JEE Main 23 Jan 2026, Shift 2

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

Physics

Q1 · MCQ · ThermodynamicsOpen
The internal energy of a gas is 3nRT. One mole of this gas is kept in a cylinder having internal cross section area of $17\ \mathrm{cm^2}$ and fitted with a light movable frictionless piston. The gas is heated slowly by supplying 126 J heat. If the temperature rises by $4\ ^\circ$ C, then the piston will move cm.
(atmospheric pressure $= 10^{5}$ Pa)
1. (1)14.5
2. (2)1.55
3. (3)15.5
4. (4)1.45
We corrected a printing error in the original paper
Source printed “The internal energy of a monoatomic gas is 3nRT. One mole of helium is kept”; corrected to the intended “The internal energy of a gas is 3nRT. One mole of this gas is kept” (a monoatomic gas has $U = \tfrac32 nRT$ , which gives 44.8 cm, no option; the key 15.5 uses $U = 3nRT$ ); “suppling”.
Q2 · MCQ · Centre of Mass, Momentum and CollisionOpen
A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio $2:2:3$ . The two pieces of equal masses fly off perpendicular to each other with a speed of 18 m/s each. The velocity of the heavier fragment is m/s.
1. (1) $10\sqrt2$
2. (2) $12\sqrt2$
3. (3)12
4. (4) $24\sqrt2$
Q3 · MCQ · Newton's Laws of MotionOpen
A block is sliding down with constant velocity on an inclined plane of slope $\theta$ and at an instant $t = 0$ this block is given an upward momentum so that it starts moving up on the inclined surface with velocity $u$ . The distance ( $S$ ) travelled by the block before its velocity becomes zero, is .
( $g$ = gravitational acceleration)
1. (1) $\dfrac{u^2}{4g\sin\theta}$
2. (2) $\dfrac{2u^2}{g\cos\theta}$
3. (3) $\dfrac{u^2}{\sqrt2\,g\cos\theta}$
4. (4) $\dfrac{u^2}{2g\cos\theta}$
We corrected a printing error in the original paper
Assumption “with constant velocity” added (the source only says “sliding down”; uniform sliding gives $\mu = \tan\theta$ , retardation $2g\sin\theta$ ); answer corrected; the source key is (4) — $u^2/(2g\cos\theta)$ follows from neither reading (frictionless gives $u^2/(2g\sin\theta)$ , no option); source printed “velocity become zero”.
Q4 · MCQ · Moving Charges and MagnetismOpen
The current passing through a conducting loop in the form of equilateral triangle of side $4\sqrt3$ cm is 2 A. The magnetic field at its centroid is $\alpha\times10^{-5}$ T. The value of $\alpha$ is .
(Given: $\mu_o = 4\pi\times10^{-7}$ SI units)
1. (1) $2\sqrt3$
2. (2) $\sqrt3$
3. (3) $3\sqrt3$
4. (4) $\dfrac{\sqrt3}{2}$
Q5 · MCQ · Motion in a Straight LineOpen
A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts decelerating with $3\ \mathrm{m/s^2}$ . At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is 5 m/s. The initial height of the aeroplane is m.
( $g = 10\ \mathrm{m/s^2}$ )
1. (1)62.5
2. (2)92.5
3. (3)20
4. (4)82.5
We corrected a printing error in the original paper
Source printed “deaccelerating”.
Q6 · MCQ · Electric Charges and FieldsOpen
Two short dipoles ( $A$ , $B$ ), $A$ having charges $\pm\,2\ \mu$ C and length 1 cm and $B$ having charges $\pm\,4\ \mu$ C and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point $P$ , equi-distant from the centres of both dipoles is N/C.
1. (1) $\dfrac{9}{16}\sqrt2\times10^{5}$
2. (2) $4.5\sqrt2\times10^{4}$
3. (3) $9\sqrt2\times10^{4}$
4. (4) $\dfrac{9}{16}\sqrt2\times10^{4}$
We corrected a printing error in the original paper
Source printed “Two shorts dipoles”.
Q7 · MCQ · Electric Potential and CapacitanceOpen
Two charges $7\ \mu$ C and $-2\ \mu$ C are placed at $(-9, 0, 0)$ cm and $(9, 0, 0)$ cm respectively in an external field $E = \dfrac{A}{r^2}\,\hat r$ , where $A = 9\times10^{5}\ \mathrm{N\,m^2/C}$ .
Considering the potential at infinity is 0, the electrostatic energy of the configuration is J.
1. (1)1.4
2. (2) $-90.7$
3. (3)49.3
4. (4)24.3
We corrected a printing error in the original paper
Source printed the unit of $A$ as “ $\mathrm{N/C.m^2}$ ” ( $E = A/r^2$ needs $\mathrm{N\,m^2/C}$ ).
Q8 · MCQ · Work, Energy and PowerOpen
A bead $P$ is sliding on a frictionless semi-circular string ( $ACB$ ) and it is at point $S$ at $t = 0$ and at this instant the horizontal component of its velocity is $v$ . Another bead $Q$ of the same mass as $P$ is ejected from point $A$ at $t = 0$ along the horizontal string $AB$ , with the speed $v$ , friction between the beads and the respective strings may be neglected in both cases. Let $t_P$ and $t_Q$ be the respective times taken by beads $P$ and $Q$ to reach the point $B$ , then the relation between $t_P$ and $t_Q$ is
1. (1) $t_P > t_Q$
2. (2) $t_P < t_Q$
3. (3) $t_P > 1.25\,t_Q$
4. (4) $t_P = t_Q$
We corrected a printing error in the original paper
Source printed “A bead $P$ sliding on” (“is” missing); the subscript printed as “ $t_p$ ” (bead $P$ ) in the stem and in options (2)–(4).
Q9 · MCQ · Electric Potential and CapacitanceOpen
A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25% more charge from the battery. The dielectric constant of mica is .
1. (1)2.5
2. (2)2.0
3. (3)1.5
4. (4)1.0
Q10 · MCQ · Units and MeasurementsOpen
To compare EMF of two cells using potentiometer the balancing lengths obtained are 200 cm and 150 cm. The least count of scale is 1 cm. The percentage error in the ratio of EMFs is
1. (1)1.45
2. (2)1.65
3. (3)1.75
4. (4)1.55
Flawed question. No option is correct: $(1/200 + 1/150)\times100 = 1.17\%$ (the source's own solution says no option matches) and no evident intended version gives the key 1.65. It is shown for completeness and is left out of practice tests.
Q11 · MCQ · Kinetic Theory of GasesOpen
An air bubble of volume $2.9\ \mathrm{cm^3}$ rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is $17\ ^\circ$ C. The volume of the bubble when it reaches the surface, where the water temperature is $27\ ^\circ$ C, is $\mathrm{cm^3}$ .
( $g = 10\ \mathrm{m/s^2}$ , density of water $= 10^{3}\ \mathrm{kg/m^3}$ , and 1 atm pressure is $10^{5}$ Pa)
1. (1)4.2
2. (2)2.0
3. (3)3.0
4. (4)4.5
Q12 · MCQ · NucleiOpen
Which of the following pair of nuclei are isobars of the element?
1. (1) ${}^{2}_{1}\mathrm{H}$ and ${}^{3}_{1}\mathrm{H}$
2. (2) ${}^{236}_{92}\mathrm{U}$ and ${}^{238}_{92}\mathrm{U}$
3. (3) ${}^{198}_{80}\mathrm{Hg}$ and ${}^{197}_{79}\mathrm{Au}$
4. (4) ${}^{3}_{1}\mathrm{H}$ and ${}^{3}_{2}\mathrm{He}$
We corrected a printing error in the original paper
Source printed option (4) as “ ${}^{3}_{1}\mathrm{H}$ and ${}^{3}_{2}\mathrm{H}$ ”.
Q13 · MCQ · Semiconductor ElectronicsOpen
For the given logic gate circuit, which of the following is the correct truth table?
1. (1)
  n m z
  0 0 1
  0 1 0
  1 1 0
  1 0 0
2. (2)
  n m z
  0 0 0
  0 1 1
  1 1 0
  1 0 1
3. (3)
  n m z
  0 0 1
  0 1 0
  1 1 1
  1 0 0
4. (4)
  n m z
  0 0 1
  0 1 1
  1 1 0
  1 0 0
Q14 · MCQ · ThermodynamicsOpen
One mole of an ideal diatomic gas expands from volume $V$ to $2V$ isothermally at a temperature $27^\circ$ C and does $W$ joule of work. If the gas undergoes same magnitude of expansion adiabatically from $27^\circ$ C doing the same amount of work $W$ , then its final temperature will be (close to) $^\circ$ C.
1. (1) $-189$
2. (2) $-56$
3. (3) $-30$
4. (4) $-117$
Q15 · MCQ · Ray OpticsOpen
A prism of angle $75^\circ$ and refractive index $\sqrt3$ is coated with thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be .
( $\sin15^\circ = 0.25$ and $\sin25^\circ = 0.43$ )
1. (1)between $15^\circ$ and $20^\circ$
2. (2) $15^\circ$
3. (3) $> 25^\circ$
4. (4) $< 15^\circ$
Q16 · MCQ · Electromagnetic InductionOpen
A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is mV.
1. (1)6.6
2. (2)13.2
3. (3)8.25
4. (4)1.32
Q17 · MCQ · Electromagnetic InductionOpen
Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current $I = 10\sin(\omega t)$ A, where $\omega = 1000$ rad./s. A circular conducting loop (B) of radius 1 cm coaxially slid through the solenoid at a speed $v = 1$ cm/s. The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is $\alpha/\sqrt2\ \mu$ A. The value of $\alpha$ is .
[Resistance of the loop $= 10\ \Omega$ ]
1. (1)197
2. (2)80
3. (3)280
4. (4)100
We corrected a printing error in the original paper
Source printed “coaxially slided”.
Q18 · MCQ · Electromagnetic WavesOpen
The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k = 3$ and permeability of $\mu = 2\mu_0$ , is
( $\mu_0$ = permeability of vacuum)
1. (1) $36:1$
2. (2) $3:2$
3. (3) $6:1$
4. (4) $\sqrt6:1$
Q19 · MCQ · Wave OpticsOpen
When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted beam with respect to the normal is .
( $\tan^{-1}(1.52) = 57.7^\circ$ , refractive indices of air and glass are 1.00 and 1.52, respectively)
1. (1) $39.6^\circ$
2. (2) $32.3^\circ$
3. (3) $42.6^\circ$
4. (4) $36.3^\circ$
Q20 · MCQ · Mechanical Properties of FluidsOpen
A small metallic sphere of diameter 2 mm and density $10.5\ \mathrm{g/cm^3}$ is dropped in glycerine having viscosity 10 Poise and density $1.5\ \mathrm{g/cm^3}$ respectively. The terminal velocity attained by the sphere is cm/s.
( $\pi = \dfrac{22}{7}$ and $g = 10\ \mathrm{m/s^2}$ )
1. (1)2.0
2. (2)1.0
3. (3)3.0
4. (4)1.5
Q21 · Numerical · NucleiOpen
The average energy released per fission for the nucleus of ${}^{235}_{92}\mathrm{U}$ is 190 MeV. When all the atoms of 47 g pure ${}^{235}_{92}\mathrm{U}$ undergo fission process, the energy released is $\alpha\times10^{23}$ MeV. The value of $\alpha$ is .
(Avogadro Number $= 6\times10^{23}$ per mole)
Q22 · Numerical · Ray OpticsOpen
The sizes of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is cm.
We corrected a printing error in the original paper
Source printed “The size of the images … are equal”.
Q23 · Numerical · Units and MeasurementsOpen
A ball of radius $r$ and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains its terminal velocity at time $t$ , given by $t = A\,\rho^{a}\,r^{b}\,\eta^{c}\,\sigma^{d}$ , where $A$ is a constant and $a$ , $b$ $c$ and $d$ are integers. The value of $\dfrac{b+c}{a+d}$ is .
Q24 · Numerical · Rotational MotionOpen
Suppose there is a uniform circular disc of mass $M$ kg and radius $r$ m shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis A of the disc is given by $\dfrac{x}{256}Mr^2$ . The value of $x$ is .
Q25 · Numerical · WavesOpen
The velocity of sound in air is doubled when the temperature is raised from $0^\circ$ C to $\alpha^\circ$ C. The value of $\alpha$ is .

Chemistry

Q1 · MCQ · Chemical KineticsOpen
Given above is the concentration vs time plot for a dissociation reaction : $\ce{A -> nB}$ .
Based on the data of the initial phase of the reaction (initial 10 min), the value of n is .
1. (1)4
2. (2)3
3. (3)2
4. (4)5
Q2 · MCQ · p-Block (13–14)Open
It is noticed that $\ce{Pb^{2+}}$ is more stable than $\ce{Pb^{4+}}$ but $\ce{Sn^{2+}}$ is less stable than $\ce{Sn^{4+}}$ . Observe the following reactions
$\ce{PbO2 + Pb -> 2PbO}$ ; $\Delta_\mathrm{r}G^\circ$ (1)
$\ce{SnO2 + Sn -> 2SnO}$ ; $\Delta_\mathrm{r}G^\circ$ (2)
Identify the correct set from the following.
1. (1) $\Delta_\mathrm{r}G^\circ(1) > 0$ ; $\Delta_\mathrm{r}G^\circ(2) < 0$
2. (2) $\Delta_\mathrm{r}G^\circ(1) < 0$ ; $\Delta_\mathrm{r}G^\circ(2) < 0$
3. (3) $\Delta_\mathrm{r}G^\circ(1) < 0$ ; $\Delta_\mathrm{r}G^\circ(2) > 0$
4. (4) $\Delta_\mathrm{r}G^\circ(1) > 0$ ; $\Delta_\mathrm{r}G^\circ(2) > 0$
We corrected a printing error in the original paper
Source printed “ $\ce{Pb^{2+}}$ is more stable than $\ce{Pb^{2+}}$ ” (second charge wrong; the intended $\ce{Pb^{4+}}$ follows from the $\ce{Sn^{2+}}$ / $\ce{Sn^{4+}}$ comparison).
Q3 · MCQ · ElectrochemistryOpen
Consider the above electrochemical cell where a metal electrode (M) is undergoing redox reaction by forming $\ce{M+}$ ( $\ce{M -> M+ + e}$ ). The cation $\ce{M+}$ is present in two different concentrations $\mathrm{c_1}$ and $\mathrm{c_2}$ as shown above. Which of the following statement is correct for generating a positive cell potential?
1. (1)If $\mathrm{c_1}$ is present at anode, then $\mathrm{c_1 = c_2}$
2. (2)If $\mathrm{c_1}$ is present at cathode, then $\mathrm{c_1 < c_2}$
3. (3)If $\mathrm{c_1}$ is present at cathode, then $\mathrm{c_1 > c_2}$
4. (4)If $\mathrm{c_1}$ is present at anode, then $\mathrm{c_1 > c_2}$
Q4 · MCQ · BiomoleculesOpen
Both human DNA and RNA are chiral molecules. The chirality in DNA and RNA arises due to the presence of
1. (1)Base unit
2. (2)Chiral phosphate unit
3. (3)D-sugar component
4. (4)L-sugar component
Q5 · MCQ · Coordination CompoundsOpen
Identify the CORRECT set of details from the following :
- (A) $\ce{[Co(NH3)6]^{3+}}$ : Inner orbital complex ; $\mathrm{d^2sp^3}$ hybridized
- (B) $\ce{[MnCl6]^{3-}}$ Outer orbital complex; $\mathrm{sp^3d^2}$ hybridized
- (C) $\ce{[CoF6]^{3-}}$ : Outer orbital complex ; $\mathrm{d^2sp^3}$ hybridized
- (D) $\ce{[FeF6]^{3-}}$ : Outer orbital complex: $\mathrm{sp^3d^2}$ hybridized
- (E) $\ce{[Ni(CN)4]^{2-}}$ : Inner orbital complex ; $\mathrm{sp^3}$ hybridized
Choose the correct answer from the options given below:
1. (1)C & D only
2. (2)A, B & D only
3. (3)A, C & E only
4. (4)A, B, C, D & E
Q6 · MCQ · Classification & PeriodicityOpen
Elements X and Y belong to Group 15. The difference between the electronegativity values of ‘X' and phosphorus is higher than that of the difference between phosphorus and ‘Y'. ‘X' & ‘Y' are respectively
1. (1)N & As
2. (2)As & Bi
3. (3)Bi & N
4. (4)As & Sb
Q7 · MCQ · Organic Basics (GOC)Open
Given below are two statements:
Statement I: $\mathrm{(CH_3)_3\overset{\oplus}{C}}$ is more stable than $\mathrm{\overset{\oplus}{C}H_3}$ as nine hyperconjugation interactions are possible in $\mathrm{(CH_3)_3\overset{\oplus}{C}}$ .
Statement II: $\mathrm{\overset{\oplus}{C}H_3}$ is less stable than $\mathrm{(CH_3)_3\overset{\oplus}{C}}$ as only three hyperconjugation interactions are possible in $\mathrm{\overset{\oplus}{C}H_3}$ .
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 true
3. (3)Both Statement I and Statement II are false
4. (4)Statement I is false but Statement II is true
Q8 · MCQ · Aldehydes, Ketones & AcidsOpen
Iodoform test can differentiate between
- (A)Methanol and Ethanol
- (B) $\ce{CH3COOH}$ and $\ce{CH3CH2COOH}$
- (C)Cyclohexene and cyclohexanone
- (D)Diethyl ether and Pentan-3-one
- (E)Anisole and acetone
Choose the correct answer from the options given below:
1. (1)A & E only
2. (2)A & D only
3. (3)A, B & E only
4. (4)B, C & E only
Q9 · MCQ · Classification & PeriodicityOpen
Given below are two statements :
Statement I : The second ionisation enthalpy of Na is larger than the corresponding ionisation enthalpy of Mg.
Statement II : The ionic radius of $\ce{O^{2-}}$ is larger than that of $\ce{F-}$ .
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
Q10 · MCQ · HydrocarbonsOpen
Identify (P)
1. (1)
2. (2)
3. (3)
4. (4)
Q11 · MCQ · Chemical KineticsOpen
Observe the following reactions at T(K)
- (I) $\ce{A -> products}$ .
- (II) $\ce{5Br^- (aq) + BrO3^- (aq) + 6H^+ (aq) -> 3Br2 (aq) + 3H2O}$ ( $l$ )
Both the reactions are started at 10.00 am. The rates of these reactions at 10.10 am are same. The value of $-\dfrac{\Delta[\mathrm{Br^-}]}{\Delta t}$ at 10.10 am is $2\times10^{-4}$ mol L $^{-1}$ min $^{-1}$ . The concentration of A at 10.10 am is $10^{-2}$ mol L $^{-1}$ . What is the first order rate constant (in min $^{-1}$ ) of reaction I?
1. (1) $2\times10^{-3}$
2. (2) $10^{-3}$
3. (3) $10^{-2}$
4. (4) $4\times10^{-3}$
We corrected a printing error in the original paper
Source printed the unit as “mol L $^{-1}$ Min $^{-1}$ ”.
Q12 · MCQ · Aldehydes, Ketones & AcidsOpen
Which of the following statements are TRUE about Haloform reaction?
- (A)Sodium hypochlorite reacts with KI to give KOI.
- (B)KOI is a reducing agent.
- (C) $\alpha$ , $\beta$ -unsaturated methylketone will give iodoform reaction.
- (D)Isopropyl alcohol will not give iodoform test.
- (E)Methanoic acid will give positive iodoform test.
Choose the correct answer from the options given below:
1. (1)A, C & E only
2. (2)A, B & C only
3. (3)A & C only
4. (4)B, D & E only
Q13 · MCQ · Chemical BondingOpen
Which statements are NOT TRUE about $\ce{XeO2F2}$ ?
- (A)It has a see-saw shape.
- (B)Xe has 5 electron pairs in its valence shell in $\ce{XeO2F2}$ .
- (C)The O–Xe–O bond angle is close to 180 $^\circ$ .
- (D)The F–Xe–F bond angle is close to 180 $^\circ$
- (E)Xe has 16 valence electrons in $\ce{XeO2F2}$ .
Choose the correct answer from the options given below.
1. (1)B, C and E only
2. (2)B and D only
3. (3)A and D only
4. (4)B, D and E only
Q14 · MCQ · Structure of AtomOpen
Identify the INCORRECT statements from the following:
- (A)Notation $\ce{^{24}_{12}Mg}$ represents 24 protons and 12 neutrons.
- (B)Wavelength of a radiation of frequency $4.5\times10^{15}$ s $^{-1}$ is $6.7\times10^{-8}$ m.
- (C)One radiation has wavelength $= \lambda_1$ (900 nm) and energy $= E_1$ . Other radiation has wavelength $= \lambda_2$ (300 nm) and energy $= E_2$ . $E_1 : E_2 = 3 : 1$ .
- (D)Number of photons of light of wavelength 2000 pm that provides 1 J of energy is $1.006\times10^{16}$ .
Choose the correct answer from the options given below:
1. (1)A and D only
2. (2)A and C only
3. (3)A and B only
4. (4)B and C only
Q15 · MCQ · Purification & CharacterisationOpen
In Carius method 0.2425 g of an organic compound gave 0.5253 g silver chloride. The percentage of chlorine in the organic compound is
1. (1)53.58%
2. (2)87.65%
3. (3)37.57%
4. (4)34.79%
We corrected a printing error in the original paper
Source printed “0.2425 g of an organic compounds”.
Q16 · MCQ · Alcohols, Phenols & EthersOpen
A mixed ether (P), when heated with excess of hot concentrated hydrogen iodide produces two different alkyl iodides which when treated with aq. NaOH give compounds (Q) and (R). Both (Q) and (R) give yellow precipitate with NaOI. Identify the mixed ether (P):
1. (1)
2. (2)
3. (3)
4. (4)
Flawed question. Two options are correct: option (4) as drawn is the same ethyl sec-butyl ether as the keyed option (1) (and even read as ethyl isopropyl ether it gives ethanol and propan-2-ol, both iodoform-positive); no evident intended version. It is shown for completeness and is left out of practice tests.
Q17 · MCQ · d- and f-BlockOpen
The oxidation state of chromium in the final product formed in the reaction between KI and acidified $\ce{K2Cr2O7}$ solution is:
1. (1)+4
2. (2)+3
3. (3)+2
4. (4)+6
Q18 · MCQ · Structure of AtomOpen
The work functions of two metals ( $\mathrm{M_A}$ and $\mathrm{M_B}$ ) are in the 1 : 2 ratio. When these metals are exposed to photons of energy 6 eV, the kinetic energy of liberated electrons of $\mathrm{M_A : M_B}$ is in the ratio of 2.642 : 1. The work functions (in eV) of $\mathrm{M_A}$ and $\mathrm{M_B}$ are respectively.
1. (1)3.1, 6.2
2. (2)2.3, 4.6
3. (3)1.4, 2.8
4. (4)1.5, 3.0
Q19 · MCQ · AminesOpen
Given below are two statements:
Statement I: can be synthesized from
using simpler reagents in the order i) Acidic $\ce{KMnO4}$ , ii) Ammonia, iii) Bromine and alkali
Statement II : can be converted into
using reagents in the order (i) Bromine- $\ce{H2O}$ (ii) $\ce{NaNO2}$ /HCl (0-5 $^\circ$ C) (iii) aq. $\ce{H3PO2}$ .
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
Q20 · MCQ · AminesOpen
A student has been given a compound “x” of molecular formula – $\ce{C6H7N}$ . ‘x' is sparingly soluble in water. However, on addition of dilute mineral acid, ‘x' becomes soluble in water. ‘x' when treated with $\ce{CHCl3}$ and KOH (alc.) ‘y' is produced. ‘y' has a specific unpleasant smell. On treatment with benzenesulphonyl chloride, ‘x' gives a compound ‘z' which is soluble in alkali. The number of different “H” atoms present in ‘z' is:-
1. (1)5
2. (2)8
3. (3)4
4. (4)7
Q21 · Numerical · EquilibriumOpen
$\ce{X2(g) + Y2(g) <=> 2Z(g)}$
$\ce{X2(g)}$ and $\ce{Y2(g)}$ are added to a 1 L flask and it is found that the system attains the above equilibrium at T(K) with the number of moles of $\ce{X2(g)}$ , $\ce{Y2(g)}$ and Z(g) being 3, 3 and 9 mol respectively (equilibrium moles). Under these conditions of equilibrium, 10 mol of Z(g) is added to the flask and the temperature is maintained at T(K). Then the number of moles of Z(g) in the flask when the new equilibrium is established is . (Nearest integer).
We corrected a printing error in the original paper
Source printed “Under this conditions of equilibrium”.
Q22 · Numerical · SolutionsOpen
Two liquids A and B form an ideal solution. At 320 K, the vapour pressure of the solution, containing 3 mol of A and 1 mol of B is 500 mm Hg. At the same temperature, if 1 mol of A is further added to this solution, vapour pressure of the solution increases by 20 mm Hg. Vapour pressure (in mm Hg) of B in the pure state is . (Nearest integer)
Q23 · Numerical · Redox ReactionsOpen
200 cc of $x\times10^{-3}$ M potassium dichromate is required to oxidise 750 cc of 0.6 M Mohr's salt solution in acidic medium.
Here $x =$
Q24 · Numerical · Coordination CompoundsOpen
Total number of unpaired electrons present in the central metal atoms/ions of $\ce{[Ni(CO)4]}$ , $\ce{[NiCl4]^{2-}}$ , $\ce{[PtCl2(NH3)2]}$ , $\ce{[Ni(CN)4]^{2-}}$ and $\ce{[Pt(CN)4]^{2-}}$ is .
We corrected a printing error in the original paper
Source printed “[Ni(CN $_4$ )] $^{2-}$ ” and “[Pt (CN $_4$ )] $^{2-}$ ”.
Q25 · Numerical · Aldehydes, Ketones & AcidsOpen
In compound (Q), the percentage of oxygen is %. (Nearest integer)
We corrected a printing error in the original paper
Answer supplied; the source prints no answer key for this question (its worked solution gives 10.19%; Q = 3-phenylcyclopent-2-en-1-one, $\ce{C11H10O}$ , 16/158 = 10.1%).

Maths

Q1 · MCQ · Limits, Continuity & DifferentiabilityOpen
If $f(x) = \begin{cases} \dfrac{a\lvert x\rvert + x^2 - 2(\sin\lvert x\rvert)(\cos\lvert x\rvert)}{x}, & x \neq 0\\[2mm] b, & x = 0\end{cases}$ is continuous at $x = 0$ , then $a + b$ is equal to:
1. (1)1
2. (2)2
3. (3)0
4. (4)4
Q2 · MCQ · TrigonometryOpen
Let $\dfrac{\pi}{2} < \theta < \pi$ and $\cot\theta = -\dfrac{1}{2\sqrt2}$ . Then the value of $\sin\left(\dfrac{15\theta}{2}\right)(\cos8\theta + \sin8\theta) + \cos\left(\dfrac{15\theta}{2}\right)(\cos8\theta - \sin8\theta)$ is equal to:
1. (1) $\dfrac{1-\sqrt2}{\sqrt3}$
2. (2) $-\dfrac{\sqrt2}{\sqrt3}$
3. (3) $\dfrac{\sqrt2-1}{\sqrt3}$
4. (4) $\dfrac{\sqrt2}{\sqrt3}$
We corrected a printing error in the original paper
Source printed “ $(\cos8 - \sin8\theta)$ ” (the $\theta$ of $\cos8\theta$ missing).
Q3 · MCQ · VectorsOpen
Let $\vec a = \hat i - 2\hat j + 3\hat k$ , $\vec b = 2\hat i + \hat j - \hat k$ , $\vec c = \lambda\hat i + \hat j + \hat k$ and $\vec v = \vec a\times\vec b$ . If $\vec v\cdot\vec c = 11$ and the length of the projection of $\vec b$ on $\vec c$ is $p$ , then $9p^2$ is equal to:
1. (1)9
2. (2)6
3. (3)4
4. (4)12
Q4 · MCQ · Straight LinesOpen
Let $A(1, 2)$ and $C(-3, -6)$ be two diagonally opposite vertices of a rhombus, whose sides $AD$ and $BC$ are parallel to the line $7x - y = 14$ . If $B(\alpha, \beta)$ and $D(\gamma, \delta)$ are the other two vertices, then $\lvert\alpha + \beta + \gamma + \delta\rvert$ is equal to:
1. (1)9
2. (2)3
3. (3)6
4. (4)1
We corrected a printing error in the original paper
Source printed “sides AD an BC”.
Q5 · MCQ · Sets, Relations & FunctionsOpen
Consider two sets $A = \{x \in \mathbb{Z} : \lvert(\lvert x - 3\rvert - 3)\rvert \le 1\}$ and $B = \left\{x \in \mathbb{R} - \{1, 2\} : \dfrac{(x-2)(x-4)}{x-1}\log_e(\lvert x - 2\rvert) = 0\right\}.$ Then the number of onto functions $f : A \to B$ is equal to:
1. (1)62
2. (2)79
3. (3)32
4. (4)81
We corrected a printing error in the original paper
Source printed “ $x \in z$ ” (lower-case z) for the set of integers.
Q6 · MCQ · Matrices & DeterminantsOpen
The system of linear equations
$\begin{align*} x + y + z &= 6\\ 2x + 5y + az &= 36\\ x + 2y + 3z &= b \end{align*}$
has
1. (1)unique solution for $a = 8$ and $b = 16$
2. (2)infinitely many solutions for $a = 8$ and $b = 14$
3. (3)infinitely many solutions for $a = 8$ and $b = 16$
4. (4)unique solution for $a = 8$ and $b = 14$
Q7 · MCQ · Quadratic EquationsOpen
The sum of all the real solutions of the equation $\log_{(x+3)}(6x^2 + 28x + 30) = 5 - 2\log_{(6x+10)}(x^2 + 6x + 9)$ is equal to:
1. (1)2
2. (2)1
3. (3)0
4. (4)4
Q8 · MCQ · Conic SectionsOpen
If the points of intersection of the ellipses $x^2 + 2y^2 - 6x - 12y + 23 = 0$ and $4x^2 + 2y^2 - 20x - 12y + 35 = 0$ lie on a circle of radius $r$ and centre $(a, b)$ , then the value of $ab + 18r^2$ is
1. (1)53
2. (2)51
3. (3)52
4. (4)55
We corrected a printing error in the original paper
Source printed “ $4x + 2y^2 - 20x - 12y + 35 = 0$ ”; corrected to the intended “ $4x^2 + 2y^2 - 20x - 12y + 35 = 0$ ” (as printed the second curve is a parabola, not an ellipse, and meets the first in only two points, so the circle is not determined).
Q9 · MCQ · Conic SectionsOpen
Let $PQ$ be a chord of the hyperbola $\dfrac{x^2}{4} - \dfrac{y^2}{b^2} = 1$ , perpendicular to the $x$ -axis such that $OPQ$ is an equilateral triangle, $O$ being the centre of the hyperbola. If the eccentricity of the hyperbola is $\sqrt3$ , then the area of the triangle $OPQ$ is:
1. (1) $2\sqrt3$
2. (2) $\dfrac{8\sqrt3}{5}$
3. (3) $\dfrac{11}{5}$
4. (4) $\dfrac{9}{5}$
Q10 · MCQ · VectorsOpen
Let $\vec a, \vec b, \vec c$ be three vectors such that $\vec a\times\vec b = 2(\vec a\times\vec c)$ . If $\lvert\vec a\rvert = 1$ , $\lvert\vec b\rvert = 4$ , $\lvert\vec c\rvert = 2$ , and the angle between $\vec b$ and $\vec c$ is $60^\circ$ , then $\lvert\vec a\cdot\vec c\rvert$ is:
1. (1)2
2. (2)4
3. (3)0
4. (4)1
Q11 · MCQ · ProbabilityOpen
Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability, that the ball drawn is white, is $\dfrac{p}{q}$ , $\gcd(p, q) = 1$ , then $p + q$ is equal to
1. (1)22
2. (2)23
3. (3)24
4. (4)21
Q12 · MCQ · Area under CurvesOpen
The area of the region enclosed between the circles $x^2 + y^2 = 4$ and $x^2 + (y - 2)^2 = 4$ is:
1. (1) $\dfrac23(2\pi - 3\sqrt3)$
2. (2) $\dfrac43(2\pi - 3\sqrt3)$
3. (3) $\dfrac43(2\pi - \sqrt3)$
4. (4) $\dfrac23(4\pi - 3\sqrt3)$
Q13 · MCQ · TrigonometryOpen
The least value of $(\cos^2\theta - 6\sin\theta\cos\theta + 3\sin^2\theta + 2)$ is
1. (1) $-1$
2. (2) $4 + \sqrt{10}$
3. (3) $4 - \sqrt{10}$
4. (4)1
Q14 · MCQ · Indefinite IntegrationOpen
Let $I(x) = \displaystyle\int\frac{3\,dx}{(4x + 6)\left(\sqrt{4x^2 + 8x + 3}\right)}$ and $I(0) = \dfrac{\sqrt3}{4} + 20$ . If $I\left(\dfrac12\right) = \dfrac{a\sqrt2}{b} + c$ , where $a, b, c \in \mathbb{N}$ , $\gcd(a, b) = 1$ , then $a + b + c$ is equal to:
1. (1)29
2. (2)28
3. (3)31
4. (4)30
Q15 · MCQ · Permutations & CombinationsOpen
The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is
1. (1)429
2. (2)384
3. (3)403
4. (4)455
Q16 · MCQ · Sets, Relations & FunctionsOpen
Let $A = \{0, 1, 2, \ldots, 9\}$ . Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $\lvert x - y\rvert$ is a multiple of 3.
Given below are two statements:
Statement I: $n(R) = 36$
Statement II: $R$ is an equivalence relation.
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 correct
2. (2)Statement I is incorrect but Statement II is correct
3. (3)Statement I is correct but Statement II is incorrect
4. (4)Both Statement I and Statement II are incorrect
We corrected a printing error in the original paper
Source printed the set $A$ with a closing parenthesis, “2,....9)”, instead of a closing brace.
Q17 · MCQ · Complex NumbersOpen
If $z = \dfrac{\sqrt3}{2} + \dfrac{i}{2}$ , $i = \sqrt{-1}$ , then $(z^{201} - i)^8$ is equal to
1. (1) $-1$
2. (2)0
3. (3)1
4. (4)256
Q18 · MCQ · StatisticsOpen
If the mean and the variance of the data
Class 4–8 8–12 12–16 16–20
Frequency 3 $\lambda$ 4 7
are $\mu$ and 19 respectively, then the value of $\lambda + \mu$ is
1. (1)18
2. (2)21
3. (3)20
4. (4)19
Q19 · MCQ · Conic SectionsOpen
An equilateral triangle $OAB$ is inscribed in the parabola $y^2 = 4x$ with the vertex $O$ at the vertex of the parabola. Then the minimum distance of the circle having $AB$ as a diameter from the origin is
1. (1) $4(3 - \sqrt3)$
2. (2) $2(8 - 3\sqrt3)$
3. (3) $4(6 + \sqrt3)$
4. (4) $2(3 + \sqrt3)$
Q20 · MCQ · Sequences & SeriesOpen
Let $\displaystyle\sum_{k=1}^{n} a_k = \alpha n^2 + \beta n$ . If $a_{10} = 59$ and $a_6 = 7a_1$ then $\alpha + \beta$ is equal to
1. (1)12
2. (2)3
3. (3)5
4. (4)7
Q21 · Numerical · Differential EquationsOpen
If the solution curve $y = f(x)$ of the differential equation $(x^2 - 4)\,y' - 2xy + 2x(4 - x^2)^2 = 0$ $x > 2$ , passes through the point $(3, 15)$ , then the local maximum value of $f$ is .
Q22 · Numerical · 3D GeometryOpen
If the image of the point $P(a, 2, a)$ in the line $\dfrac{x}{2} = \dfrac{y + a}{1} = \dfrac{z}{1}$ is $Q$ and the image of $Q$ in the line $\dfrac{x - 2b}{2} = \dfrac{y - a}{1} = \dfrac{z + 2b}{-5}$ is $P$ , then $a + b$ is equal to .
We corrected a printing error in the original paper
Source printed “and the of image of Q in the line”.
Q23 · Numerical · Definite IntegrationOpen
The number of elements in the set $S = \left\{x : x \in [0, 100] \text{ and } \int_0^x t^2\sin(x - t)\,dt = x^2\right\}$ is .
Q24 · Numerical · Matrices & DeterminantsOpen
Let $A = \begin{bmatrix} 0 & 2 & -3\\ -2 & 0 & 1\\ 3 & -1 & 0\end{bmatrix}$ and $B$ be a matrix such that $B(I - A) = I + A$ . Then the sum of the diagonal elements of $B^{T}B$ is equal to .
Q25 · Numerical · Permutations & CombinationsOpen
Let $S$ denote the set of 4-digit numbers $abcd$ such that $a > b > c > d$ and $P$ denote the set of 5-digit numbers having product of its digits equal to 20. Then $n(S) + n(P)$ is equal to .

Class	4–8	8–12	12–16	16–20
Frequency	3	$\lambda$	4	7