum_{n=1}^{40}\left(P_n\right)^{\frac1n} = \dfrac{3^{\alpha} - 1}{3^{\beta}}$ and $\gcd(\alpha, \beta) = 1$ , then $\alpha + \beta$ is equal to
1. (1)73
2. (2)74
3. (3)75
4. (4)76
Q5 · MCQ · VectorsOpen
Let $\vec a = 2\hat i + \hat j - 2\hat k$ , $\vec b = \hat i + \hat j$ and $\vec c = \vec a \times \vec b$ . Let $\vec d$ be a vector such that $\lvert\vec d - \vec a\rvert = \sqrt{11}$ , $\lvert\vec c \times \vec d\rvert = 3$ and the angle between $\vec c$ and $\vec d$ is $\dfrac{\pi}{4}$ . Then $\vec a \cdot \vec d$ is equal to
1. (1)11
2. (2)3
3. (3)0
4. (4)1
Q6 · MCQ · Sets, Relations & FunctionsOpen
If the domain of the function $f(x) = \log_{(10x^2 - 17x + 7)}\left(18x^2 - 11x + 1\right)$ is $(-\infty, a) \cup (b, c) \cup (d, \infty) - \{e\}$ , then $90(a + b + c + d + e)$ equals:
1. (1)170
2. (2)177
3. (3)307
4. (4)316
Q7 · MCQ · Conic SectionsOpen
Let each of the two ellipses $E_1 : \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ , $(a > b)$ and $E_2 : \dfrac{x^2}{A^2} + \dfrac{y^2}{B^2} = 1$ , $(A < B)$ have eccentricity $\dfrac45$ . Let the lengths of the latus recta of $E_1$ and $E_2$ be $\ell_1$ and $\ell_2$ , respectively, such that $2\ell_1^2 = 9\ell_2$ . If the distance between the foci of $E_1$ is 8, then the distance between the foci of $E_2$ is
1. (1) $\dfrac{96}{5}$
2. (2) $\dfrac{32}{5}$
3. (3) $\dfrac{16}{5}$
4. (4) $\dfrac85$
Q8 · MCQ · TrigonometryOpen
The value of $\dfrac{\sqrt3\operatorname{cosec}20^\circ - \sec20^\circ}{\cos20^\circ\cos40^\circ\cos60^\circ\cos80^\circ}$ is equal to
1. (1)32
2. (2)16
3. (3)64
4. (4)12
Q9 · MCQ · Complex NumbersOpen
Let $S = \left\{z \in \mathbb{C} : \left\lvert\dfrac{z - 6i}{z - 2i}\right\rvert = 1 \text{ and } \left\lvert\dfrac{z - 8 + 2i}{z + 2i}\right\rvert = \dfrac35\right\}$ . Then $\displaystyle\sum_{z \in S}\lvert z\rvert^2$ is equal to
1. (1)398
2. (2)413
3. (3)423
4. (4)385
We corrected a printing error in the original paper
Source printed the summation index as “ $z \in s$ ” (lower-case $s$ ; the set is $S$ ).
Q10 · MCQ · TrigonometryOpen
If $\cot x = \dfrac{5}{12}$ for some $x \in \left(\pi, \dfrac{3\pi}{2}\right)$ , then $\sin7x\left(\cos\dfrac{13x}{2} + \sin\dfrac{13x}{2}\right) + \cos7x\left(\cos\dfrac{13x}{2} - \sin\dfrac{13x}{2}\right)$ is equal to
1. (1) $\dfrac{4}{\sqrt{26}}$
2. (2) $\dfrac{6}{\sqrt{26}}$
3. (3) $\dfrac{1}{\sqrt{13}}$
4. (4) $\dfrac{5}{\sqrt{13}}$
Q11 · MCQ · Indefinite IntegrationOpen
Let $f(t) = \displaystyle\int\left(\dfrac{1 - \sin(\log_e t)}{1 - \cos(\log_e t)}\right)dt$ , $t > 1$ . If $f\left(e^{\pi/2}\right) = -e^{\pi/2}$ and $f\left(e^{\pi/4}\right) = \alpha\, e^{\pi/4}$ , then $\alpha$ equals
1. (1) $-1 - \sqrt2$
2. (2) $-1 - 2\sqrt2$
3. (3) $1 + \sqrt2$
4. (4) $-1 + \sqrt2$
Q12 · MCQ · Sets, Relations & FunctionsOpen
Let $R$ be a relation defined on the set $\{1, 2, 3, 4\} \times \{1, 2, 3, 4\}$ by $R = \{((a, b), (c, d)) : 2a + 3b = 3c + 4d\}.$ Then the number of elements in $R$ is
1. (1)6
2. (2)18
3. (3)12
4. (4)15
Q13 · MCQ · Straight LinesOpen
Let $A(1, 0)$ , $B(2, -1)$ and $C\left(\dfrac73, \dfrac43\right)$ be three points. If the equation of the bisector of the angle $ABC$ is $\alpha x + \beta y = 5$ , then the value of $\alpha^2 + \beta^2$ is
1. (1)8
2. (2)5
3. (3)13
4. (4)10
Q14 · MCQ · Binomial TheoremOpen
Let $S = \dfrac{1}{25!} + \dfrac{1}{3!\,23!} + \dfrac{1}{5!\,21!} + \ldots$ up to 13 terms. If $13S = \dfrac{2^k}{n!}$ , $k \in \mathbb{N}$ , then $n + k$ is equal to
1. (1)51
2. (2)52
3. (3)49
4. (4)50
Q15 · MCQ · Sequences & SeriesOpen
Consider an A.P.: $a_1, a_2, \ldots, a_n$ ; $a_1 > 0$ . If $a_2 - a_1 = \dfrac{-3}{4}$ , $a_n = \dfrac14 a_1$ , and $\displaystyle\sum_{i=1}^{n} a_i = \dfrac{525}{2}$ , then $\displaystyle\sum_{i=1}^{17} a_i$ is equal to
1. (1)476
2. (2)952
3. (3)238
4. (4)136
Q16 · MCQ · Limits, Continuity & DifferentiabilityOpen
Let $\alpha, \beta \in \mathbb{R}$ be such that the function $f(x) = \begin{cases} 2\alpha(x^2 - 2) + 2\beta x, & x < 1\\ (\alpha + 3)x + (\alpha - \beta), & x \ge 1\end{cases}$ be differentiable at all $x \in \mathbb{R}$ . Then $34(\alpha + \beta)$ is equal to
1. (1)84
2. (2)48
3. (3)36
4. (4)24
Q17 · MCQ · ProbabilityOpen
From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is :-
1. (1) $\dfrac{7}{10^7}$
2. (2) $\dfrac{81}{10^8}$
3. (3) $\dfrac{67}{10^8}$
4. (4) $\dfrac{73}{10^8}$
Q18 · MCQ · StatisticsOpen
The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation $\alpha$ in this data is replaced by $\beta$ , then the mean and variance become 10.1 and 1.99, respectively. Then $\alpha + \beta$ equals.
1. (1)10
2. (2)15
3. (3)5
4. (4)20
We corrected a printing error in the original paper
Source printed “If an observations $\alpha$ ”.
Q19 · MCQ · Area under CurvesOpen
Let $A_1$ be the bounded area enclosed by the curves $y = x^2 + 2$ , $x + y = 8$ and $y$ -axis that lies in the first quadrant. Let $A_2$ be the bounded area enclosed by the curves $y = x^2 + 2$ , $y^2 = x$ , $x = 2$ , and $y$ -axis that lies in the first quadrant. Then $A_1 - A_2$ is equal to
1. (1) $\dfrac23\left(2\sqrt2 + 1\right)$
2. (2) $\dfrac23\left(4\sqrt2 + 1\right)$
3. (3) $\dfrac23\left(\sqrt2 + 1\right)$
4. (4) $\dfrac23\left(3\sqrt2 + 1\right)$
Q20 · MCQ · Quadratic EquationsOpen
The number of the real solutions of the equation : $x\lvert x + 3\rvert + \lvert x - 1\rvert - 2 = 0$ is
1. (1)3
2. (2)2
3. (3)5
4. (4)4
Q21 · Numerical · Differential EquationsOpen
Let a differentiable function $f$ satisfy the equation $\int_0^{36} f\left(\dfrac{tx}{36}\right)dt = 4\alpha f(x).$ If $y = f(x)$ is a standard parabola passing through the points $(2, 1)$ and $(-4, \beta)$ , Then $\beta^{\alpha}$ is equal to .
Q22 · Numerical · 3D GeometryOpen
Let a line $L$ passing through the point $P(1, 1, 1)$ be perpendicular to the lines $\dfrac{x - 4}{4} = \dfrac{y - 1}{1} = \dfrac{z - 1}{1} \quad\text{and}\quad \dfrac{x - 17}{1} = \dfrac{y - 71}{1} = \dfrac{z}{0}.$ Let the line $L$ intersect the $yz$ -plane at the point $Q$ . Another line parallel to $L$ and passing through the point $S(1, 0, -1)$ intersects the $yz$ -plane at the point $R$ . Then the square of the area of the parallelogram $PQRS$ is equal to .
Q23 · Numerical · Permutations & CombinationsOpen
The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0, 1, 2, 5, 9, if the repetition of the digits is allowed, is .
Q24 · Numerical · Applications of DerivativesOpen
Let $(2\alpha, \alpha)$ be the largest interval in which the function $f(t) = \dfrac{\lvert t + 1\rvert}{t^2}$ , $t < 0$ , is strictly decreasing. Then the local maximum value of the function $g(x) = 2\log_e(x - 2) + \alpha x^2 + 4x - \alpha$ , $x > 2$ , is .
Q25 · Numerical · Matrices & DeterminantsOpen
The number of $3 \times 2$ matrices $A$ , which can be formed using the elements of the set $\{-2, -1, 0,\allowbreak 1, 2\}$ such that the sum of all the diagonal elements of $A^{T}A$ is 5, is .