JEE Main 5 Apr 2026, Shift 2

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

Physics

Match List-I with List-II.

List-I	List-II
(A) Meter (L)	I. $\sqrt{\dfrac{hc}{\mathrm{G}}}$
[6pt] (B) Second (S)	II. $\sqrt{\dfrac{\mathrm{G}h}{\mathrm{c}^5}}$
[6pt] (C) Kilogram (M)	III. $\sqrt{\dfrac{\mathrm{K^2L^2c^3}}{\mathrm{G}h}}$
[6pt] (D) Kelvin (K)	IV. $\sqrt{\dfrac{\mathrm{G}h}{\mathrm{c}^3}}$

where h (Planck's constant), G (gravitational constant) and c (speed of light in vacuum) are taken as fundamental units.

Choose the correct answer from the options given below:

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

We corrected a printing error in the original paper

Source printed “c (speed of light in vacuum) as fundamental units” (verb missing).

Q2 · MCQ · Units and MeasurementsOpen
In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10V and 5 A, respectively. The least counts of voltmeter and ammeter are 500 mV and 200 mA, respectively. The estimated error in the resistance measurement is $\Omega$
1. (1)0.25
2. (2)2
3. (3)2.5
4. (4)0.18
Q3 · MCQ · Work, Energy and PowerOpen
A mass of 1 kg kept in an inclined plane with $30^\circ$ inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of 4 m/s. The work done by the frictional force in time 2s is J.
(Take $g = 10\ \mathrm{m/s^2}$ )
1. (1)20
2. (2)25
3. (3)30
4. (4)10
We corrected a printing error in the original paper
Source printed “kept in a inclined plane”.
Q4 · MCQ · Motion in a Straight LineOpen
The velocity( $v$ ) versus time ( $t$ ) plot of a particle is shown in the figure, for a time interval of 40s. The total distance travelled by the particle and the average velocity during this period are, respectively
1. (1)25 m and zero
2. (2)50 m and zero
3. (3)100 m and zero
4. (4)100 m and 2.5 m/s
Q5 · MCQ · Rotational MotionOpen
A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle $\theta_1$ and in the next 2 s it rotates through an angle $\theta_2$ . The ratio $\dfrac{\theta_2}{\theta_1}$ is.
1. (1)6
2. (2)3
3. (3)4
4. (4) $\dfrac13$
Q6 · MCQ · Rotational MotionOpen
An object of uniform density rolls up the curved path with the initial velocity $v_0$ as shown in the figure. If the maximum height attained by an object is $\dfrac{7v_0^2}{10g}$ ( $g$ = acceleration due to gravity), the object is a.
1. (1)solid cylinder
2. (2)ring
3. (3)disc
4. (4)solid sphere
Q7 · MCQ · GravitationOpen
A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth ( $R_e$ ). The increase in potential energy will be.
( $g$ is acceleration due to gravity at the surface of earth)
1. (1) $\dfrac12 mgR_e$
2. (2) $\dfrac34 mgR_e$
3. (3) $\dfrac14 mgR_e$
4. (4) $\dfrac23 mgR_e$
Q8 · MCQ · Mechanical Properties of FluidsOpen
Eight mercury drops, each of radius $r$ , coalesce to form a bigger drop. The surface energy released in this process is. ( $S$ is the surface tension of mercury).
1. (1) $8\pi r^2S$
2. (2) $16\pi r^2S$
3. (3) $64\pi r^2S$
4. (4) $4\pi r^2S$
Q9 · MCQ · Kinetic Theory of GasesOpen
An ideal gas at pressure $P$ and temperature $T$ is expanding such that $PT^3$ = constant. The coefficient of volume expansion of the gas is.
1. (1) $\dfrac{2}{T}$
2. (2) $\dfrac{1}{T}$
3. (3) $\dfrac{4}{T}$
4. (4) $\dfrac{3}{T}$

Q10 · MCQ · OscillationsOpen

Match List-I with List-II.

List-I		List-II
A.	$\sin^2\omega t$	I.	Periodic with time period $T = \dfrac{\pi}{\omega}$ but not simple harmonic motion (SHM)
B.	$\sin^3(2\omega t)$	II.	Periodic with time period $T = \dfrac{2\pi}{\omega}$ but Not SHM
C.	$\sin(\omega t) + \cos(\pi\omega t)$	III.	periodic with time period $T = \dfrac{\pi}{\omega}$ and SHM
D.	$\cos\omega t + \cos 2\omega t$	IV.	Non-periodic

Choose the correct answer from the options given below.

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

Q11 · MCQ · Electromagnetic InductionOpen
A metal rod of length $L$ rotates about one end at origin with a uniform angular velocity $\omega$ . The magnetic field radially falls off as $B(r) = B_0e^{-\lambda r}$ ; $\lambda$ being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is:
1. (1) $B_0\omega\left[\dfrac{1}{\lambda^2} - e^{-\lambda L}\left(\dfrac{1}{\lambda^2} + \dfrac{L}{\lambda}\right)\right]$
2. (2) $B_0\omega\left[\dfrac{1}{\lambda^2} + e^{-\lambda L}\left(\dfrac{1}{\lambda^2} + \dfrac{L}{\lambda}\right)\right]$
3. (3) $B_0\omega\left[\dfrac{4}{\lambda^2} - e^{-2\lambda L}\left(\dfrac{1}{\lambda^2} + \dfrac{2L}{\lambda}\right)\right]$
4. (4) $B_0\omega\left[\dfrac{3}{\lambda^2} - e^{-3\lambda L}\left(\dfrac{3}{\lambda^2} + \dfrac{L}{\lambda}\right)\right]$
We corrected a printing error in the original paper
Source printed “rotates about on end at origin”.
Q12 · MCQ · Current ElectricityOpen
Under steady state condition the potential difference across the capacitor in the circuit isV.
1. (1)0.5
2. (2)1.5
3. (3)0
4. (4)2
Q13 · MCQ · Work, Energy and PowerOpen
A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec v = \left(\dfrac{v_0}{\sqrt2}\hat{\mathrm x} + \dfrac{v_0}{\sqrt2}\hat{\mathrm y}\right)$ . There exists a uniform magnetic field $\vec B = B_0\hat{\mathrm z}$ and a space varying electric field $\vec E = E_0e^{-\lambda x}\hat{\mathrm x}$ within the region $0 \le x \le L$ . After travelling a distance such that x-coordinate has changed from $x = 0$ to $x = L$ , the change in the kinetic energy is.
1. (1) $\dfrac{qE_0}{\lambda}\left[1 - e^{-\lambda L}\right]$
2. (2) $\left(\dfrac{v_0qB_0}{2\lambda}\right)\left[2 - e^{-2\lambda L}\right]$
3. (3) $\dfrac{qE_0}{\lambda}\left[1 + e^{-\lambda L}\right]$
4. (4) $q\left[\dfrac{E_0 + v_0B_0}{\lambda}\right]\left[1 - e^{-\lambda L/2}\right]$
Q14 · MCQ · Electromagnetic WavesOpen
Given below are two statements : one is labelled as Assertion (A) : and the other is labelled as Reason (R).
Assertion (A) : The electromagnetic wave exerts pressure on the surface on which it is allowed to fall.
Reason (R) : There is no mass associated with the electromagnetic waves.
In the light of the above statements, choose the correct answer from the options given below :
1. (1)Both (A) and (R) are true and (R) is the correct explanation of (A)
2. (2)Both (A) and (R) are true but (R) is not the correct explanation of (A)
3. (3)(A) is true but (R) is false
4. (4)(A) is false but (R) is true
We corrected a printing error in the original paper
Source printed “on which they are allowed to fall”.
Q15 · MCQ · Ray OpticsOpen
A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses?
1. (1)behaves as concave lens if $|f_{\text{convex}}| > |f_{\text{concave}}|$
2. (2)behaves as concave lens if $|f_{\text{convex}}| < |f_{\text{concave}}|$
3. (3)behaves as convex lens if $|f_{\text{convex}}| > |f_{\text{concave}}|$
4. (4)Focal length of the lens system will change if the positions of two lenses are interchanged
We corrected a printing error in the original paper
Source printed “if the position of two lenses are interchanged”.
Q16 · MCQ · Ray OpticsOpen
An object AB is placed 15 cm on the left of a convex lens P of focal length 10 cm. Another convex lens Q is now placed 15 cm right of lens P. If the focal length of lens Q is 15 cm, the final image is
1. (1)virtual, formed at 7.5 cm right of lens Q, with a size bigger than that of AB
2. (2)real, formed at 7.5 cm right of lens Q, with a size same as that of AB
3. (3)formed at infinity.
4. (4)real, formed at 7 cm right of lens Q, with a size smaller than that of AB
We corrected a printing error in the original paper
Source printed option (2) “with a size same than that of AB”.
Q17 · MCQ · Wave OpticsOpen
The maximum intensity in a Young's double slit experiment is $I_0$ . Distance between the slits ( $d$ ) is $5\lambda$ , where $\lambda$ is the wavelength of light used. The intensity of the fringe, exactly opposite to one of the slits on the screen, placed at $D = 10\,d$ is
1. (1) $\dfrac{I_0}{4}$
2. (2) $\dfrac{I_0}{2}$
3. (3) $I_0$
4. (4) $\dfrac{3I_0}{4}$
Q18 · MCQ · Dual Nature of Radiation and MatterOpen
An electron is travelling with a velocity $v$ in free space and when it enters a medium, its velocity is reduced by 20%. The de Broglie wavelength of electron in the medium is $\alpha\lambda_0$ , where $\lambda_0$ is its de Broglie wavelength in free space. The value of $\alpha$ is
1. (1)1.20
2. (2)1.0
3. (3)1.25
4. (4)0.75
Q19 · MCQ · NucleiOpen
Assuming the experimental mass of ${}^{12}_{6}\mathrm{C}$ nucleus as 12u, the mass defect of ${}^{12}_{6}\mathrm{C}$ nucleus is $\mathrm{MeV/c^2}$ . (Mass of proton $= 1.00727$ u. mass of neutron $= 1.00866$ u, 1 u $= 931.5\ \mathrm{MeV/c^2}$ and c is the speed of the light in vacuum.)
1. (1)127.5
2. (2)89.03
3. (3)272.0
4. (4)92.0
We corrected a printing error in the original paper
Source printed “experimental mass of ${}^{12}_{6}$ C as 12u, the mass defect of ${}^{12}_{6}$ C atom”; corrected to the intended “ ${}^{12}_{6}$ C nucleus” in both places (the data give proton, not hydrogen-atom, masses and no electron mass; the key 89.03 is the nuclear defect).
Q20 · MCQ · Semiconductor ElectronicsOpen
In a semiconductor p-n diode, the doping concentrations on p-side and n-side are $10^{15}$ atoms/ $\mathrm{cm^3}$ and $10^{18}$ atoms/ $\mathrm{cm^3}$ , respectively. Which one of the following statements is true?
1. (1)Widths of depletion region on either side of the interface are equal
2. (2)The depletion region width is more on p-side compared to that in n-side
3. (3)The depletion region width is more on n-side compared to that in p-side
4. (4)No depletion region forms because of unequal doping concentrations on p and n-sides
We corrected a printing error in the original paper
Source printed “Which one of the following statement is true?”.
Q21 · Numerical · Mechanical Properties of SolidsOpen
A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is $600\times10^{-6}\ \mathrm{m^3}$ . The elastic potential energy stored in the wire in stretched condition would be J.
(Given Young modulus of copper $= 1.1\times10^{11}\ \mathrm{N/m^2}$ )
Q22 · Numerical · Thermal Properties of MatterOpen
The heat extracted out of x gram of water initially at $50^\circ$ C to cool it down to $0^\circ$ C is sufficient to evaporate $(1000 - x)$ gram of water also initially at $50^\circ$ C. The value of x (closest integer) is.
(Take latent heat of water 2256 kJ/kg, specific heat capacity of water 4200 J/kg. K)
We corrected a printing error in the original paper
Source printed the latent heat as “2256 kJ/kg. K”.
Q23 · Numerical · Alternating CurrentOpen
A series LCR circuit with $R = 20\ \Omega$ , $L = 1.6$ H and $C = 40\ \mu\mathrm{F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is $\Omega$ .
Q24 · Numerical · Current ElectricityOpen
When an external resistance of $5\ \Omega$ is connected across terminals of a cell, a current of 0.25 A flows through it. When the $5\ \Omega$ resistor is replaced by a $2\ \Omega$ resistor, a current of 0.5 A flows through it. The internal resistance of the cell is $\Omega$ .
Q25 · Numerical · Electromagnetic InductionOpen
A circular loop of radius 20 cm and resistance $2\ \Omega$ is placed in a time varying magnetic field $\vec B = (2t^2 + 2t + 3)$ T. At $t = 0$ , for the plane of the loop being perpendicular to the magnetic field, the induced current in the loop at $t = 3$ s is $\dfrac{\alpha}{50}$ A. The value of $\alpha$ is (Take $\pi = 22/7$ )
We corrected a printing error in the original paper
Source printed “perpendicular to the magnetic field and, the induced current”.

Chemistry

Q1 · MCQ · Some Basic ConceptsOpen
What volume of hydrogen gas at STP would be liberated by action of 50 mL of $\ce{H2SO4}$ of 50% purity (density $= 1.3$ g mL $^{-1}$ ) on 20 g of zinc ?
Given : Molar mass of H, O, S, Zn are 1, 16, 32, 65 g mol $^{-1}$ respectively.
1. (1)5.824 L
2. (2)7.428 L
3. (3)6.892 L
4. (4)8.375 L
Q2 · MCQ · Structure of AtomOpen
Which of the following statement(s) is/are true ?
- (A)If two orbitals have the same value of $(n + l)$ , the orbital with lower value of $n$ will have lower energy.
- (B)Energies of the orbitals in the same subshell increase with increase in atomic number.
- (C)The size of 2p $_x$ orbital is less than the size of 3p $_x$ orbital.
- (D)Among 5f, 6s, 4d, 5p and 5d orbitals, none of the orbitals have 2 radial nodes.
Choose the correct answer from the options given below :
1. (1)A, B and C only
2. (2)A and C only
3. (3)C and D only
4. (4)A only
Q3 · MCQ · Chemical BondingOpen
The covalent radii of atoms A and B are $r_\mathrm{A}$ and $r_\mathrm{B}$ , respectively. The covalent bond length and total length of AB molecule are respectively :
1. (1) $(r_\mathrm{A} + r_\mathrm{B})$ , $2(r_\mathrm{A} + r_\mathrm{B})$
2. (2) $\dfrac{1}{2}(r_\mathrm{A} + r_\mathrm{B})$ , $(r_\mathrm{A} + r_\mathrm{B})$
3. (3) $(r_\mathrm{A} + r_\mathrm{B})$ , $(r_\mathrm{A} + r_\mathrm{B})$
4. (4) $2(r_\mathrm{A} + r_\mathrm{B})$ , $\dfrac{1}{2}(r_\mathrm{A} + r_\mathrm{B})$

Q4 · MCQ · ThermodynamicsOpen

Consider the following data for the reaction

$\ce{X2(g) + Y2(g) <=> 2XY(g)}$

at 600 K. The $\Delta_\mathrm{r}G^\ominus$ (in kJ mol $^{-1}$ ) for the reaction is:

Compound

\Delta_f H^\ominus_{600\,\mathrm{K}}

(kJ mol

^{-1}

)

S^\ominus_{600\,\mathrm{K}}

(J mol

^{-1}

^{-1}

)

XY(g)

200

\ce{X2}

(g)

140

\ce{Y2}

(g)

250

(1) $-21000$
(2) $-10$
(3) $-1000$
(4) $-9.012$

Q5 · MCQ · ThermodynamicsOpen
The correct order of molar heat capacities measured at 298 K and 1 bar is :
1. (1)Copper (s) $>$ Bromine (l) $>$ Helium (g)
2. (2)Bromine (l) $>$ Copper (s) $>$ Helium (g)
3. (3)Helium (g) $>$ Bromine (l) $>$ Copper (s)
4. (4)Helium (g) $>$ Bromine (l) $=$ Copper (s)
Q6 · MCQ · EquilibriumOpen
The reaction $\ce{A(g) <=> B(g) + C(g)}$ was initiated with the amount ‘a' of A(g). At equilibrium it is found that the amount of A(g) remaining is $(a - x)$ at a total pressure of $p$ .
The equilibrium constant $K_\mathrm{p}$ of the reaction can be calculated from the expression :
1. (1) $\dfrac{x^2}{a^2 + x^2}\times p$
2. (2) $\dfrac{x^2}{a^2 - x^2}\times p$
3. (3) $\dfrac{a + x^2}{x^2}\times p$
4. (4) $\dfrac{a - x^2}{x^2}\times p$
Q7 · MCQ · ElectrochemistryOpen
One half cell in a voltaic cell is constructed by dipping silver rod in $\ce{AgNO3}$ solution of unknown concentration, other half cell is Zn rod dipped in 1 molar solution of $\ce{ZnSO4}$ .
A voltage of 1.60 V is measured at 298 K for this cell. What is the concentration of $\ce{Ag+}$ ions used in terms of $\log x$ ( $x = [\ce{Ag+}]$ ) ?
$E^\ominus_{\mathrm{Zn^{2+}/Zn}} = -0.76$ V, $E^\ominus_{\mathrm{Ag^{+}/Ag}} = +0.80$ V,
$\dfrac{2.303RT}{F} = 0.059$ V
1. (1) $\dfrac{2}{3.9}$
2. (2) $\dfrac{4}{5.9}$
3. (3) $\dfrac{2.9}{2}$
4. (4) $\dfrac{5.9}{4}$
Q8 · MCQ · Classification & PeriodicityOpen
Given below are two statements :
Statement-I : The number of pairs among [ $\ce{Al2O3}$ , $\ce{Cr2O3}$ ], [ $\ce{Cl2O7}$ , $\ce{Mn2O7}$ ], [ $\ce{Na2O}$ , $\ce{V2O3}$ ] and [ $\ce{CO}$ , $\ce{N2O}$ ] that contain oxides of same nature (acidic, basic, neutral or amphoteric) is 4.
Statement-II : Among $\ce{Na2O}$ , $\ce{Al2O3}$ , $\ce{CO}$ and $\ce{Cl2O7}$ , the most basic and acidic oxides are $\ce{Na2O}$ and $\ce{Cl2O7}$ , respectively.
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.
Q9 · MCQ · p-Block (13–14)Open
Given below are two statements :
Statement-I : Aluminium upon reaction with NaOH forms $\ce{[Al(OH)6]^{3-}}$ ion.
Statement-II : The geometry of $\ce{ICl4-}$ , $\ce{ClO3-}$ and $\ce{IBr2-}$ is square planar, pyramidal and linear respectively.
In the light of the above statements, choose the correct answer from the options given below :
1. (1)Both Statement-I and Statement-II are true.
2. (2)Both Statement-I and Statement-II are false.
3. (3)Statement-I is true but Statement-II is false.
4. (4)Statement-I is false but Statement-II is true.
Q10 · MCQ · d- and f-BlockOpen
Given below are two statements :
Statement-I : Presence of large number of unpaired electrons in transition metal atoms results in higher enthalpies of their atomisation.
Statement-II : $d_{xy} = d_{xz} = d_{yz} < d_{x^2-y^2} = d_{z^2}$ and $d_{x^2-y^2} = d_{z^2} < d_{xy} = d_{xz} = d_{yz}$ are the d-orbital splittings in $\ce{[Fe(H2O)6]^{3+}}$ and $\ce{[Ni(Cl)4]^{2-}}$ complex ions respectively.
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)Both Statement-I and Statement-II are incorrect.
3. (3)Statement-I is correct but Statement-II is incorrect.
4. (4)Statement-I is incorrect but Statement-II is correct.
Q11 · MCQ · Coordination CompoundsOpen
Identify the correct statements from the following:
- (A) $\ce{[Fe(C2O4)3]^{3-}}$ is the most stable complex among $\ce{[Fe(OH)6]^{3-}}$ , $\ce{[Fe(C2O4)3]^{3-}}$ and $\ce{[Fe(SCN)6]^{3-}}$
- (B)The stability of $\ce{[Cu(NH3)4]^{2+}}$ is greater than that of $\ce{[Cu(en)2]^{2+}}$
- (C)The hybridization of Fe in $\ce{K4[Fe(CN)6]}$ is d $^2$ sp $^3$
- (D) $\ce{[Fe(NO2)3Cl3]^{3-}}$ exhibits linkage isomerism
- (E) $\ce{NO2-}$ and $\ce{SCN-}$ ligands are NOT ambidentate ligands
Choose the correct answer from the options given below :
1. (1)A, B, C, D and E
2. (2)B, C and D only
3. (3)A, C and D only
4. (4)A, C and E only

Q12 · MCQ · Purification & CharacterisationOpen

Match List-I with List-II.

	List-I (Purification technique)		List-II (Used to separate)
A.	Simple distillation	I.	Steam volatile compound
B.	Fractional distillation	II.	Two liquids with large difference in boiling points
C.	Steam distillation	III.	Liquid decomposing at its boiling point
D.	Distillation under reduced pressure	IV.	Two liquids with close boiling points

Choose the correct answer from the options given below :

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

We corrected a printing error in the original paper

Answer corrected; the source key is (3) — steam distillation separates steam-volatile compounds (C-I) and distillation under reduced pressure is used for liquids that decompose at their boiling point (D-III).

Q13 · MCQ · HydrocarbonsOpen
IUPAC names of some alkenes are given below :
Find out the correct stability order.
- (A)2-Methylbut-2-ene
- (B)cis-But-2-ene
- (C)2,3-Dimethylbut-2-ene
- (D)Prop-1-ene
Choose the correct answer from the options given below :
1. (1)C $>$ A $>$ B $>$ D
2. (2)C $>$ A $>$ D $>$ B
3. (3)B $>$ D $>$ A $>$ C
4. (4)A $>$ B $>$ C $>$ D
We corrected a printing error in the original paper
Source printed “IUPAC name of the some alkenes are given below”.
Q14 · MCQ · Organic Basics (GOC)Open
Identify the correct IUPAC name of hydrocarbon (x) containing three primary carbon atoms and with molar mass 72 g mol $^{-1}$ .
1. (1)1,1-Dimethylcyclopropane
2. (2)2,2-Dimethylpropane
3. (3)2-Methylbutane
4. (4)n-pentane
Q15 · MCQ · Aldehydes, Ketones & AcidsOpen
Complete the following reaction sequence and give the name of major product ‘P'.
1. (1)2-Chloropropanoic acid
2. (2)3-Chloropropanoic acid
3. (3)1-Chloropropane
4. (4)2-Chloropropane
Q16 · MCQ · Aldehydes, Ketones & AcidsOpen
Given below are two statements :
Statement-I : The condensation reaction between $\ce{CH3-CH=O}$ and under optimum pH will produce
Statement-II : The molecule, will generate $\ce{Ph-CH=O}$ in the presence of dilute acid.
In the light of the above statements, choose the correct answer from the options given below :
1. (1)Both Statement-I and Statement-II are true.
2. (2)Both Statement-I and Statement-II are false.
3. (3)Statement-I is true but Statement-II is false.
4. (4)Statement-I is false but Statement-II is true.
Q17 · MCQ · AminesOpen
Given below are two statements :
Statement-I : Heating benzamide with bromine in an ethanolic solution of sodium hydroxide will give benzylamine.
Statement-II : Nitration of aniline with $\ce{HNO3}$ / $\ce{H2SO4}$ at 288 K produces m-nitroaniline in higher amount than o-nitroaniline (pH adjusted).
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.
Q18 · MCQ · BiomoleculesOpen
Identify the incorrect statement about tertiary structure of proteins.
1. (1)They can be fibrous or globular in structure.
2. (2)The main forces that stabilize the structure are hydrogen bonding, disulphide links, van der Waals and electrostatic forces of attraction.
3. (3)The structure remains intact when exposed to pH changes.
4. (4)A linear polypeptide chain will convert to a secondary structure and then further folding of the secondary structure will convert to tertiary structure.
Q19 · MCQ · BiomoleculesOpen
Given below are two statements :
Statement-I : and are two anomers of D-(+)-glucose.
Statement-II : The open chain forms of D-glucose and D-fructose contain three similar chiral carbons at C $_3$ , C $_4$ and C $_5$ .
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.
Q20 · MCQ · Practical / Qualitative AnalysisOpen
A paper dipped in a dil. $\ce{H2SO4}$ solution of ‘X' upon treatment with $\ce{SO2}$ gas turns into green. The compound ‘X' is :
1. (1)KI-starch
2. (2) $\ce{KMnO4}$
3. (3) $\ce{Pb(CH3COO)2}$
4. (4) $\ce{K2Cr2O7}$
Q21 · Numerical · Coordination CompoundsOpen
The total number of unpaired electrons present in the d $^3$ , d $^4$ (low spin) d $^5$ (high spin), d $^6$ (high spin) and d $^7$ (low spin) octahedral complex systems is .
Q22 · Numerical · Haloalkanes & HaloarenesOpen
RMgI when treated with ice cold water liberated a gas which occupied 1.4 dm $^3$ /g at STP. The gas produced is further reacted with iodine in presence of $\ce{HIO3}$ to give compound (X). Compound (X) in presence of Na and dry ether produced compound (Y). Molar mass of compound (Y) is g mol $^{-1}$ . (Nearest integer)
Q23 · Numerical · SolutionsOpen
20 g hemoglobin in a 1 L aqueous solution (A) at 300 K is separated from pure water by semi permeable membrane. At equilibrium the height of solution in a tube dipped in a solution (A) is found to be 80.0 mm higher than the tube dipped in water.
The molar mass of hemoglobin is kg mol $^{-1}$ . (Nearest integer)
(Given : $g = 10$ m s $^{-2}$ , $R = 8.3$ kPa dm $^3$ K $^{-1}$ mol $^{-1}$ , density of solution $= 1000$ kg m $^{-3}$ )
Q24 · Numerical · ElectrochemistryOpen
At 298 K, the molar conductivity of x% (w/w) MX solution (aqueous) is 123.5 S cm $^2$ mol $^{-1}$ . The conductance of same solution is $1.9\times10^{-3}$ S. The value of x is $\times\,10^{-2}$ .
(Given : cell constant $= 1.3$ cm $^{-1}$ ; molar mass of MX is 75 g mol $^{-1}$ , density of aqueous solution of MX at 298 K is 1.0 g mL $^{-1}$ )
Q25 · Numerical · Chemical KineticsOpen
For a reaction $\ce{A -> P}$ at T K, the half life ( $t_{1/2}$ ) is plotted as a function of initial concentration $[\mathrm{A}]_0$ of A as given below :
The value of x in the given figure is s (Nearest integer)

Maths

Q1 · MCQ · Quadratic EquationsOpen
Let $\alpha, \beta$ be the roots of the equation $x^2 - x + p = 0$ and $\gamma, \delta$ be the roots of the equation $x^2 - 4x + q = 0$ ; $p, q \in \mathbb{Z}$ . If $\alpha, \beta, \gamma, \delta$ are in G.P., then $\lvert p + q\rvert$ equals:
1. (1)16
2. (2)32
3. (3)34
4. (4)38
We corrected a printing error in the original paper
Source printed “be the roots the equation $x^2 - 4x + q = 0$ ” (missing “of”).
Q2 · MCQ · Complex NumbersOpen
Let $z_1, z_2 \in \mathbb{C}$ be the distinct solutions of the equation $z^2 + 4z - (1 + 12i) = 0$ . Then $\lvert z_1\rvert^2 + \lvert z_2\rvert^2$ is equal to:
1. (1)18
2. (2)22
3. (3)29
4. (4)34
Q3 · MCQ · Matrices & DeterminantsOpen
If $f : \mathbb{N} \to \mathbb{Z}$ is defined by $f(n) = \begin{vmatrix} n & -1 & -5\\ -2n^2 & 3(2k+1) & 2k+1\\ -3n^3 & 3k(2k+1) & 3k(k+2)+1 \end{vmatrix},\ k \in \mathbb{N}, \text{ and}$ $\displaystyle\sum_{n=1}^{k} f(n) = 98$ , then $k$ is equal to:
1. (1)3
2. (2)4
3. (3)5
4. (4)6
Q4 · MCQ · Matrices & DeterminantsOpen
Let $M$ be a $3 \times 3$ matrix such that $M\begin{pmatrix}1\\0\\0\end{pmatrix} = \begin{pmatrix}1\\2\\3\end{pmatrix},\quad M\begin{pmatrix}0\\1\\0\end{pmatrix} = \begin{pmatrix}0\\1\\2\end{pmatrix} \quad\text{and}\quad M\begin{pmatrix}0\\0\\1\end{pmatrix} = \begin{pmatrix}-1\\1\\1\end{pmatrix}.$ If $M\begin{pmatrix}x\\y\\z\end{pmatrix} = \begin{pmatrix}1\\7\\11\end{pmatrix}$ , then $x + y + z$ equals:
1. (1)4
2. (2)5
3. (3)7
4. (4)11
We corrected a printing error in the original paper
Answer corrected; the source key is (3) — the columns of $M$ are $(1,2,3)$ , $(0,1,2)$ , $(-1,1,1)$ , so $x - z = 1$ , $2x + y + z = 7$ , $3x + 2y + z = 11$ give $(x,y,z) = (2,2,1)$ and $x + y + z = 5$ , option (2).
Q5 · MCQ · Sequences & SeriesOpen
If the sum of the first 10 terms of the series $\frac{1}{1 + 1^4\times4} + \frac{2}{1 + 2^4\times4} + \frac{3}{1 + 3^4\times4} + \frac{4}{1 + 4^4\times4} + \ldots$ is $\dfrac{m}{n}$ , $\gcd(m, n) = 1$ , then $m + n$ is equal to:
1. (1)256
2. (2)264
3. (3)276
4. (4)284
Q6 · MCQ · Sequences & SeriesOpen
Let $A_1, A_2, A_3, \ldots, A_{39}$ be 39 arithmetic means between the numbers 59 and 159. Then the mean of $A_{25}$ , $A_{28}$ , $A_{31}$ and $A_{36}$ is equal to:
1. (1)129
2. (2)136
3. (3)131.50
4. (4)134
Q7 · MCQ · Binomial TheoremOpen
The coefficient of $x^2$ in the expansion of $\left(2x^2 + \dfrac{1}{x}\right)^{10}$ , $x \neq 0$ , is:
1. (1)3240
2. (2)3360
3. (3)3480
4. (4)3600
We corrected a printing error in the original paper
Answer corrected; the source key is (3) — the general term is $\binom{10}{r}2^{10-r}x^{20-3r}$ , so $r = 6$ and the coefficient is $\binom{10}{6}2^4 = 3360$ , option (2).
Q8 · MCQ · ProbabilityOpen
The probabilities that players $A$ and $B$ of a team are selected for the captaincy for a tournament are 0.6 and 0.4, respectively. If $A$ is selected the captain, the probability that the team wins the tournament is 0.8 and if $B$ is selected the captain, the probability that the team wins the tournament is 0.7. Then the probability, that the team wins the tournament, is:
1. (1)0.74
2. (2)0.76
3. (3)0.72
4. (4)0.78
Q9 · MCQ · Permutations & CombinationsOpen
A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing at least two balls of each colour, is:
1. (1)4100
2. (2)4140
3. (3)4230
4. (4)4290
Q10 · MCQ · StatisticsOpen
A variable $X$ takes values $0, 0, 2, 6, 12, 20, \ldots, n(n-1)$ with frequencies ${}^{n}C_{0}$ , ${}^{n}C_{1}$ , ${}^{n}C_{2}$ , ${}^{n}C_{3}$ , ${}^{n}C_{4}$ , ${}^{n}C_{5}$ , $\ldots$ , ${}^{n}C_{n}$ , respectively. If the mean of this data is 60, then its median is:
1. (1)56
2. (2)42
3. (3)72
4. (4)90
Q11 · MCQ · CirclesOpen
Let the point $P$ be the vertex of the parabola $y = x^2 - 6x + 12$ . If a line passing through the point $P$ intersects the circle $x^2 + y^2 - 2x - 4y + 3 = 0$ at the points $R$ and $S$ , then the maximum value of $(PR + PS)^2$ is:
1. (1)10
2. (2)20
3. (3)25
4. (4)5
Q12 · MCQ · Conic SectionsOpen
Let the directrix of the parabola $P : y^2 = 8x$ , cut $x$ -axis at the point $A$ . Let $B(\alpha, \beta)$ , $\alpha > 1$ , be a point on $P$ such that the slope of $AB$ is $3/5$ . If $BC$ is a focal chord of $P$ , then six times the area of $\Delta ABC$ is:
1. (1)80
2. (2)160
3. (3)174
4. (4)192
Q13 · MCQ · Conic SectionsOpen
Let the eccentricity $e$ of a hyperbola satisfy the equation $6e^2 - 11e + 3 = 0$ . If the foci of the hyperbola are $(3, 5)$ $(3, -4)$ , then the length of its latus rectum is:
1. (1) $\dfrac{11}{3}$
2. (2) $\dfrac{17}{3}$
3. (3) $\dfrac{15}{2}$
4. (4) $\dfrac{17}{2}$
Q14 · MCQ · 3D GeometryOpen
Let a triangle $PQR$ be such that $P$ and $Q$ lie on the line $\dfrac{x+3}{8} = \dfrac{y-4}{2} = \dfrac{z+1}{2}$ and are at a distance of 6 units from $R(1, 2, 3)$ . If $(\alpha, \beta, \gamma)$ is the centroid of $\Delta PQR$ , then $\alpha + \beta + \gamma$ is equal to:
1. (1)4
2. (2)5
3. (3)6
4. (4)8
Q15 · MCQ · 3D GeometryOpen
If the distance of the point $(a, 2, 5)$ from the image of the point $(1, 2, 7)$ in the line $\dfrac{x}{1} = \dfrac{y-1}{1} = \dfrac{z-2}{2}$ is 4, then the sum of all possible values of $a$ is equal to:
1. (1)11
2. (2)9
3. (3)6
4. (4)4
Q16 · MCQ · VectorsOpen
Let $O$ be the origin, $\overrightarrow{OP} = \vec a$ and $\overrightarrow{OQ} = \vec b$ . If $R$ is the point on $\overrightarrow{OP}$ such that $\overrightarrow{OP} = 5\overrightarrow{OR}$ , and $M$ is the point such that $\overrightarrow{OQ} = 5\overrightarrow{RM}$ , then $\overrightarrow{PM}$ is equal to:
1. (1) $\dfrac15\left(\vec a - 4\vec b\right)$
2. (2) $\dfrac15\left(\vec b - 4\vec a\right)$
3. (3) $\dfrac15\left(-\vec a + 4\vec b\right)$
4. (4) $\dfrac15\left(-\vec b + 4\vec a\right)$
Q17 · MCQ · Limits, Continuity & DifferentiabilityOpen
Let $f(x) = \displaystyle\lim_{y\to0}\frac{(1 - \cos(xy))\tan(xy)}{y^3}$ . Then the number of solutions of the equation $f(x) = \sin x$ , $x \in \mathbb{R}$ is:
1. (1)0
2. (2)2
3. (3)3
4. (4)1
Q18 · MCQ · Definite IntegrationOpen
Let $\left(2^{1-a} + 2^{1+a}\right)$ , $f(a)$ , $\left(3^{a} + 3^{-a}\right)$ be a A.P. and $\alpha$ be the minimum value of $f(a)$ . Then the value of the integral $\int_{\log_e(\alpha-1)}^{\log_e(\alpha)} \frac{dx}{\left(e^{2x} - e^{-2x}\right)}$ is:
1. (1) $\dfrac12\log_e\left(\dfrac43\right)$
2. (2) $\dfrac14\log_e\left(\dfrac43\right)$
3. (3) $\dfrac12\log_e\left(\dfrac85\right)$
4. (4) $\dfrac14\log_e\left(\dfrac85\right)$
Q19 · MCQ · Differential EquationsOpen
Let $f : [1, \infty) \to \mathbb{R}$ be a differentiable function defined as $f(x) = \int_1^x f(t)\,dt + (1 - x)(\log_e x - 1) + e.$ Then the value of $f(f(1))$ is:
1. (1) $(1 + e^{e})$
2. (2) $(1 + e)$
3. (3) $(1 + e + e^{e})$
4. (4) $1 + 2e$
We corrected a printing error in the original paper
Source printed “Then the value fo $f(f(1))$ ”.
Q20 · MCQ · Differential EquationsOpen
Let $f(x)$ and $g(x)$ be twice differentiable functions satisfying $f''(x) = g''(x)$ for all $x \in \mathbb{R}$ , $f'(1) = 2g'(1) = 4$ and $g(2) = 3f(2) = 9$ . Then $f(25) - g(25)$ is equal to:
1. (1)20
2. (2)40
3. (3) $-20$
4. (4) $-40$
Q21 · Numerical · Sets, Relations & FunctionsOpen
Let $A = \{1, 4, 7\}$ and $B = \{2, 3, 8\}$ . Then the number of elements, in the relation $R = \{((a_1, b_1), (a_2, b_2)) \in ((A \times B) \times (A \times B)) : a_1 + b_2 \text{ divides } a_2 + b_1\}$ is .
Q22 · Numerical · Straight LinesOpen
From the point $(-1, -1)$ , two rays are sent making angles of $45^\circ$ with the line $x + y = 0$ . These rays get reflected from the mirror $x + 2y = 1$ . If the equations of the reflected rays are $ax + by = 9$ and $cx + dy = 7$ , $a, b, c, d \in \mathbb{Z}$ , then the value of $ad + bc$ is .
Q23 · Numerical · TrigonometryOpen
If $S = \left\{\theta \in [-\pi, \pi] : \cos\theta\cos\dfrac{5\theta}{2} = \cos7\theta\cos\dfrac{7\theta}{2}\right\}$ , then $n(S)$ is equal to .
Q24 · Numerical · Area under CurvesOpen
Let $f : \mathbb{R} \to \mathbb{R}$ be a function such that $f(x) + 3f\left(\dfrac{\pi}{2} - x\right) = \sin x$ , $x \in \mathbb{R}$ . Let maximum value of $f$ on $\mathbb{R}$ be $\alpha$ . If the area of the region bounded by the curves $g(x) = x^2$ and $h(x) = \beta x^3$ , $\beta > 0$ , is $\alpha^2$ , then $30\beta^3$ is equal to .
Q25 · Numerical · Differential EquationsOpen
Let $y = y(x)$ be the solution of the differential equation $(\tan x)^{1/2}\,dy = \left(\sec^3x - (\tan x)^{3/2}y\right)dx,$ $0 < x < \dfrac{\pi}{2}$ , $y\left(\dfrac{\pi}{4}\right) = \dfrac{6\sqrt2}{5}$ . If $y\left(\dfrac{\pi}{3}\right) = \dfrac45\alpha$ , then $\alpha^4$ equals .