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JEE Advanced 2023 Paper 1 Question Paper with Answers

50 questions · Physics, Chemistry & Mathematics

50 of the 51 questions from the JEE Advanced 2023 Paper 1 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

1 question is held back while we re-check the transcription or the answer key.

Physics
16
Chemistry
17
Mathematics
17

Physics — JEE Advanced 2023 Paper 1

Q1·PhysicsMultiple correct
A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a building of height 3 h from the ground, as shown in the figure. A spherical ball of mass m is released on the slide from rest at a height h from the top of the terrace. The ball leaves the slide with a velocity u⃗0=u0x^\vec{u}_0 = u_0\hat{x}u0​=u0​x^ and falls on the ground at a distance d from the building making an angle θ\thetaθ with the horizontal. It bounces off with a velocity v⃗\vec{v}v and reaches a maximum height h1h_1h1​. The acceleration due to gravity is g and the coefficient of restitution of the ground is 1/31/\sqrt{3}1/3​. Which of the following statement(s) is(are) correct?
  1. (A)u⃗0=2gh x^\vec{u}_0 = \sqrt{2gh}\,\hat{x}u0​=2gh​x^
  2. (B)v⃗=2gh (x^−z^)\vec{v} = \sqrt{2gh}\,(\hat{x} - \hat{z})v=2gh​(x^−z^)
  3. (C)θ=600\theta = 60^0θ=600
  4. (D)d/h1=23d/h_1 = 2\sqrt{3}d/h1​=23​

Correct answer: (A), (C), (D)

Step-by-step solution →
Q2·PhysicsMultiple correct
A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is δ=60∘\delta = 60^\circδ=60∘ (see Figure-1). The angle of minimum deviation for red light from the same prism is δmin=30∘\delta_{min} = 30^\circδmin​=30∘ (see Figure-2). The refractive index of the prism material for blue light is 3\sqrt{3}3​. Which of the following statement(s) is(are) correct?
  1. (A)The blue light is polarized in the plane of incidence.
  2. (B)The angle of the prism is 45∘45^\circ45∘.
  3. (C)The refractive index of the material of the prism for red light is 2\sqrt{2}2​.
  4. (D)The angle of refraction for blue light in air at the exit plane of the prism is 60060^0600

Correct answer: (A), (C), (D)

Step-by-step solution →
Q3·PhysicsMultiple correct
In a circuit shown in the figure, the capacitor C is initially uncharged and the key K is open. In this condition, a current of 1 A flows through the 1 Ω\OmegaΩ resistor. The key is closed at time t=t0t = t_0t=t0​. Which of the following statement(s) is(are) correct? [Given: e−1=0.36e^{-1} = 0.36e−1=0.36]
  1. (A)The value of the resistance of R is 3 Ω\OmegaΩ
  2. (B)For t<t0t < t_0t<t0​, the value of current I1I_1I1​ is 2A
  3. (C)At t=t0+7.2 μst = t_0 + 7.2\ \mu st=t0​+7.2 μs, the current in the capacitor is 0.6 A.
  4. (D)For t→∞t \rightarrow \inftyt→∞, the charge on the capacitor is 12 μC\mu CμC.

Correct answer: (A), (B), (C), (D)

Step-by-step solution →
Q4·PhysicsSingle correct
A bar of mass M = 1.00 kg and length L = 0.20 m is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. A small mass m = 0.10 kg is moving on the same horizontal surface with 5.00 ms−1ms^{-1}ms−1 speed on a path perpendicular to the bar. It hits the bar at a distance L/2 from the pivoted end and returns back on the same path with speed v. After this elastic collision, the bar rotates with an angular velocity ω\omegaω. Which of the following statement is correct?
  1. (A)ω=6.98\omega = 6.98ω=6.98 rad s−1s^{-1}s−1 and v=4.30 ms−1v = 4.30\ ms^{-1}v=4.30 ms−1
  2. (B)ω=3.75\omega = 3.75ω=3.75 rad s−1s^{-1}s−1 and v=4.30 ms−1v = 4.30\ ms^{-1}v=4.30 ms−1
  3. (C)ω=3.75\omega = 3.75ω=3.75 rad s−1s^{-1}s−1 and v=10.0 ms−1v = 10.0\ ms^{-1}v=10.0 ms−1
  4. (D)ω=6.80\omega = 6.80ω=6.80 rad s−1s^{-1}s−1 and v=4.10 ms−1v = 4.10\ ms^{-1}v=4.10 ms−1

Correct answer: (A)

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Q5·PhysicsSingle correct
A container has a base of 50 cm ×\times× 5 cm and height 50 cm, as shown in the figure. It has two parallel electrically conducting walls each of area 50 cm ×\times× 50 cm. The remaining walls of the container are thin and non-conducting. The container is being filled with a liquid of dielectric constant 3 at a uniform rate of 250 cm3 s−1cm^3\ s^{-1}cm3 s−1. What is the value of the capacitance of the container after 10 seconds? [Given: Permittivity of free space ε0=9×10−12 C2N−1m−2\varepsilon_0 = 9 \times 10^{-12}\ C^2N^{-1}m^{-2}ε0​=9×10−12 C2N−1m−2 , the effects of the non-conducting walls on the capacitance are negligible
  1. (A)27 pF
  2. (B)63 pF
  3. (C)81 pF
  4. (D)135 pF

Correct answer: (B)

Step-by-step solution →
Q6·PhysicsSingle correct
One mole of an ideal gas expands adiabatically from an initial state (TA,V0)(T_A, V_0)(TA​,V0​) to final state (Tf,5V0)(T_f, 5V_0)(Tf​,5V0​). Another mole of the same gas expands isothermally from a different initial state (TB,V0)(T_B, V_0)(TB​,V0​) to the same final state (Tf,5V0)(T_f, 5V_0)(Tf​,5V0​). The ratio of the specific heats at constant pressure and constant volume of this ideal gas is γ\gammaγ. What is the ratio TA/TBT_A/T_BTA​/TB​?
  1. (A)5γ−15^{\gamma-1}5γ−1
  2. (B)51−γ5^{1-\gamma}51−γ
  3. (C)5γ5^{\gamma}5γ
  4. (D)51+γ5^{1+\gamma}51+γ

Correct answer: (A)

Step-by-step solution →
Q7·PhysicsSingle correct
Two satellites P and Q are moving in different circular orbits around the Earth (radius R). The heights of P and Q from the Earth surface are hPh_PhP​ and hQh_QhQ​, respectively, where hP=R/3h_P = R/3hP​=R/3. The accelerations of P and Q due to Earth's gravity are gPg_PgP​ and gQg_QgQ​, respectively. If gP/gQ=36/25g_P/g_Q = 36/25gP​/gQ​=36/25, what is the value of hQh_QhQ​?
  1. (A)3R/5
  2. (B)R/6
  3. (C)6R/5
  4. (D)5R/6

Correct answer: (A)

Step-by-step solution →
Q8·PhysicsNumerical
A Hydrogen-like atom has atomic number Z. Photons emitted in the electronic transitions from level n = 4 to level n = 3 in these atoms are used to perform photoelectric effect experiment on a target metal. The maximum kinetic energy of the photoelectrons generated is 1. 95 eV. If the photoelectric threshold wavelength for the target metal is 310 nm, the value of Z is ________. [Given: hc = 1240 eV-nm and Rhc = 13.6 eV, where R is the Rydberg constant, h is the Planck's constant and c is the speed of light in vacuum]

Correct answer: 3

Step-by-step solution →
Q9·PhysicsNumerical
In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is 10 ±\pm± 0.1 cm and the distance of its real image from the lens is 20 ±\pm± 0.2 cm. The error in the determination of focal length of the lens is n%. The value of n is ________.

Correct answer: 1

Step-by-step solution →
Q10·PhysicsNumerical
A closed container contains a homogeneous mixture of two moles of an ideal monatomic gas (γ=5/3\gamma = 5/3γ=5/3) and one mole of an ideal diatomic gas (γ=7/5\gamma = 7/5γ=7/5). Here, γ\gammaγ is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mixture does a work of 66 Joule when heated at constant pressure. The change in its internal energy is ________ Joule.

Correct answer: 121

Step-by-step solution →
Q11·PhysicsNumerical
A person of height 1.6 m is walking away from a lamp post of height 4 m along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is 60 cm s−1s^{-1}s−1, The speed of the tip of the person's shadow on the ground with respect to the person is ________ cm s−1s^{-1}s−1

Correct answer: 40

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Q12·PhysicsNumerical
Two point-like objects of masses 20 gm and 30 gm are fixed at the two ends of a rigid massless rod of length 10 cm. This system is suspended vertically from a rigid ceiling using a thin wire attached to its center of mass, as shown in the figure. The resulting torsional pendulum undergoes small oscillations. The torsional constant of the wire is 1.2×10−81.2 \times 10^{-8}1.2×10−8 Nm rad−1rad^{-1}rad−1 . The angular frequency of the oscillations in n×10−3n \times 10^{-3}n×10−3 rad s−1s^{-1}s−1 . The value of n is ______

Correct answer: 10

Step-by-step solution →
Q13·PhysicsSingle correct
List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option.
List-IList-II
P.92238U→91234Pa{}^{238}_{92}\mathrm{U} \rightarrow {}^{234}_{91}\mathrm{Pa}92238​U→91234​Pa1.one α\alphaα particle and one β+\beta^{+}β+ particle
Q.82214Pb→82210Pb{}^{214}_{82}\mathrm{Pb} \rightarrow {}^{210}_{82}\mathrm{Pb}82214​Pb→82210​Pb2.three β−\beta^{-}β− particles and one α\alphaα particle
R.81210Tℓ→82206Pb{}^{210}_{81}\mathrm{T}\ell \rightarrow {}^{206}_{82}\mathrm{Pb}81210​Tℓ→82206​Pb3.two β−\beta^{-}β− particles and one α\alphaα particle
S.91228Pa→88224Ra{}^{228}_{91}\mathrm{Pa} \rightarrow {}^{224}_{88}\mathrm{Ra}91228​Pa→88224​Ra4.one α\alphaα particle and one β−\beta^{-}β− particle
5.one α\alphaα particle and two β+\beta^{+}β+ particles
  1. (A)P →\rightarrow→ 4, Q →\rightarrow→ 3, R →\rightarrow→ 2, S →\rightarrow→ 1
  2. (B)P →\rightarrow→ 4, Q →\rightarrow→ 1, R →\rightarrow→ 2, S →\rightarrow→ 5
  3. (C)P →\rightarrow→ 5, Q →\rightarrow→ 3, R →\rightarrow→ 1, S →\rightarrow→ 4
  4. (D)P →\rightarrow→ 5, Q →\rightarrow→ 1, R →\rightarrow→ 3, S →\rightarrow→ 2

Correct answer: (A)

Step-by-step solution →
Q14·PhysicsSingle correct
Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option. [Given: Wien's constant as 2.9×10−32.9 \times 10^{-3}2.9×10−3 m-K and hce=1.24×10−6V−m\frac{hc}{e} = 1.24 \times 10^{-6} V - mehc​=1.24×10−6V−m ]
List-IList-II
P.2000 K1.The radiation at peak wavelength can lead to emission of photoelectrons from a metal of work function 4 eV
Q.3000 K2.The radiation at peak wavelength is visible to human eye.
R.5000 K3.The radiation at peak emission wavelength will result in the widest central maximum of a single slit diffraction
S.10000 K4.The power emitted per unit area is 1/16 of that emitted by a blackbody at temperature 6000 K.
5.The radiation at peak emission wavelength can be used to image human bones.
  1. (A)P →\rightarrow→ 3, Q →\rightarrow→ 5, R →\rightarrow→ 2, S →\rightarrow→ 3
  2. (B)P →\rightarrow→ 3, Q →\rightarrow→ 2, R →\rightarrow→ 4, S →\rightarrow→ 1
  3. (C)P →\rightarrow→ 3, Q →\rightarrow→ 4, R →\rightarrow→ 2, S →\rightarrow→ 1
  4. (D)P →\rightarrow→ 1, Q →\rightarrow→ 2, R →\rightarrow→ 5, S →\rightarrow→ 3

Correct answer: (C)

Step-by-step solution →
Q15·PhysicsSingle correct
A series LCR circuit is connected to a 45 sin⁡(ωt)\sin(\omega t)sin(ωt) Volt source. The resonant angular frequency of the circuit is 10510^5105 rad s−1s^{-1}s−1 and current amplitude at resonance is I0I_0I0​. When the angular frequency of the source is ω=8×104\omega = 8 \times 10^4ω=8×104 rad s−1s^{-1}s−1, the current amplitude in the circuit is 0.05 I00.05\ I_00.05 I0​. If L = 50 mH, match each entry in List-I with an appropriate value from List-II and choose the correct option.
List-IList-II
P.I0I_0I0​ in mA1.44.4
Q.The quality factor of the circuit2.18
R.The bandwidth of the circuit in rad s−1s^{-1}s−13.400
S.The peak power dissipated at resonance in Watt.4.2250
5.500
  1. (A)P →\rightarrow→ 2, Q →\rightarrow→ 3, R →\rightarrow→ 5, S →\rightarrow→ 1
  2. (B)P →\rightarrow→ 3, Q →\rightarrow→ 1, R →\rightarrow→ 4, S →\rightarrow→ 2
  3. (C)P →\rightarrow→ 4, Q →\rightarrow→ 5, R →\rightarrow→ 3, S →\rightarrow→ 1
  4. (D)P →\rightarrow→ 4, Q →\rightarrow→ 2, R →\rightarrow→ 1, S →\rightarrow→ 5

Correct answer: (B)

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Q16·PhysicsSingle correct
A thin conducting rod MN of mass 20 gm, length 25 cm and resistance 10 Ω\OmegaΩ is held on frictionless, long, perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field B0=4B_0 = 4B0​=4 T directed perpendicular to the plane of the rod-rail arrangement. The rod is released from rest at time t = 0 and it moves down along the rails. Assume air drag is negligible. Match each quantity in List-I with an appropriate value from List-II, and choose the correct option. [Given: The acceleration due to gravity g = 10 m s−2s^{-2}s−2 and e−1=0.4e^{-1} = 0.4e−1=0.4]
List-IList-II
P.At t=0.2t = 0.2t=0.2 s, the magnitude of the induced emf in Volt1.0.07
Q.At t=0.2t = 0.2t=0.2 s, the magnitude of the magnetic force in Newton2.0.14
R.At t=0.2t = 0.2t=0.2 s, the power dissipated as heat in Watt3.1.20
S.The magnitude of terminal velocity of the rod in m s−1s^{-1}s−14.0.12
5.2.00
  1. (A)P →\rightarrow→ 5, Q →\rightarrow→ 2, R →\rightarrow→ 3, S →\rightarrow→ 1
  2. (B)P →\rightarrow→ 3, Q →\rightarrow→ 1, R →\rightarrow→ 4, S →\rightarrow→ 5
  3. (C)P →\rightarrow→ 4, Q →\rightarrow→ 3, R →\rightarrow→ 1, S →\rightarrow→ 2
  4. (D)P →\rightarrow→ 3, Q →\rightarrow→ 4, R →\rightarrow→ 2, S →\rightarrow→ 5

Correct answer: (D)

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Chemistry — JEE Advanced 2023 Paper 1

Q17·ChemistryMultiple correct
The correct statement(s) related to processes involved in the extraction of metals is (are)
  1. (A)Roasting of Malachite produces Cuprite.
  2. (B)Calcination of Calamine produces Zincite.
  3. (C)Copper pyrites is heated with silica in a reverberatory furnace to remove iron.
  4. (D)Impure silver is treated with aqueous KCN in the presence of oxygen followed by reduction with zinc metal.

Correct answer: (B), (C), (D)

Step-by-step solution →
Q18·ChemistryMultiple correct
In the following reactions, P, Q, R, and S are the major products. The correct statement(s) about P, Q, R, and S is (are)
  1. (A)Both P and Q have asymmetric carbon(s).
  2. (B)Both Q and R have asymmetric carbon(s).
  3. (C)Both P and R have asymmetric carbon(s).
  4. (D)P has asymmetric carbon(s), S does not have any asymmetric carbon.

Correct answer: (C), (D)

Step-by-step solution →
Q19·ChemistryMultiple correct
Consider the following reaction scheme and choose the correct option(s) for the major products Q, R and S.
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q20·ChemistrySingle correct
In the scheme given below, X and Y, respectively, are
  1. (A)CrO42−\mathrm{CrO_4^{2-}}CrO42−​ and Br2\mathrm{Br_2}Br2​
  2. (B)MnO42−\mathrm{MnO_4^{2-}}MnO42−​ and Cl2\mathrm{Cl_2}Cl2​
  3. (C)MnO4−\mathrm{MnO_4^{-}}MnO4−​ and Cl2\mathrm{Cl_2}Cl2​
  4. (D)MnSO4\mathrm{MnSO_4}MnSO4​ and HOCl\mathrm{HOCl}HOCl

Correct answer: (C)

Step-by-step solution →
Q21·ChemistrySingle correct
Plotting 1/Λm1/\Lambda_\mathrm{m}1/Λm​ against cΛmc\Lambda_\mathrm{m}cΛm​ for aqueous solutions of a monobasic weak acid (HX) resulted in a straight line with y-axis intercept of P and slope of S. The ratio P/S is [Λm\Lambda_\mathrm{m}Λm​ = molar conductivity Λm0\Lambda_\mathrm{m}^{0}Λm0​ = limiting molar conductivity c = molar concentration Ka\mathrm{K_a}Ka​ = dissociation constant of HX]
  1. (A)KaΛm0\mathrm{K_a}\Lambda_\mathrm{m}^{0}Ka​Λm0​
  2. (B)KaΛm0/2\mathrm{K_a}\Lambda_\mathrm{m}^{0}/2Ka​Λm0​/2
  3. (C)2KaΛm02\mathrm{K_a}\Lambda_\mathrm{m}^{0}2Ka​Λm0​
  4. (D)1/(KaΛm0)1/\left(\mathrm{K_a}\Lambda_\mathrm{m}^{0}\right)1/(Ka​Λm0​)

Correct answer: (A)

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Q22·ChemistrySingle correct
On decreasing the pH from 7 to 2, the solubility of a sparingly soluble salt (MX) of a weak acid (HX) increased from 10−4 mol L−110^{-4}\ \mathrm{mol\ L^{-1}}10−4 mol L−1 to 10−3 mol L−110^{-3}\ \mathrm{mol\ L^{-1}}10−3 mol L−1. The pKa\mathrm{pK_a}pKa​ of HX is
  1. (A)3
  2. (B)4
  3. (C)5
  4. (D)2

Correct answer: (B)

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Q23·ChemistrySingle correct
In the given reaction scheme, P is a phenyl alkyl ether, Q is an aromatic compound; R and S are the major products. The correct statement about S is
  1. (A)It primarily inhibits noradrenaline degrading enzymes.
  2. (B)It inhibits the synthesis of prostaglandin.
  3. (C)It is a narcotic drug.
  4. (D)It is ortho-acetylbenzoic acid.

Correct answer: (B)

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Q24·ChemistryNumerical
The stoichiometric reaction of 516 g of dimethyldichlorosilane with water results in a tetrameric cyclic product X in 75% yield. The weight (in g) of X obtained is___. [Use, molar mass (g mol−1\mathrm{g\ mol^{-1}}g mol−1): H = 1, C = 12, O = 16, Si = 28, Cl = 35.5]

Correct answer: 222

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Q25·ChemistryNumerical
A gas has a compressibility factor of 0.5 and a molar volume of 0.4 dm3 mol−1\mathrm{dm^3\ mol^{-1}}dm3 mol−1 at a temperature of 800 K and pressure x atm. If it shows ideal gas behaviour at the same temperature and pressure, the molar volume will be y dm3 mol−1\mathrm{dm^3\ mol^{-1}}dm3 mol−1. The value of x/y is ___. [Use: Gas constant, R = 8×10−2 L atm K−1 mol−18 \times 10^{-2}\ \mathrm{L\ atm\ K^{-1}\ mol^{-1}}8×10−2 L atm K−1 mol−1]

Correct answer: 100

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Q26·ChemistryNumerical
The plot of log⁡kf\log k_flogkf​ versus 1/T for a reversible reaction A(g)⇌P(g)\mathrm{A(g)} \rightleftharpoons \mathrm{P(g)}A(g)⇌P(g) is shown Pre-exponential factors for the forward and backward reactions are 1015 s−110^{15}\ \mathrm{s^{-1}}1015 s−1 and 1011 s−110^{11}\ \mathrm{s^{-1}}1011 s−1, respectively. If the value of log⁡K\log KlogK for the reaction at 500 K is 6, the value of ∣log⁡kb∣\left| \log k_b \right|∣logkb​∣ at 250 K is ___. [KKK = equilibrium constant of the reaction kfk_fkf​ = rate constant of forward reaction kbk_bkb​ = rate constant of backward reaction]

Correct answer: 5

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Q27·ChemistryNumerical
One mole of an ideal monoatomic gas undergoes two reversible processes (A →\rightarrow→ B and B →\rightarrow→ C) as shown in the given figure: A →\rightarrow→ B is an adiabatic process. If the total heat absorbed in the entire process (A →\rightarrow→ B and B →\rightarrow→ C) is RT2ln⁡10\mathrm{RT_2}\ln 10RT2​ln10, the value of 2log⁡V32\log \mathrm{V_3}2logV3​ is ___. [Use, molar heat capacity of the gas at constant pressure, Cp,m=52R\mathrm{C_{p,m}} = \frac{5}{2}\mathrm{R}Cp,m​=25​R ]

Correct answer: 7

Step-by-step solution →
Q28·ChemistryNumerical
In a one-litre flask, 6 moles of A undergoes the reaction A (g)⇌P (g)\mathrm{A\ (g)} \rightleftharpoons \mathrm{P\ (g)}A (g)⇌P (g). The progress of product formation at two temperatures (in Kelvin), T1\mathrm{T_1}T1​ and T2\mathrm{T_2}T2​, is shown in the figure: If T1=2T2\mathrm{T_1} = 2\mathrm{T_2}T1​=2T2​ and (ΔG2θ−ΔG1θ)=RT2ln⁡x,\left(\Delta \mathrm{G_2^{\theta}} - \Delta \mathrm{G_1^{\theta}}\right) = \mathrm{RT_2}\ln x,(ΔG2θ​−ΔG1θ​)=RT2​lnx, then the value of x is ...... [[ΔG1θ\Delta \mathrm{G_1^{\theta}}ΔG1θ​ and ΔG2θ\Delta \mathrm{G_2^{\theta}}ΔG2θ​ are standard Gibb's free energy change for the reaction at temperatures T1\mathrm{T_1}T1​ and T2\mathrm{T_2}T2​, respectively.]

Correct answer: 8

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Q29·ChemistryNumerical
The total number of sp2sp^2sp2 hybridised carbon atoms in the major product P (a non-heterocyclic compound) of the following reaction is ___.

Correct answer: 28

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Q30·ChemistrySingle correct
Match the reactions (in the given stoichiometry of the reactants) in List-I with one of their products given in List-II and choose the correct option.
List-IList-II
P.P2O3+3H2O→\mathrm{P_2O_3 + 3H_2O} \rightarrowP2​O3​+3H2​O→1.P(O)(OCH3)Cl2\mathrm{P(O)(OCH_3)Cl_2}P(O)(OCH3​)Cl2​
Q.P4+3NaOH+3H2O→\mathrm{P_4 + 3NaOH + 3H_2O} \rightarrowP4​+3NaOH+3H2​O→2.H3PO3\mathrm{H_3PO_3}H3​PO3​
R.PCl5+CH3COOH→\mathrm{PCl_5 + CH_3COOH} \rightarrowPCl5​+CH3​COOH→3.PH3\mathrm{PH_3}PH3​
S.H3PO2+2H2O+4AgNO3→\mathrm{H_3PO_2 + 2H_2O + 4AgNO_3} \rightarrowH3​PO2​+2H2​O+4AgNO3​→4.POCl3\mathrm{POCl_3}POCl3​
5.H3PO4\mathrm{H_3PO_4}H3​PO4​
  1. (A)P →\rightarrow→ 2; Q →\rightarrow→ 3; R →\rightarrow→ 1; S →\rightarrow→ 5
  2. (B)P →\rightarrow→ 3; Q →\rightarrow→ 5; R →\rightarrow→ 4; S →\rightarrow→ 2
  3. (C)P →\rightarrow→ 5; Q →\rightarrow→ 2; R →\rightarrow→ 1; S →\rightarrow→ 3
  4. (D)P →\rightarrow→ 2; Q →\rightarrow→ 3; R →\rightarrow→ 4; S →\rightarrow→ 5

Correct answer: (D)

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Q31·ChemistrySingle correct
Match the electronic configurations in List-I with appropriate metal complex ions in List-II and choose the correct option. [Atomic Number: Fe = 26, Mn = 25, Co = 27]
List-IList-II
P.t2g6eg0\mathrm{t_{2g}^{6}e_{g}^{0}}t2g6​eg0​1.[Fe(H2O)6]2+[\mathrm{Fe(H_2O)_6}]^{2+}[Fe(H2​O)6​]2+
Q.t2g3eg2\mathrm{t_{2g}^{3}e_{g}^{2}}t2g3​eg2​2.[Mn(H2O)6]2+[\mathrm{Mn(H_2O)_6}]^{2+}[Mn(H2​O)6​]2+
R.e2t23\mathrm{e^{2}t_{2}^{3}}e2t23​3.[Co(NH3)6]3+[\mathrm{Co(NH_3)_6}]^{3+}[Co(NH3​)6​]3+
S.t2g4eg2\mathrm{t_{2g}^{4}e_{g}^{2}}t2g4​eg2​4.[FeCl4]−[\mathrm{FeCl_4}]^{-}[FeCl4​]−
5.[CoCl4]2−\left[\mathrm{CoCl_4}\right]^{2-}[CoCl4​]2−
  1. (A)P →\rightarrow→ 1; Q →\rightarrow→ 4; R →\rightarrow→ 2; S →\rightarrow→ 3
  2. (B)P →\rightarrow→ 1; Q →\rightarrow→ 2; R →\rightarrow→ 4; S →\rightarrow→ 5
  3. (C)P →\rightarrow→ 3; Q →\rightarrow→ 2; R →\rightarrow→ 5; S →\rightarrow→ 1
  4. (D)P →\rightarrow→ 3; Q →\rightarrow→ 2; R →\rightarrow→ 4; S →\rightarrow→ 1

Correct answer: (D)

Step-by-step solution →
Q32·ChemistrySingle correct
Match the reactions in List-I with the features of their products in List-II and choose the correct option.
List-IList-II
P.(-)-1-Bromo-2-ethylpentane (single enantiomer) →SN2 reactionaq. NaOH\xrightarrow[\text{S}_\text{N}\text{2 reaction}]{\text{aq. NaOH}}aq. NaOHSN​2 reaction​1.Inversion of configuration
Q.(-)-2-Bromopentane (single enantiomer) →SN2 reactionaq. NaOH\xrightarrow[\text{S}_\text{N}\text{2 reaction}]{\text{aq. NaOH}}aq. NaOHSN​2 reaction​2.Retention of configuration
R.(-)-3-Bromo-3-methylhexane (single enantiomer) →SN1 reactionaq. NaOH\xrightarrow[\text{S}_\text{N}\text{1 reaction}]{\text{aq. NaOH}}aq. NaOHSN​1 reaction​3.Mixture of enantiomers
S.(single enantiomer) →SN1 reactionaq. NaOH\xrightarrow[\text{S}_\text{N}\text{1 reaction}]{\text{aq. NaOH}}aq. NaOHSN​1 reaction​4.Mixture of structural isomers
5.Mixture of diastereomers
  1. (A)P →\rightarrow→ 1; Q →\rightarrow→ 2; R →\rightarrow→ 5; S →\rightarrow→ 3
  2. (B)P →\rightarrow→ 2; Q →\rightarrow→ 1; R →\rightarrow→ 3; S →\rightarrow→ 5
  3. (C)P →\rightarrow→ 1; Q →\rightarrow→ 2; R →\rightarrow→ 5; S →\rightarrow→ 4
  4. (D)P →\rightarrow→ 2; Q →\rightarrow→ 4; R →\rightarrow→ 3; S →\rightarrow→ 5

Correct answer: (B)

Step-by-step solution →
Q33·ChemistrySingle correct
The major products obtained from the reactions in List-II are the reactants for the named reactions mentioned in List-I. Match List-I with List-II and choose the correct option.
List-IList-II
P.Etard reaction1.Acetophenone →Zn-Hg, HCl\xrightarrow{\text{Zn-Hg, HCl}}Zn-Hg, HCl​
Q.Gattermann reaction2.Toluene →(ii) SOCl2(i) KMnO4, KOH, Δ\xrightarrow[\text{(ii) SOCl}_2]{\text{(i) KMnO}_4\text{, KOH, }\Delta}(i) KMnO4​, KOH, Δ(ii) SOCl2​​
R.Gattermann-Koch reaction3.Benzene →anhyd. AlCl3CH3Cl\xrightarrow[\text{anhyd. AlCl}_3]{\text{CH}_3\text{Cl}}CH3​Clanhyd. AlCl3​​
S.Rosenmund reduction4.Aniline →273-278 KNaNO2/HCl\xrightarrow[\text{273-278 K}]{\text{NaNO}_2/\text{HCl}}NaNO2​/HCl273-278 K​
5.Phenol →Zn, Δ\xrightarrow{\text{Zn, }\Delta}Zn, Δ​
  1. (A)P →\rightarrow→ 2; Q →\rightarrow→ 4; R →\rightarrow→ 1; S →\rightarrow→ 3
  2. (B)P →\rightarrow→ 1; Q →\rightarrow→ 3; R →\rightarrow→ 5; S →\rightarrow→ 2
  3. (C)P →\rightarrow→ 3; Q →\rightarrow→ 2; R →\rightarrow→ 1; S →\rightarrow→ 4
  4. (D)P →\rightarrow→ 3; Q →\rightarrow→ 4; R →\rightarrow→ 5; S →\rightarrow→ 2

Correct answer: (D)

Step-by-step solution →

Mathematics — JEE Advanced 2023 Paper 1

Q34·MathematicsMultiple correct
Let S=(0,1)∪(1,2)∪(3,4)S = (0, 1) \cup (1, 2) \cup (3, 4)S=(0,1)∪(1,2)∪(3,4) and T={0,1,2,3}T = \{0, 1, 2, 3\}T={0,1,2,3} . Then which of the following statements is(are) true?
  1. (A)There are infinitely many functions from SSS to TTT
  2. (B)There are infinitely many strictly increasing functions from SSS to TTT
  3. (C)The number of continuous functions from SSS to TTT is at most 120
  4. (D)Every continuous function from SSS to TTT is differentiable

Correct answer: (A), (C), (D)

Step-by-step solution →
Q35·MathematicsMultiple correct
Let T1T_1T1​ and T2T_2T2​ be two distinct common tangents to the ellipse E:x26+y23=1E : \frac{x^2}{6} + \frac{y^2}{3} = 1E:6x2​+3y2​=1 and the parabola P:y2=12xP : y^2 = 12xP:y2=12x. Suppose that the tangent T1T_1T1​ touches PPP and EEE at the points A1A_1A1​ and A2A_2A2​, respectively and the tangent T2T_2T2​ touches PPP and EEE at the points A4A_4A4​ and A3A_3A3​ , respectively. Then which of the following statements is(are) true?
  1. (A)The area of the quadrilateral A1A2A3A4A_1A_2A_3A_4A1​A2​A3​A4​ is 35 square units
  2. (B)The area of the quadrilateral A1A2A3A4A_1A_2A_3A_4A1​A2​A3​A4​ is 36 square units
  3. (C)The tangents T1T_1T1​ and T2T_2T2​ meet the x -axis at the point (−3,0)(-3, 0)(−3,0)
  4. (D)The tangents T1T_1T1​ and T2T_2T2​ meet the x -axis at the point (−6,0)(-6, 0)(−6,0)

Correct answer: (A), (C)

Step-by-step solution →
Q36·MathematicsMultiple correct
Let f:[0,1]→[0,1]f : [0, 1] \rightarrow [0, 1]f:[0,1]→[0,1] be the function defined by f(x)=x33−x2+59x+1736f(x) = \frac{x^3}{3} - x^2 + \frac{5}{9}x + \frac{17}{36}f(x)=3x3​−x2+95​x+3617​ . Consider the square region S=[0,1]×[0,1]S = [0, 1] \times [0, 1]S=[0,1]×[0,1]. Let G={(x,y)∈S:y>f(x)}G = \{(x, y) \in S : y > f(x)\}G={(x,y)∈S:y>f(x)} be called the green region and R={(x,y)∈S:y<f(x)}R = \{(x, y) \in S : y < f(x)\}R={(x,y)∈S:y<f(x)} be called the red region. Let Lh={(x,h)∈S:x∈[0,1]}L_h = \{(x, h) \in S : x \in [0, 1]\}Lh​={(x,h)∈S:x∈[0,1]} be the horizontal line drawn at a height h∈[0,1]h \in [0, 1]h∈[0,1]. Then which of the following statements is(are) true?
  1. (A)There exists an h∈[14,23]h \in \left[\frac{1}{4}, \frac{2}{3}\right]h∈[41​,32​] such that the area of the green region above the line LhL_hLh​ equals the area of the green region below the line LhL_hLh​
  2. (B)There exists an h∈[14,23]h \in \left[\frac{1}{4}, \frac{2}{3}\right]h∈[41​,32​] such that the area of the red region above the line LhL_hLh​ equals the area of the red region below the line LhL_hLh​
  3. (C)There exists an h∈[14,23]h \in \left[\frac{1}{4}, \frac{2}{3}\right]h∈[41​,32​] such that the area of the green region above the line LhL_hLh​ equals the area of the red region below the line LhL_hLh​
  4. (D)There exists an h∈[14,23]h \in \left[\frac{1}{4}, \frac{2}{3}\right]h∈[41​,32​] such that the area of the red region above the line LhL_hLh​ equals the area of the green region below the line LhL_hLh​

Correct answer: (B), (C), (D)

Step-by-step solution →
Q37·MathematicsSingle correct
Let f:(0,1)→Rf : (0, 1) \rightarrow Rf:(0,1)→R be the function defined as f(x)=nf(x) = \sqrt{n}f(x)=n​ if x∈[1n+1,1n)x \in \left[\frac{1}{n+1}, \frac{1}{n}\right)x∈[n+11​,n1​) where n∈Nn \in Nn∈N. Let g:(0,1)→Rg : (0, 1) \rightarrow Rg:(0,1)→R be a function such that ∫x2x1−tt dt<g(x)<2x\int_{x^2}^{x} \sqrt{\frac{1-t}{t}}\,dt < g(x) < 2\sqrt{x}∫x2x​t1−t​​dt<g(x)<2x​ for all x∈(0,1)x \in (0, 1)x∈(0,1) . Then lim⁡x→0f(x)g(x)\lim_{x \rightarrow 0} f(x)g(x)limx→0​f(x)g(x)
  1. (A)does NOT exist
  2. (B)is equal to 1
  3. (C)is equal to 2
  4. (D)is equal to 3

Correct answer: (C)

Step-by-step solution →
Q38·MathematicsSingle correct
Let Q be the cube with the set of vertices {(x1,x2,x3)∈R3:x1,x2,x3∈{0,1}}\{(x_1, x_2, x_3) \in R^3 : x_1, x_2, x_3 \in \{0, 1\}\}{(x1​,x2​,x3​)∈R3:x1​,x2​,x3​∈{0,1}} . Let F be the set of all twelve lines containing the diagonals of the six faces of the cube Q. Let S be the set of all four lines containing the main diagonals of the cube Q; for instance, the line passing through the vertices (0, 0, 0) and (1, 1, 1) is in S. For lines ℓ1\ell_1ℓ1​ and ℓ2\ell_2ℓ2​, let d(ℓ1,ℓ2)d(\ell_1, \ell_2)d(ℓ1​,ℓ2​) denote the shortest distance between them. Then the maximum value of d(ℓ1,ℓ2)d(\ell_1, \ell_2)d(ℓ1​,ℓ2​) as ℓ1\ell_1ℓ1​ varies over F and ℓ2\ell_2ℓ2​ varies over S, is
  1. (A)16\frac{1}{\sqrt{6}}6​1​
  2. (B)18\frac{1}{\sqrt{8}}8​1​
  3. (C)13\frac{1}{\sqrt{3}}3​1​
  4. (D)112\frac{1}{\sqrt{12}}12​1​

Correct answer: (A)

Step-by-step solution →
Q39·MathematicsSingle correct
Let X:{(x,y)∈Z×Z:x28+y220<1 and y2<5x}X : \left\{(x, y) \in Z \times Z : \frac{x^2}{8} + \frac{y^2}{20} < 1 \text{ and } y^2 < 5x \right\}X:{(x,y)∈Z×Z:8x2​+20y2​<1 and y2<5x} . Three distinct points P, Q and R are randomly chosen from X . Then the probability that P, Q and R form a triangle whose area is a positive integer, is
  1. (A)71220\frac{71}{220}22071​
  2. (B)73220\frac{73}{220}22073​
  3. (C)79220\frac{79}{220}22079​
  4. (D)83220\frac{83}{220}22083​

Correct answer: (B)

Step-by-step solution →
Q40·MathematicsSingle correct
Let P be a point on the parabola y2=4axy^2 = 4axy2=4ax , where a>0a > 0a>0. The normal to the parabola at P meets the x-axis at a point Q. The area of the triangle PFQ, where F is the focus of the parabola, is 120. If the slope m of the normal and a are both positive integers, then the pair (a, m) is
  1. (A)(2, 3)
  2. (B)(1, 3)
  3. (C)(2, 4)
  4. (D)(3, 4)

Correct answer: (A)

Step-by-step solution →
Q41·MathematicsNumerical
Let tan⁡−1(x)∈(−π2,π2)\tan^{-1}(x) \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)tan−1(x)∈(−2π​,2π​), for x∈Rx \in Rx∈R. Then the number of real solutions of the equation 1+cos⁡(2x)=2tan⁡−1(tan⁡x)\sqrt{1 + \cos(2x)} = \sqrt{2}\tan^{-1}(\tan x)1+cos(2x)​=2​tan−1(tanx) in the set (−3π2,−π2)∪(−π2,π2)∪(π2,3π2)\left(-\frac{3\pi}{2}, -\frac{\pi}{2}\right) \cup \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \cup \left(\frac{\pi}{2}, \frac{3\pi}{2}\right)(−23π​,−2π​)∪(−2π​,2π​)∪(2π​,23π​) is equal to

Correct answer: 3

Step-by-step solution →
Q42·MathematicsNumerical
Let n≥2n \geq 2n≥2 be a natural number and f:[0,1]→Rf : [0, 1] \rightarrow Rf:[0,1]→R be the function defined by f(x)={n(1−2nx)if 0≤x≤12n2n(2nx−1)if 12n≤x≤34n4n(1−nx)if 34n≤x≤1nnn−1(nx−1)if 1n≤x≤1f(x) = \begin{cases} n(1 - 2nx) & \text{if } 0 \leq x \leq \frac{1}{2n} \\ 2n(2nx - 1) & \text{if } \frac{1}{2n} \leq x \leq \frac{3}{4n} \\ 4n(1 - nx) & \text{if } \frac{3}{4n} \leq x \leq \frac{1}{n} \\ \frac{n}{n-1}(nx - 1) & \text{if } \frac{1}{n} \leq x \leq 1 \end{cases}f(x)=⎩⎨⎧​n(1−2nx)2n(2nx−1)4n(1−nx)n−1n​(nx−1)​if 0≤x≤2n1​if 2n1​≤x≤4n3​if 4n3​≤x≤n1​if n1​≤x≤1​ If n is such that the area of the region bounded by the curves x=0x = 0x=0 , x=1x = 1x=1 , y=0y = 0y=0 and y=f(x)y = f(x)y=f(x) is 4 , then the maximum value of the function f is

Correct answer: 8

Step-by-step solution →
Q43·MathematicsNumerical
Let 75⋯5⏞r77\overbrace{5\cdots5}^{r}775⋯5r7 denote the (r + 2) digit number where the first and the last digits are 7 and the remaining r digits are 5. Consider the sum S=77+757+7557+…+75⋯5⏞987S = 77 + 757 + 7557 + \ldots + 7\overbrace{5\cdots5}^{98}7S=77+757+7557+…+75⋯5987. If S=75⋯5⏞997+mnS = \frac{7\overbrace{5\cdots5}^{99}7 + m}{n}S=n75⋯5997+m​ , where m and n are natural numbers less than 3000, then the value of m + n is

Correct answer: 1219

Step-by-step solution →
Q44·MathematicsNumerical
Let A={1967+1686 isin⁡θ7−3icos⁡θ:θ∈R}A = \left\{\frac{1967 + 1686\,i\sin\theta}{7 - 3i\cos\theta} : \theta \in R\right\}A={7−3icosθ1967+1686isinθ​:θ∈R}. If A contains exactly one positive integer n, then the value of n is

Correct answer: 281

Step-by-step solution →
Q45·MathematicsNumerical
Let P be the plane 3x+2y+3z=16\sqrt{3}x + 2y + 3z = 163​x+2y+3z=16 and let S={αi^+βj^+γk^:α2+β2+γ2=1 and the distance of (α,β,γ) from the plane P is 72}S = \left\{\alpha\hat{i} + \beta\hat{j} + \gamma\hat{k} : \alpha^2 + \beta^2 + \gamma^2 = 1 \text{ and the distance of } (\alpha, \beta, \gamma) \text{ from the plane P is } \frac{7}{2}\right\}S={αi^+βj^​+γk^:α2+β2+γ2=1 and the distance of (α,β,γ) from the plane P is 27​}. Let u⃗,v⃗\vec{u}, \vec{v}u,v and w⃗\vec{w}w be three distinct vectors in S such that ∣u⃗−v⃗∣=∣v⃗−w⃗∣=∣w⃗−u⃗∣\left|\vec{u} - \vec{v}\right| = \left|\vec{v} - \vec{w}\right| = \left|\vec{w} - \vec{u}\right|∣u−v∣=∣v−w∣=∣w−u∣. Let V be the volume of the parallelepiped determined by vectors, u⃗,v⃗\vec{u}, \vec{v}u,v and w⃗\vec{w}w . Then the value of 803V\frac{80}{\sqrt{3}}V3​80​V is

Correct answer: 45

Step-by-step solution →
Q46·MathematicsNumerical
Let a and b be two nonzero real numbers. If the coefficient of x5x^5x5 in the expansion of (ax2+7027bx)4\left(ax^2 + \frac{70}{27bx}\right)^4(ax2+27bx70​)4 is equal to the coefficient of x−5x^{-5}x−5 in the expansion of (ax−1bx2)7\left(ax - \frac{1}{bx^2}\right)^7(ax−bx21​)7 , then the value of 2b is

Correct answer: 3

Step-by-step solution →
Q47·MathematicsSingle correct
Let α\alphaα, β\betaβ and γ\gammaγ be real numbers. Consider the following system of linear equations x+2y+z=7x + 2y + z = 7x+2y+z=7 x+αz=11x + \alpha z = 11x+αz=11 2x−3y+βz=γ2x - 3y + \beta z = \gamma2x−3y+βz=γ Match each entry in List-I to the correct entries in List-II. The correct option is:
List – IList – II
P.If β=12(7α−3)\beta = \frac{1}{2}(7\alpha - 3)β=21​(7α−3) and γ=28\gamma = 28γ=28, then the system has1.A unique solution
Q.If β=12(7α−3)\beta = \frac{1}{2}(7\alpha - 3)β=21​(7α−3) and γ≠28\gamma \neq 28γ=28, then the system has2.No solution
R.If β≠12(7α−3)\beta \neq \frac{1}{2}(7\alpha - 3)β=21​(7α−3) where α=1\alpha = 1α=1 and γ≠28\gamma \neq 28γ=28, then the system has3.Infinitely many solution
S.If β≠12(7α−3)\beta \neq \frac{1}{2}(7\alpha - 3)β=21​(7α−3) where α=1\alpha = 1α=1 and γ=28\gamma = 28γ=28, then the system has4.x=11x = 11x=11, y=−2y = -2y=−2 and z=0z = 0z=0 as a solution
5.x=−15x = -15x=−15, y=4y = 4y=4 and z=0z = 0z=0 as a solution
  1. (A)(P) → (3) (Q) → (2) (R) → (1) (S) → (4)
  2. (B)(P) → (3) (Q) → (2) (R) → (5) (S) → (4)
  3. (C)(P) → (2) (Q) → (1) (R) → (4) (S) → (5)
  4. (D)(P) → (2) (Q) → (1) (R) → (1) (S) → (3)

Correct answer: (A)

Step-by-step solution →
Q48·MathematicsSingle correct
Consider the given data with frequency distribution xix_ixi​ 3 8 11 10 5 4 fif_ifi​ 5 2 3 2 4 4 Match each entry in List-I to the correct entries in List-II. The correct option is:
List – IList – II
P.The mean of the above data is1.2.5
Q.The median of the above data is2.5
R.The mean deviation about the mean of the above data is3.6
S.The mean deviation about the median of the above data is4.2.7
5.2.4
  1. (A)(P) → (3) (Q) → (2) (R) → (4) (S) → (5)
  2. (B)(P) → (3) (Q) → (2) (R) → (1) (S) → (5)
  3. (C)(P) → (2) (Q) → (3) (R) → (4) (S) → (1)
  4. (D)(P) → (3) (Q) → (3) (R) → (5) (S) → (5)

Correct answer: (A)

Step-by-step solution →
Q49·MathematicsSingle correct
Let ℓ1\ell_1ℓ1​ and ℓ2\ell_2ℓ2​ be the lines r1⃗=λ(i^+j^+k^)\vec{r_1} = \lambda\left(\hat{i} + \hat{j} + \hat{k}\right)r1​​=λ(i^+j^​+k^) and r2⃗=(j^−k^)+μ(i^+k^)\vec{r_2} = \left(\hat{j} - \hat{k}\right) + \mu\left(\hat{i} + \hat{k}\right)r2​​=(j^​−k^)+μ(i^+k^), respectively. Let X be the set of all the planes H that contain the line ℓ1\ell_1ℓ1​. For a plane H, let d(H) denote the smallest possible distance between the points of ℓ2\ell_2ℓ2​ and H . Let H0H_0H0​ be a plane in X for which d(H0)d(H_0)d(H0​) is the maximum value of d(H) as H varies over all planes in X . Match each entry in List-I to the correct entries in List-II. The correct option is:
List – IList – II
P.The value of d(H0)d(H_0)d(H0​) is1.3\sqrt{3}3​
Q.The distance of the point (0, 1, 2) from H0H_0H0​ is2.13\frac{1}{\sqrt{3}}3​1​
R.The distance of origin from H0H_0H0​ is3.0
S.The distance of origin from the point of intersection of planes y=zy = zy=z , x=1x = 1x=1 and H0H_0H0​ is4.2\sqrt{2}2​
5.12\frac{1}{\sqrt{2}}2​1​
  1. (A)(P) → (2) (Q) → (4) (R) → (5) (S) → (1)
  2. (B)(P) → (5) (Q) → (4) (R) → (3) (S) → (1)
  3. (C)(P) → (2) (Q) → (1) (R) → (3) (S) → (2)
  4. (D)(P) → (5) (Q) → (1) (R) → (4) (S) → (2)

Correct answer: (B)

Step-by-step solution →
Q50·MathematicsSingle correct
Let z be a complex number satisfying ∣z∣3+2z2+4zˉ−8=0|z|^3 + 2z^2 + 4\bar{z} - 8 = 0∣z∣3+2z2+4zˉ−8=0, where zˉ\bar{z}zˉ denotes the complex conjugate of z . Let the imaginary part of z be nonzero. Match each entry in List-I to the correct entries in List-II. The correct option is:
List – IList – II
P.∣z∣2|z|^2∣z∣2 is equal to1.12
Q.∣z−zˉ∣2\left|z - \bar{z}\right|^2∣z−zˉ∣2 is equal to2.4
R.∣z∣2+∣z+zˉ∣2|z|^2 + \left|z + \bar{z}\right|^2∣z∣2+∣z+zˉ∣2 is equal to3.8
S.∣z+1∣2\left|z + 1\right|^2∣z+1∣2 is equal to4.10
5.7
  1. (A)(P) → (1) (Q) → (3) (R) → (5) (S) → (4)
  2. (B)(P) → (2) (Q) → (1) (R) → (3) (S) → (5)
  3. (C)(P) → (2) (Q) → (4) (R) → (5) (S) → (1)
  4. (D)(P) → (2) (Q) → (3) (R) → (5) (S) → (4)

Correct answer: (B)

Step-by-step solution →

Chapters tested in this paper

  • Properties of Solids and Liquids 172/186
  • Three Dimensional Geometry 176/186
  • Matrices and Determinants 180/186
  • Coordination Compounds 176/186
  • Sets, Relations and Functions 165/186
  • Current Electricity 160/186
  • Sequence and Series 164/186
  • p-Block Elements 164/186
  • Rotational Motion 172/186
  • Redox Reactions and Electrochemistry 177/186
  • Geometrical Optics 172/186
  • Kinematics 156/186
  • Vector Algebra 173/186
  • Probability 176/186
  • Binomial Theorem and Its Simple Applications 158/186
  • Limits and Continuity 149/186
  • d- and f-Block Elements 126/186
  • Thermodynamics 154/186
  • Aldehydes and Ketones 135/186
  • Equilibrium 163/186
  • Chemical Thermodynamics 165/186
  • Units and Measurements 149/186
  • Complex Numbers 165/186
  • Chemical Kinetics 169/186
  • Gravitation 152/186
  • Amines 133/186
  • Electromagnetic Induction 120/186
  • Area Under Curves 139/186
  • Oscillations 117/186
  • Alternating Currents 108/186
  • Nuclei 116/186
  • Organic Compounds Containing Halogens 109/186
  • Capacitors and Dielectrics 115/186
  • Atoms 112/186
  • Parabola 101/186
  • Statistics 118/186
  • Ellipse 103/186
  • Isolation of Metals 106/186
  • Inverse Trigonometric Functions 93/186
  • Carboxylic Acids and Derivatives 54/186
  • Chemistry in Everyday Life 60/186
  • States of Matter: Gases and Liquids 52/186
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