JEE Main 2 Apr 2026, Shift 1

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

Physics

Q1 · MCQ · Units and MeasurementsOpen
The dimensional formula of $\dfrac12\epsilon_0E^2$ ( $\epsilon_0 =$ permittivity of vacuum and $E =$ electric field) is $\mathrm{M^aL^bT^c}$ . The value of $2a - b + c =$ .
1. (1)0
2. (2)1
3. (3) $-1$
4. (4)2
Q2 · MCQ · Units and MeasurementsOpen
The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm. The length measured by a scale of least count 0.1 cm is 150 cm. When a weight of 100 N is applied to the wire, the extension in length is 0.5 cm, measured by a micrometer of least count 0.001 cm. The error in the measured Young's modulus is $\alpha\times10^{9}\ \mathrm{N/m^2}$ . The value of $\alpha$ is .
(Ignore the contribution of the load to Young's modulus error calculation)
1. (1)1.3
2. (2)1.65
3. (3)0.13
4. (4)0.25
Q3 · MCQ · Motion in a PlaneOpen
The velocity of a particle is given as $\vec v = -x\hat i + 2y\hat j - z\hat k$ m/s. The magnitude of acceleration at point (1, 2, 4) is $\mathrm{m/s^2}$ .
1. (1) $\sqrt6$
2. (2)9
3. (3) $\sqrt{33}$
4. (4)0

The position of an object having mass 0.1 kg as a function of time

t

is given as

\vec r = \left(10t^2\hat i + 5t^3\hat j\right)

m. At

t = 1

s, which of the following statements are correct?

A.	The linear momentum $\vec p = \left(2\hat i + 1.5\hat j\right)$ kg.m/s.
B.	The force acting on the object $\vec F = \left(2\hat i + 3\hat j\right)$ N.
C.	The angular momentum of the object about its origin $\vec L = 15\hat k$ J s.
D.	The torque acting on the object about its origin $\vec\tau = 20\hat k$ N m.

Choose the correct answer from the options given below.

(1)A, B and C only
(2)B, C and D only
(3)A, C and D only
(4)A, B and D only

We corrected a printing error in the original paper

Source printed “from the option given below”.

Q5 · MCQ · GravitationOpen
A planet ( $P_1$ ) is moving around the star of mass $2M$ in the orbit of radius $R$ . Another planet ( $P_2$ ) is moving around another star of mass $4M$ in an orbit of radius $2R$ . Ratio of time periods of revolution of $P_2$ and $P_1$ is .
1. (1) $\dfrac12$
2. (2)2
3. (3)4
4. (4) $\dfrac14$
We corrected a printing error in the original paper
Source printed “in a orbit”.
Q6 · MCQ · Rotational MotionOpen
A particle is rotating in a circular path and at any instant its motion can be described as $\theta = \dfrac{5t^4}{40} - \dfrac{t^3}{3}$ . The angular acceleration of the particle after 10 seconds is $\mathrm{rad/s^2}$ .
1. (1)150
2. (2)120
3. (3)130
4. (4)170
Q7 · MCQ · Electric Potential and CapacitanceOpen
A parallel plate air capacitor has a capacitance $C$ . When it is half filled as shown in figure with a dielectric constant $K = 5$ , the percentage increase in the capacitance is .
1. (1)33.34
2. (2)66.67
3. (3)200
4. (4)400
We corrected a printing error in the original paper
Source printed “half filled as show in figure”.
Q8 · MCQ · ThermodynamicsOpen
Heat is supplied to a diatomic gas at constant pressure. Then the ratio of $\Delta Q : \Delta U : \Delta W$ is .
1. (1)2 : 3 : 5
2. (2)5 : 3 : 2
3. (3)2 : 5 : 7
4. (4)7 : 5 : 2
Q9 · MCQ · Electric Potential and CapacitanceOpen
Two charged conducting spheres $S_1$ and $S_2$ of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the electric fields on $S_1$ and $S_2$ spheres are $E_{S1}$ and $E_{S2}$ respectively. The value of $\dfrac{E_{S1}}{E_{S2}}$ is .
1. (1) $\dfrac32$
2. (2) $\dfrac23$
3. (3) $\dfrac49$
4. (4) $\dfrac94$
We corrected a printing error in the original paper
Source printed “the ratio of electric fields on $S_1$ and $S_2$ spheres are $E_{S1}$ and $E_{S2}$ ” (extra words “ratio of”).
Q10 · MCQ · WavesOpen
The equation of a plane progressive wave is given by $y = 5\cos\pi\left(200t - \dfrac{x}{150}\right)$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is m/s
1. (1)120
2. (2)150
3. (3)200
4. (4)300
Q11 · MCQ · Electric Charges and FieldsOpen
Two short electric dipoles A and B having dipole moment $p_1$ and $p_2$ respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point x is making an angle of $60^\circ$ with the line joining points O and x. The ratio of the dipole moments $p_2/p_1$ is .
1. (1) $\dfrac{\sqrt3}{2}$
2. (2) $2\sqrt3$
3. (3) $\dfrac{1}{\sqrt3}$
4. (4) $\sqrt3$
Q12 · MCQ · Semiconductor ElectronicsOpen
For the given circuit (shown in part (A)) the time dependent input voltage $v_{\mathrm{in}}(t)$ and corresponding output $v_o(t)$ are shown in part (B) and part (C), respectively. Identify the components that are used in the circuit between points X and Y.
1. (1)
2. (2)
3. (3)
4. (4)
Q13 · MCQ · Electromagnetic InductionOpen
When a coil is placed in a time dependent magnetic field the power dissipated in it is $P$ . The number of turns, area of the coil and radius of the coil wire are $N$ , $A$ and $r$ respectively. For a second coil's number of turns, area of the coil and radius of the coil wire are $2N$ , $2A$ and $3r$ respectively. When the first coil is replaced with second coil the power dissipated in it is $\sqrt2\,\alpha P$ . The value of $\alpha$ is .
1. (1)36
2. (2) $128\sqrt2$
3. (3)16
4. (4)64
We corrected a printing error in the original paper
Source printed “For a second coils number of turns”.
Q14 · MCQ · Moving Charges and MagnetismOpen
Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are $B_1$ and $B_2$ respectively, then the ratio $\dfrac{B_1}{B_2}$ is .
1. (1) $\dfrac{2+\pi}{1+\pi}$
2. (2) $\dfrac{1+\pi}{1-\pi}$
3. (3) $\dfrac{2+\pi}{1-\pi}$
4. (4) $\dfrac{1+\pi}{2-\pi}$
Q15 · MCQ · Ray OpticsOpen
For a thin symmetric prism made of glass (refractive index 1.5), the ratio of incident angle and minimum deviation will be .
1. (1)3 : 4
2. (2)3 : 2
3. (3)2 : 1
4. (4)1 : 2
Q16 · MCQ · Ray OpticsOpen
Refer the figure given below. $\mu_1$ and $\mu_2$ are refractive indices of air and lens material. The height of image will be cm.
1. (1)1
2. (2)0.5
3. (3)1.2
4. (4)0.25
Q17 · MCQ · Dual Nature of Radiation and MatterOpen
For a certain metal, when monochromatic light of wavelength $\lambda$ is incident, the stopping potential for photoelectrons is $3V_0$ . When the same metal is illuminated by light of wavelength $2\lambda$ , then the stopping potential becomes $V_0$ . The threshold wavelength for photoelectric emission for the given metal is $\alpha\lambda$ . The value of $\alpha$ is .
1. (1)1
2. (2)4
3. (3)2
4. (4)3
Q18 · MCQ · Electromagnetic WavesOpen
An electromagnetic wave travelling in x-direction is described by field equation $E_y = 300\sin\omega\left(t - \frac{x}{c}\right).$ If the electron is restricted to move in y-direction only with speed of $1.5\times10^{6}$ m/s then ratio of maximum electric and magnetic forces acting on the electron is .
1. (1)200
2. (2)150
3. (3)400
4. (4)300
Q19 · MCQ · AtomsOpen
Angular momentum of an electron in a hydrogen atom is $\dfrac{3h}{\pi}$ , then the energy of the electron is eV.
1. (1) $-1.51$
2. (2) $-0.85$
3. (3) $-0.38$
4. (4) $-0.28$
Q20 · MCQ · Mechanical Properties of FluidsOpen
A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is $\alpha\times10^{-6}$ J. The value of $\alpha$ is . (Take surface tension of liquid $= 0.08$ N/m)
1. (1)10
2. (2)7
3. (3)8
4. (4)11
Q21 · Numerical · Wave OpticsOpen
In single slit diffraction pattern, the wavelength of light used is 628 nm and slit width is 0.2 mm, the angular width of central maximum is $\alpha\times10^{-2}$ degrees. The value of $\alpha$ is .
Q22 · Numerical · ThermodynamicsOpen
A vessel contains $0.15\ \mathrm{m^3}$ of a gas at pressure 8 bar and temperature $140^\circ$ C with $c_p = 3R$ and $c_v = 2R$ . It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is kJ. ( $R$ is gas constant)
Q23 · Numerical · Moving Charges and MagnetismOpen
$1\ \mu$ C charge is moving with velocity $\vec v = \left(\hat i - 2\hat j + 3\hat k\right)$ m/s in the region of magnetic field $\vec B = \left(2\hat i + 3\hat j - 5\hat k\right)$ T. The magnitude of force acting on it is $\sqrt\alpha\times10^{-6}$ N. The value of $\alpha$ is .
We corrected a printing error in the original paper
Source printed “ $1\ \mu$ C charge moving with velocity” (no verb).
Q24 · Numerical · Mechanical Properties of SolidsOpen
A uniform wire of length $l$ of weight $w$ is suspended from the roof with a weight of $W$ at the other end. The stress in the wire at $\dfrac{l}{3}$ distance from the top is $\left(\dfrac{W}{A} + \dfrac{2}{\gamma}\dfrac{w}{A}\right)$ , where, $A$ is the cross sectional area of the wire. The value of $\gamma$ is .
We corrected a printing error in the original paper
Answer corrected; the source key is (6) — it takes the weight of the wire below the point as $w/3$ , but at $l/3$ from the top the wire below weighs $2w/3$ , so the stress is $W/A + \frac{2}{3}\,w/A$ and $\gamma = 3$ .
Q25 · Numerical · Mechanical Properties of FluidsOpen
A tube is filled with water and a wooden cube $10\ \mathrm{cm}\times10\ \mathrm{cm}\times10\ \mathrm{cm}$ is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by 3.87 cm. The mass of the metal coin is gram. (Take water density as $1\ \mathrm{g/cm^3}$ and density of wood as $0.4\ \mathrm{g/cm^3}$ )

Chemistry

Q1 · MCQ · Some Basic ConceptsOpen
The mass of iron converted into $\ce{Fe3O4}$ by the action of 18 g of steam is :
(Given : Molar mass of H, O and Fe are 1, 16 and 56 g mol $^{-1}$ respectively)
Assume iron is present in excess :
1. (1)2.1 g
2. (2)4.2 g
3. (3)21 g
4. (4)42 g
Q2 · MCQ · Structure of AtomOpen
What is the energy (in J atom $^{-1}$ ) required for the following process ?
$\ce{Li^2+(g) -> Li^3+(g) + e-}$
(Take the ionization energy for the H atom in the ground state as $2.18\times10^{-18}$ J atom $^{-1}$ )
1. (1) $8.72\times10^{-18}$
2. (2) $1.962\times10^{-18}$
3. (3) $1.962\times10^{-17}$
4. (4) $6.54\times10^{-17}$
Q3 · MCQ · Chemical BondingOpen
Given below are two statements :
Statement (I) : The correct sequence of bond lengths in the following species is :
$\ce{O2+}$ $<$ $\ce{O2}$ $<$ $\ce{O2-}$ $<$ $\ce{O2^2-}$
Statement (II) : The correct sequence of number of unpaired electrons in the following species is :
$\ce{O2}$ $>$ $\ce{O2+}$ $>$ $\ce{O2-}$ $>$ $\ce{O2^2-}$
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
Q4 · MCQ · ThermodynamicsOpen
Consider the following data
(i) $\ce{2Al(s) + 6HCl(aq) -> Al2Cl6(aq) + 3H2(g)}$ + 1200 kJ/mol.
(ii) $\ce{H2(g) + Cl2(g) -> 2HCl(g)}$ + 164 kJ/mol.
(iii) $\ce{HCl(g) + aq -> HCl(aq)}$ + 83 kJ/mol.
(iv) $\ce{Al2Cl6(s) + aq -> Al2Cl6(aq)}$ + 663 kJ/mol.
The enthalpy of formation of anhydrous solid $\ce{Al2Cl6}$ is :
1. (1) $-648$ kJ mol $^{-1}$
2. (2) $-1350$ kJ mol $^{-1}$
3. (3) $-2002$ kJ mol $^{-1}$
4. (4) $-1527$ kJ mol $^{-1}$
Q5 · MCQ · SolutionsOpen
19.5 g of fluoro acetic acid (molar mass = 78 g mol $^{-1}$ ) is dissolved in 500g of water at 298 K. The depression in the freezing point of water was 1 $^\circ$ C. What is $K_\mathrm{a}$ of fluoro acetic acid ?
(For water, $K_\mathrm{f} = 1.86$ K kg mol $^{-1}$ ). Assume molarity and molality to have same values.
1. (1) $10^{-6}$
2. (2) $4\times10^{-4}$
3. (3) $3\times10^{-5}$
4. (4) $3\times10^{-3}$
Q6 · MCQ · EquilibriumOpen
The solubility product constants of $\ce{Ag2CrO4}$ and AgBr are 32x and 4y respectively at 298 K.
The value of $\left(\dfrac{{\text{molarity of }\ce{Ag2CrO4}}}{\text{molarity of AgBr}}\right)$ can be expressed as :
1. (1) $\dfrac{2\sqrt[3]{\mathrm{x}}}{\mathrm{y}}$
2. (2) $2\sqrt{\dfrac{\mathrm{x}}{\mathrm{y}}}$
3. (3) $\sqrt{\dfrac{\mathrm{x}}{\mathrm{y}}}$
4. (4) $\dfrac{\sqrt[3]{\mathrm{x}}}{\sqrt{\mathrm{y}}}$
Q7 · MCQ · ElectrochemistryOpen
An electrochemical cell is constructed using half cells in the direction of spontaneous change
$\ce{Fe(OH)2(s) + 2e- -> Fe(s) + 2OH-(aq)}$ $E^0 = -0.88$ V
and $\ce{AgBr(s) + e- -> Ag(s) + Br-(aq)}$ $E^0 = +0.07$ V
Which of the following option is correct ?
1. (1)Overall reaction $\ce{Fe(s) + 2OH^{-1}(aq) + 2AgBr(s) <=> Fe(OH)2(s) + 2Ag(s) + 2Br-(aq)}$
2. (2) $E^0_\mathrm{cell} = -0.95$ V
3. (3)Fe is reduced in the electrochemical cell
4. (4) $E^0_\mathrm{cell}$ is an extensive property
Q8 · MCQ · Chemical KineticsOpen
$t_{100\%}$ is the time required for the 100% completion of the reaction while $t_{1/2}$ is the time required for 50% of the reaction to be completed. Which of the following option correctly represents the relation between $t_{100\%}$ and $t_{1/2}$ for zero and first order reactions respectively ?
1. (1) $t_{100\%} = (t_{1/2})^2$ and $t_{100\%} = (t_{1/2})^{-\infty}$
2. (2) $t_{100\%} = 2t_{1/2}$ and $t_{100\%} = (t_{1/2})^{\infty}$
3. (3) $t_{100\%} = 2t_{1/2}$ and $t_{100\%} = (2t_{1/2})^2$
4. (4) $t_{100\%} = (t_{1/2})^{\infty}$ and $t_{100\%} = 2t_{1/2}$
Q9 · MCQ · Classification & PeriodicityOpen
Given below are two statements :
Statement (I) : The first ionisation enthalpy of the elements Na, Mg, Cl and Ar follows the order
Na $>$ Mg $>$ Cl $>$ Ar
Statement (II) : Among Ca, Al, Fe and B, the third ionisation enthalpy is very high for Ca.
In the light of the above statements, choose the correct answer from the options given below :
1. (1)Both Statement I and Statement II are true
2. (2)Both Statement I and Statement II are false
3. (3)Statement I is true but Statement II is false
4. (4)Statement I is false but Statement II is true
Q10 · MCQ · Redox ReactionsOpen
Given below are two statements :
Statement (I) : Oxidising power of halogens decreases in the order $\ce{F2}$ $>$ $\ce{Cl2}$ $>$ $\ce{Br2}$ $>$ $\ce{I2}$ , which is the basis of “Layer test”.
Statement (II) : “Layer test” to identify $\ce{Br2}$ and $\ce{I2}$ in aqueous solution involves the oxidation of bromide or iodide into $\ce{Br2}$ or $\ce{I2}$ respectively with $\ce{Cl2}$ , which is a type of displacement redox reaction.
In the light of the above statements, choose the correct answer from the options given below :
1. (1)Both Statement I and Statement II are true
2. (2)Both Statement I and Statement II are false
3. (3)Statement I is true but Statement II is false
4. (4)Statement I is false but Statement II is true
Q11 · MCQ · d- and f-BlockOpen
Which of the following sets includes all the species that will change the orange colour of $\ce{K2Cr2O7}$ in acidic medium ?
1. (1) $\ce{Fe^2+}$ , $\ce{Sn^2+}$ , $\ce{I-}$ , $\ce{S^2-}$
2. (2) $\ce{S^2-}$ , $\ce{Fe^3+}$ , $\ce{I-}$ , $\ce{C2O4^2-}$
3. (3) $\ce{Fe^2+}$ , $\ce{NO2-}$ , $\ce{SO2}$ , $\ce{Sn^4+}$
4. (4) $\ce{Fe^3+}$ , $\ce{SO4^2-}$ , $\ce{S^2-}$ , $\ce{Sn^4+}$

Q12 · MCQ · Coordination CompoundsOpen

Match List – I with List – II.

List – I		List – II
Chromium (III) Complexes		$\boldsymbol{\Delta_0}$ (cm $^{\mathbf{-1}}$ )
(en = ethylene diamine)
A.	$\ce{[Cr(CN)6]^3-}$	I.	15,060
B.	$\ce{[CrF6]^3-}$	II.	17,400
C.	$\ce{[Cr(H2O)6]^3+}$	III.	22,300
D.	$\ce{[Cr(en)3]^3+}$	IV.	26,600

Choose the correct answer from the options given below :

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

We corrected a printing error in the original paper

Source printed “[Cr(H $_2$ O) $_6$ )] $^{3+}$ ” (stray closing parenthesis).

Q13 · MCQ · Purification & CharacterisationOpen
Given below are two statements :
Statement (I) : 1,2,3-Trihydroxypropane can be separated from water by simple distillation.
Statement (II) : An azeotropic mixture cannot be separated by fractional 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 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 “An azotropic mixture”.
Q14 · MCQ · Haloalkanes & HaloarenesOpen
Given below are two statements :
Statement (I) : Benzyl chloride reacts faster in S $_\mathrm{N}$ 1 mechanism than ethyl chloride.
Statement (II) : Ethyl carbocation intermediate is less stabilized by hyperconjugation than benzyl carbocation by resonance.
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
Q15 · MCQ · Organic Basics (GOC)Open
In IUPAC nomenclature, the correct order of decreasing priority of functional group is :
1. (1) $-\mathrm{CONH_2}$ , $\mathord{>}\mathrm{C{=}O}$ , $-\mathrm{CHO}$ , $-\mathrm{NH_2}$ , $-\mathrm{C{\equiv}C}-$
2. (2) $-\mathrm{CONH_2}$ , $-\mathrm{COOCH_3}$ , $-\mathrm{CHO}$ , $-\mathrm{NH_2}$ , $-\mathrm{OH}$
3. (3) $-\mathrm{CONH_2}$ , $-\mathrm{CHO}$ , $\mathord{>}\mathrm{C{=}O}$ , $-\mathrm{NH_2}$ , $-\mathrm{C{\equiv}C}-$
4. (4) $-\mathrm{CONH_2}$ , $-\mathrm{CHO}$ , $-\mathrm{CN}$ , $-\mathrm{NH_2}$ , $-\mathrm{C{\equiv}C}-$
Q16 · MCQ · HydrocarbonsOpen
For the given molecule, “x”, the preferred site for the attack of the electrophile is :
1. (1)Predominantly at “r”
2. (2)“r” and “u”
3. (3)“p” and “s”
4. (4)Predominantly at “u”

Q17 · MCQ · Practical / Qualitative AnalysisOpen

Match List-I with List-II.

	List-I		List-II
	Mixture of Compounds		Reagent used to distinguish
A.	Diethyl amine + Ethyl amine	I.	Bromine water
B.	Acetaldehyde + Acetone	II.	$\ce{CHCl3}$ + KOH, $\Delta$
C.	Ethanol + Phenol	III.	Neutral $\ce{FeCl3}$
D.	Benzoic acid + Cinnamic acid	IV.	Ammoniacal silver nitrate

Choose the correct answer from the options given below :

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

We corrected a printing error in the original paper

Source printed “Ammonical silver nitrate”.

Q18 · MCQ · AminesOpen
Consider the three aromatic molecules (P, Q and R) whose structures have been given below :
The correct order regarding the reactivity of these compounds with $\mathrm{Ph{-}\underset{{\scriptstyle(+)}}{N}{\equiv}N\;Cl^{(-)}}$ under optimum but slightly acidic medium is :
1. (1)P $>$ Q $>$ R
2. (2)R $>$ P $>$ Q
3. (3)R $>$ Q $>$ P
4. (4)P $>$ R $>$ Q
Q19 · MCQ · BiomoleculesOpen
Match List-I with List-II.
List-I List-II
Vitamin Name
A. Vitamin B $_1$ I. Pyridoxine
B. Vitamin B $_2$ II. Ascorbic acid
C. Vitamin B $_6$ III. Thiamine
D. Vitamin C IV. Riboflavin
Choose the correct answer from the options given below :
1. (1)A-II, B-I, C-III, D-IV
2. (2)A-IV, B-III, C-II, D-I
3. (3)A-III, B-IV, C-I, D-II
4. (4)A-I, B-III, C-II, D-IV
Q20 · MCQ · Practical / Qualitative AnalysisOpen
A salt with few drops of conc. HCl gives apple green colour in flame test. The group precipitate of the salt is dissolved in acetic acid and treated with $\ce{K2CrO4}$ to give yellow precipitate. When the sodium carbonate extract of the salt solution is heated with conc. $\ce{HNO3}$ and ammonium molybdate, it resulted in a canary yellow precipitate. The cation and anion present in the salt are respectively.
1. (1) $\ce{Ca^2+}$ and $\ce{SO4^2-}$
2. (2) $\ce{Ba^2+}$ and $\ce{PO4^3-}$
3. (3) $\ce{Mn^2+}$ and $\ce{PO4^3-}$
4. (4) $\ce{Ba^2+}$ and $\ce{SO4^2-}$
We corrected a printing error in the original paper
Source printed “it resulted a canary yellow precipitate”.
Q21 · Numerical · Coordination CompoundsOpen
5.33 g of $\ce{CrCl3*6H2O}$ , which is a 1 : 3 electrolyte, is dissolved in water and is passed through a cation exchanger. The chloride ions in the eluted solution, on treatment with $\ce{AgNO3}$ result in 8.61 g of AgCl. The ratio of moles of complex reacted and moles of AgCl formed is $\times10^{-2}$ . (Nearest integer)
[Molar mass in g mol $^{-1}$ Cr : 52, Ag : 108, Cl : 35.5, H : 1, O : 16]
We corrected a printing error in the original paper
Source printed “The chloride ions … on treatment with AgNO $_3$ results in”.
Q22 · Numerical · HydrocarbonsOpen
Consider the isomers of hydrocarbon with molecular formula $\ce{C5H10}$ . These isomers do not decolourise $\ce{KMnO4}$ solution. These isomers are subjected to chlorination with chlorine in presence of light to give monochloro compounds. The total number of monochloro compounds (structural isomers only) formed is .
Q23 · Numerical · HydrocarbonsOpen
One mole of an alkane (x) requires 8 mole oxygen for complete combustion. Sum of number of carbon and hydrogen atoms in the alkane (x) is .
Q24 · Numerical · Chemical KineticsOpen
For reaction $\ce{A -> P}$ , rate constant $k = 1.5\times10^{3}$ s $^{-1}$ at 27 $^\circ$ C. If activation energy for the above reaction is 60 kJ mol $^{-1}$ , then the temperature (in $^\circ$ C) at which rate constant, $k = 4.5\times10^{3}$ s $^{-1}$ is . (Nearest integer)
Given : $\log 2 = 0.30$ , $\log 3 = 0.48$ , $R = 8.3$ J K $^{-1}$ mol $^{-1}$ , $\ln 10 = 2.3$
Q25 · Numerical · ThermodynamicsOpen
At the transition temperature T, $\ce{A <=> B}$ and $\Delta G^0 = 105 - 35\log T$ where A and B are two states of substance X. The transition temperature in $^\circ$ C when pressure is 1 atm is . (Nearest integer)

Maths

Q1 · MCQ · Quadratic EquationsOpen
Let $\alpha, \alpha + 2$ , $\alpha \in \mathbb{Z}$ , be the roots of the quadratic equation $x(x+2) + (x+1)(x+3) + (x+2)(x+4) + \ldots + (x+n-1)(x+n+1) = 4n$ for some $n \in \mathbb{N}$ . Then $(n + \alpha)$ is equal to:
1. (1)0
2. (2)1
3. (3)2
4. (4)3
Q2 · MCQ · Complex NumbersOpen
Let $x$ and $y$ be real numbers such that $50\left(\dfrac{2x}{1+3i} - \dfrac{y}{1-2i}\right) = 31 + 17i,\quad i = \sqrt{-1}.$ Then the value of $10(x - 3y)$ is:
1. (1)20
2. (2)31
3. (3)35
4. (4)75
We corrected a printing error in the original paper
Source printed “Let $x$ and $y$ be real number”.
Q3 · MCQ · Matrices & DeterminantsOpen
Let $\alpha, \beta \in \mathbb{R}$ be such that the system of linear equations
$\begin{align*} x + 2y + z &= 5\\ 2x + y + \alpha z &= 5\\ 8x + 4y + \beta z &= 18 \end{align*}$
has no solution. Then $\dfrac{\beta}{\alpha}$ is equal to:
1. (1) $-4$
2. (2)4
3. (3)8
4. (4) $-8$
Q4 · MCQ · Matrices & DeterminantsOpen
Let $A = \begin{bmatrix} 1 & 2\\ 1 & \alpha\end{bmatrix}$ and $B = \begin{bmatrix} 3 & 3\\ \beta & 2\end{bmatrix}$ . If $A^2 - 4A + I = O$ and $B^2 - 5B - 6I = O$ , then among the two statements:
- (S1): $[(B - A)(B + A)]^{T} = \begin{bmatrix} 13 & 15\\ 7 & 10\end{bmatrix}$
and
- (S2): $\det(\operatorname{adj}(A + B)) = -5$ ,
1. (1)only (S1) is correct
2. (2)only (S2) is correct
3. (3)both (S1) and (S2) are correct
4. (4)both (S1) and (S2) are wrong
Q5 · MCQ · Sequences & SeriesOpen
Let $A$ be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let $B$ be the set of first 71 terms of an A.P., whose first term is 9 and the common difference is 7. Then the number of elements in $A \cap B$ , which are divisible by 3, is:
1. (1)4
2. (2)5
3. (3)6
4. (4)7
We corrected a printing error in the original paper
Source printed “the number of elements is $A \cap B$ ”.
Q6 · MCQ · Permutations & CombinationsOpen
The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, is;
1. (1)15400
2. (2)17800
3. (3)16800
4. (4)29400
Q7 · MCQ · Binomial TheoremOpen
The number of elements in the set $S = \left\{(r, k) : k \in \mathbb{Z} \text{ and } {}^{36}C_{r+1} = \dfrac{6\left({}^{35}C_r\right)}{(k^2 - 3)}\right\},$ is
1. (1)2
2. (2)4
3. (3)8
4. (4)16
Q8 · MCQ · StatisticsOpen
If the mean of the data
Class 5-10 10-15 15-20 20-25 25-30 30-35
Frequency 2 $k$ 28 54 $k+1$ 5
is 21, then $k$ is one of the roots of the equation:
1. (1) $2x^2 - 23x - 10 = 0$
2. (2) $4x^2 - 35x + 24 = 0$
3. (3) $2x^2 - 19x - 10 = 0$
4. (4) $2x^2 - 35x + 98 = 0$
Q9 · MCQ · Straight LinesOpen
Let the mid points of the sides of a triangle $ABC$ be $\left(\dfrac52, 7\right)$ , $\left(\dfrac52, 3\right)$ and $(4, 5)$ . If its incentre is $(h, k)$ , then $3h + k$ is equal to:
1. (1)11
2. (2)12
3. (3)13
4. (4)14
Q10 · MCQ · Conic SectionsOpen
Let an ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ , $a < b$ , pass through the point $(4, 3)$ and have eccentricity $\dfrac{\sqrt5}{3}$ . Then the length of its latus rectum is:
1. (1) $\dfrac{4\sqrt5}{3}$
2. (2) $2\sqrt5$
3. (3) $\dfrac{7\sqrt5}{3}$
4. (4) $\dfrac{8\sqrt5}{3}$
Q11 · MCQ · TrigonometryOpen
If $\sin\left(\dfrac{\pi}{18}\right)\sin\left(\dfrac{5\pi}{18}\right)\sin\left(\dfrac{7\pi}{18}\right) = K$ , then the value of $\sin\left(\dfrac{10K\pi}{3}\right)$ is:
1. (1) $\dfrac{\sqrt3 + 1}{2\sqrt2}$
2. (2) $\dfrac{\sqrt3 - 1}{\sqrt2}$
3. (3) $\dfrac{\sqrt3}{2}$
4. (4) $\dfrac12$
Q12 · MCQ · TrigonometryOpen
Let $S = \{x \in [-\pi, \pi] : \sin x\,(\sin x + \cos x) = a,\ a \in \mathbb{Z}\}$ . Then $n(S)$ is equal to:
1. (1)3
2. (2)6
3. (3)7
4. (4)9
Q13 · MCQ · 3D GeometryOpen
If the point of intersection of the lines $\dfrac{x+1}{3} = \dfrac{y+a}{5} = \dfrac{z+b+1}{7}$ and $\dfrac{x-2}{1} = \dfrac{y-b}{4} = \dfrac{z-2a}{7}$ lies on xy-plane, then the value of $a + b$ is:
1. (1)2
2. (2)5
3. (3)7
4. (4)9
Q14 · MCQ · VectorsOpen
If $\vec a$ and $\vec b$ are two vectors such that $\lvert\vec a\rvert = 2$ and $\lvert\vec b\rvert = 3$ , then the maximum value of $3\left\lvert\left(3\vec a + 2\vec b\right)\right\rvert + 4\left\lvert\left(3\vec a - 2\vec b\right)\right\rvert$ is:
1. (1)30
2. (2)36
3. (3)60
4. (4)72
Q15 · MCQ · 3D GeometryOpen
Let a line $L$ passing through the point $(1, 1, 1)$ be perpendicular to both the vectors $2\hat i + 2\hat j + \hat k$ and $\hat i + 2\hat j + 2\hat k$ . If $P(a, b, c)$ is the foot of perpendicular from the origin on the line $L$ , then the value of $34(a + b + c)$ is:
1. (1)50
2. (2)80
3. (3)100
4. (4)120
We corrected a printing error in the original paper
Source printed the second vector as “ $\hat i + 2\hat j + \hat k$ ”; corrected to the intended “ $\hat i + 2\hat j + 2\hat k$ ” (the source's own solution uses it; as printed $34(a+b+c) = 95.2$ , no option).
Q16 · MCQ · Limits, Continuity & DifferentiabilityOpen
If $\displaystyle\lim_{x\to2}\frac{\sin\left(x^3 - 5x^2 + ax + b\right)}{\left(\sqrt{x-1} - 1\right)\log_e(x-1)} = m$ , then $a + b + m$ is equal to:
1. (1)5
2. (2)6
3. (3)8
4. (4)10
Q17 · MCQ · Differential EquationsOpen
If the curve $y = f(x)$ passes through the point $(1, e)$ and satisfies the differential equation $dy = y\,(2 + \log_e x)\,dx$ , $x > 0$ , then $f(e)$ is equal to:
1. (1) $e^{e}$
2. (2) $e^{e^2}$
3. (3) $e^{2e}$
4. (4) $e^{2^e}$
Q18 · MCQ · Applications of DerivativesOpen
The number of critical points of the function $f(x) = \begin{cases} \left\lvert\dfrac{\sin x}{x}\right\rvert, & x \neq 0\\[6pt] 1, & x = 0\end{cases}$ in the interval $(-2\pi, 2\pi)$ is equal to:
1. (1)1
2. (2)3
3. (3)5
4. (4)7
Q19 · MCQ · Definite IntegrationOpen
Let $[\cdot]$ denote the greatest integer function. Then the value of $\displaystyle\int_0^3\left(\frac{e^x + e^{-x}}{[x]!}\right)dx$ is:
1. (1) $e^2 + e^3 - \dfrac{1}{e^2} - \dfrac{1}{e^3}$
2. (2) $\dfrac12\left(e^2 + e^3 - \dfrac{1}{e^2} - \dfrac{1}{e^3}\right)$
3. (3) $e^2 + e^3 - \dfrac{1}{2e^2} - \dfrac{1}{2e^3}$
4. (4) $\dfrac12(e^2 + e^3) - \dfrac{1}{e^2} - \dfrac{1}{e^3}$
Q20 · MCQ · Differential EquationsOpen
Let $y = y(x)$ be the solution curve of the differential equation $(1 + \sin x)\dfrac{dy}{dx} + (y + 1)\cos x = 0$ , $y(0) = 0$ . If the curve $y = y(x)$ passes through the point $\left(\alpha, \dfrac{-1}{2}\right)$ , then a value of $\alpha$ is:
1. (1) $\dfrac{\pi}{6}$
2. (2) $\dfrac{\pi}{4}$
3. (3) $\dfrac{\pi}{3}$
4. (4) $\dfrac{\pi}{2}$
Q21 · Numerical · Sets, Relations & FunctionsOpen
If the domain of the function $f(x) = \sqrt{\log_{(0.6)}\left(\left\lvert\dfrac{2x-5}{x^2-4}\right\rvert\right)}$ is $(-\infty, a] \cup \{b\} \cup [c, d) \cup (e, \infty)$ , then the value of $a + b + c + d + e$ is .
Q22 · Numerical · Sequences & SeriesOpen
If $\displaystyle\sum_{k=1}^{n} a_k = 6n^3$ , then $\displaystyle\sum_{k=1}^{6}\left(\frac{a_{k+1} - a_k}{36}\right)^2$ is equal to .
Q23 · Numerical · ProbabilityOpen
Let $a, b, c \in \{1, 2, 3, 4\}$ . If the probability, that $ax^2 + 2\sqrt2\,bx + c > 0$ for all $x \in \mathbb{R}$ , is $\dfrac{m}{n}$ , $\gcd(m, n) = 1$ , then $m + n$ is equal to .
Q24 · Numerical · CirclesOpen
Let a circle $C$ have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of $C$ on the line $x + y = 1$ is $\sqrt{14}$ , then the square of the radius of $C$ is .
Q25 · Numerical · Definite IntegrationOpen
If $\alpha = \displaystyle\int_0^{2\sqrt3}\log_2\left(x^2 + 4\right)dx + \int_2^4\sqrt{2^x - 4}\,dx$ , then $\alpha^2$ is equal to .

	List-I		List-II
	Vitamin		Name
A.	Vitamin B $_1$	I.	Pyridoxine
B.	Vitamin B $_2$	II.	Ascorbic acid
C.	Vitamin B $_6$	III.	Thiamine
D.	Vitamin C	IV.	Riboflavin

Class	5-10	10-15	15-20	20-25	25-30	30-35
Frequency	2	$k$	28	54	$k+1$	5