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JEE Main 1 February 2023 Shift 2 Question Paper with Answers

1 February 2023 · January session · 89 questions

89 of the 90 questions from the JEE Main 1 February 2023 Shift 2 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

1 question is held back from this paper while we re-check the transcription or the answer key. We would rather show you nothing than show you an answer we are not confident is right.

Physics
30
Chemistry
30
Mathematics
29

Physics — JEE Main 1 February 2023 Shift 2

Q1·PhysicsSingle correct
For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure. The temperature corresponding to the point 'K' is:
  1. (A)−273°C-273°C−273°C
  2. (B)−100°C-100°C−100°C
  3. (C)−40°C-40°C−40°C
  4. (D)−373°C-373°C−373°C

Correct answer: (A)

Step-by-step solution →
Q2·PhysicsSingle correct
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: For measuring the potential difference across a resistance of 600 Ω600\,\Omega600Ω, the voltmeter with resistance 1000 Ω1000\,\Omega1000Ω will be preferred over voltmeter with resistance 4000 Ω4000\,\Omega4000Ω. Reason R: Voltmeter with higher resistance will draw smaller current than voltmeter with lower resistance. In the light of the above statements, choose the most appropriate answer from the options given below:
  1. (A)Both A and R are correct and R is the correct explanation of A
  2. (B)Both A and R are correct but R is not the correct explanation of A
  3. (C)A is not correct but R is correct
  4. (D)A is correct but R is not correct

Correct answer: (C)

Step-by-step solution →
Q3·PhysicsSingle correct
Figures (a), (b), (c) and (d) show variation of force with time. The impulse is highest in figure.
  1. (A)Fig (c)
  2. (B)Fig (b)
  3. (C)Fig (d)
  4. (D)Fig (a)

Correct answer: (B)

Step-by-step solution →
Q4·PhysicsSingle correct
An electron of a hydrogen like atom, having Z=4Z=4Z=4, jumps from 4th4^{th}4th energy state to 2nd2^{nd}2nd energy state. The energy released in this process, will be: (Given Rch=13.6Rch=13.6Rch=13.6 eV) where RRR = Rydberg constant, ccc = Speed of light in vacuum, hhh = Planck's constant
  1. (A)40.8 eV40.8\,eV40.8eV
  2. (B)3.4 eV3.4\,eV3.4eV
  3. (C)10.5 eV10.5\,eV10.5eV
  4. (D)13.6 eV13.6\,eV13.6eV

Correct answer: (A)

Step-by-step solution →
Q5·PhysicsSingle correct
The ratio of average electric energy density and total average energy density of electromagnetic wave is:
  1. (A)333
  2. (B)12\dfrac1221​
  3. (C)111
  4. (D)222

Correct answer: (B)

Step-by-step solution →
Q6·Physics·Geometrical OpticsSingle correct
Two objects A and B are placed at 151515 cm and 252525 cm from the pole in front of a concave mirror having radius of curvature 404040 cm. The distance between images formed by the mirror is _________.
  1. (A)100100100 cm
  2. (B)606060 cm
  3. (C)160160160 cm
  4. (D)404040 cm

Correct answer: (C)

Step-by-step solution →
Q7·PhysicsSingle correct
Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of resistance R would be:
  1. (A)n2Rn−1\dfrac{n^2R}{n-1}n−1n2R​
  2. (B)(n−1)Rn\dfrac{(n-1)R}{n}n(n−1)R​
  3. (C)(n−1)Rn2\dfrac{(n-1)R}{n^2}n2(n−1)R​
  4. (D)(n−1)R(2n−1)\dfrac{(n-1)R}{(2n-1)}(2n−1)(n−1)R​

Correct answer: (C)

Step-by-step solution →
Q8·PhysicsSingle correct
A Carnot engine operating between two reservoirs has efficiency 13\dfrac1331​. When the temperature of cold reservoir raised by xxx, its efficiency decreases to 16\dfrac1661​. The value of xxx, if the temperature of hot reservoir is 99°C99°C99°C, will be:
  1. (A)666666 K
  2. (B)626262 K
  3. (C)333333 K
  4. (D)16.516.516.5 K

Correct answer: (B)

Step-by-step solution →
Q9·Physics·Capacitors and DielectricsSingle correct
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one. Reason R: Capacitance of metallic spheres depend on the radii of spheres. In the light of the above statements, choose the correct answer from the options given below.
  1. (A)Both A and R are true and R is the correct explanation of A
  2. (B)Both A and R are true but R is not the correct explanation of A
  3. (C)A is true but R is false
  4. (D)A is false but R is true

Correct answer: (C)

Step-by-step solution →
Q10·PhysicsSingle correct
If the velocity of light c, universal gravitational constant G and Planck's constant h are chosen as fundamental quantities. The dimensions of mass in the new system is:
  1. (A)[h1/2c−1/2G2][h^{1/2}c^{-1/2}G^2][h1/2c−1/2G2]
  2. (B)[h−1/2c1/2G1/2][h^{-1/2}c^{1/2}G^{1/2}][h−1/2c1/2G1/2]
  3. (C)[h1/2c1/2G−1/2][h^{1/2}c^{1/2}G^{-1/2}][h1/2c1/2G−1/2]
  4. (D)[h1c1G−1][h^{1}c^{1}G^{-1}][h1c1G−1]

Correct answer: (C)

Step-by-step solution →
Q11·PhysicsSingle correct
Choose the correct statement about Zener diode:
  1. (A)It works as a voltage regulator in forward bias and behaves like simple pn junction diode in reverse bias.
  2. (B)It works as a voltage regulator only in forward bias.
  3. (C)It works as a voltage regulator in both forward and reverse bias.
  4. (D)It works as a voltage regulator in reverse bias and behaves like simple pn junction diode in forward bias.

Correct answer: (D)

Step-by-step solution →
Q12·PhysicsSingle correct
The Young's modulus of a steel wire of length 666 m and cross-sectional area 333 mm2^22, is 2×10112\times10^{11}2×1011 N/m2^22. The wire is suspended from its support on a given planet. A block of mass 444 kg is attached to the free end of the wire. The acceleration due to gravity on the planet is 14\dfrac1441​ of its value on the earth. The elongation of wire is (Take ggg on the earth =10=10=10 m/s2^22):
  1. (A)0.10.10.1 cm
  2. (B)0.10.10.1 mm
  3. (C)111 cm
  4. (D)111 mm

Correct answer: (B)

Step-by-step solution →
Q13·PhysicsSingle correct
In an amplitude modulation, a modulating signal having amplitude of X V is superimposed with a carrier signal of amplitude Y V in first case. Then, in second case, the same modulating signal is superimposed with different carrier signal of amplitude 2Y V. The ratio of modulation index in the two cases respectively will be:
  1. (A)2:12:12:1
  2. (B)1:21:21:2
  3. (C)4:14:14:1
  4. (D)1:11:11:1

Correct answer: (A)

Step-by-step solution →
Q14·PhysicsSingle correct
The threshold frequency of a metal is f0f_0f0​. When the light of frequency 2f02f_02f0​ is incident on the metal plate, the maximum velocity of photoelectrons is v1v_1v1​. When the frequency of incident radiation is increased to 5f05f_05f0​, the maximum velocity of photoelectrons emitted is v2v_2v2​. The ratio of v1v_1v1​ to v2v_2v2​ is:
  1. (A)v1v2=18\dfrac{v_1}{v_2}=\dfrac18v2​v1​​=81​
  2. (B)v1v2=14\dfrac{v_1}{v_2}=\dfrac14v2​v1​​=41​
  3. (C)v1v2=116\dfrac{v_1}{v_2}=\dfrac{1}{16}v2​v1​​=161​
  4. (D)v1v2=12\dfrac{v_1}{v_2}=\dfrac12v2​v1​​=21​

Correct answer: (D)

Step-by-step solution →
Q15·Physics·Electromagnetic InductionSingle correct
A coil is wrapped in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed: A. By changing the magnitude of the magnetic field within the coil. B. By changing the area of coil within the magnetic field. C. By changing the angle between the direction of magnetic field and the plane of the coil. D. By reversing the magnetic field direction abruptly without changing its magnitude. Choose the most appropriate answer from the options given below:
  1. (A)A and B only
  2. (B)A, B and D only
  3. (C)B, C and D only
  4. (D)A and C only

Correct answer: (C)

Step-by-step solution →
Q16·Physics·OscillationsSingle correct
Choose the correct length (L) versus square of time period (T2^22) graph for a simple pendulum executing simple harmonic motion.
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (A)

Step-by-step solution →
Q17·Physics·Magnetic Field of CurrentSingle correct
As shown in the figure, a long straight conductor with semicircular arc of radius π10\dfrac{\pi}{10}10π​ m is carrying current I=3I=3I=3 A. The magnitude of the magnetic field at the center O of the arc is: (The permeability of the vacuum =4π×10−7 NA−2=4\pi\times10^{-7}\,NA^{-2}=4π×10−7NA−2)
  1. (A)1 μT1\,\mu T1μT
  2. (B)3 μT3\,\mu T3μT
  3. (C)4 μT4\,\mu T4μT
  4. (D)6 μT6\,\mu T6μT

Correct answer: (B)

Step-by-step solution →
Q18·PhysicsSingle correct
A block of mass 101010 kg lying on a horizontal surface is pulled by a force F acting at an angle 30°30°30° with horizontal. For μs=0.25\mu_s=0.25μs​=0.25, the block will just start to move for the value of F: [Given g=10g=10g=10 ms−2^{-2}−2]
  1. (A)202020 N
  2. (B)33.333.333.3 N
  3. (C)25.225.225.2 N
  4. (D)35.735.735.7 N

Correct answer: (C)

Step-by-step solution →
Q19·PhysicsSingle correct
The escape velocities of two planets A and B are in the ratio 1:21:21:2. If the ratio of their radii respectively is 1:31:31:3, then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be:
  1. (A)32\dfrac3223​
  2. (B)23\dfrac2332​
  3. (C)34\dfrac3443​
  4. (D)43\dfrac4334​

Correct answer: (C)

Step-by-step solution →
Q20·PhysicsSingle correct
For a body projected at an angle with the horizontal from the ground, choose the correct statement.
  1. (A)The vertical component of momentum is maximum at the highest point.
  2. (B)The Kinetic Energy (K.E.) is zero at the highest point of projectile motion.
  3. (C)The horizontal component of velocity is zero at the highest point.
  4. (D)Gravitational potential energy is maximum at the highest point.

Correct answer: (D)

Step-by-step solution →
Q21·Physics·OscillationsNumerical
A block is fastened to a horizontal spring. The block is pulled to a distance x=10x=10x=10 cm from its equilibrium position (at x=0x=0x=0) on a frictionless surface from rest. The energy of the block at x=5x=5x=5 cm is 0.250.250.25 J. The spring constant of the spring is _________ Nm−1^{-1}−1.

Correct answer: 50

Step-by-step solution →
Q22·Physics·Electromagnetic InductionNumerical
A square shaped coil of area 707070 cm2^22 having 600600600 turns rotates in a magnetic field of 0.40.40.4 wbm−2^{-2}−2, about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes 500500500 revolution in a minute, the instantaneous emf when the plane of the coil is inclined at 60°60°60° with the field, will be _________ V. (Take π=227\pi=\dfrac{22}{7}π=722​)

Correct answer: 44

Step-by-step solution →
Q23·Physics·Wave OpticsNumerical
In Young's double slit experiment, a thin plate of thickness t=10 μmt=10\,\mu mt=10μm and refractive index μ=1.2\mu=1.2μ=1.2 is inserted in front of slit S1S_1S1​. The experiment is conducted in air (μ=1\mu=1μ=1) and uses a monochromatic light of wavelength λ=500\lambda=500λ=500 nm. Due to the insertion of the plate, central maxima is shifted by a distance of xβ0x\beta_0xβ0​. β0\beta_0β0​ is the fringe-width before the insertion of the plate. The value of the xxx is _________.

Correct answer: 4

Step-by-step solution →
Q24·PhysicsNumerical
Moment of inertia of a disc of mass MMM and radius 'RRR' about any of its diameter is MR24\dfrac{MR^2}{4}4MR2​. The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be x2MR2\dfrac{x}{2}MR^22x​MR2. The value of xxx is _________.

Correct answer: 3

Step-by-step solution →
Q25·PhysicsNumerical
For a train engine moving with speed of 202020 ms−1^{-1}−1, the driver must apply brakes at a distance of 500500500 m before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed x\sqrt{x}x​ ms−1^{-1}−1. The value of xxx is _________. (Assuming same retardation is produced by brakes)

Correct answer: 200

Step-by-step solution →
Q26·Physics·Electric Field and Coulomb's LawNumerical
A cubical volume is bounded by the surfaces x=0, x=a, y=0, y=a, z=0, z=ax=0,\ x=a,\ y=0,\ y=a,\ z=0,\ z=ax=0, x=a, y=0, y=a, z=0, z=a. The electric field in the region is given by E⃗=E0xi^\vec E=E_0 x\hat iE=E0​xi^, where E0=4×104 NC−1m−1E_0=4\times10^4\,NC^{-1}m^{-1}E0​=4×104NC−1m−1. If a=2a=2a=2 cm, the charge contained in the cubical volume is Q×10−14Q\times10^{-14}Q×10−14 C. The value of Q is _________. (Take ε0=9×10−12 C2/Nm2\varepsilon_0=9\times10^{-12}\,C^2/Nm^2ε0​=9×10−12C2/Nm2)

Correct answer: 288

Step-by-step solution →
Q27·PhysicsNumerical
A force F=(5+3y2)F=(5+3y^2)F=(5+3y2) acts on a particle in the yyy-direction, where F is in newton and yyy is in meter. The work done by the force during a displacement from y=2y=2y=2 m to y=5y=5y=5 m is _________ J.

Correct answer: 132

Step-by-step solution →
Q28·PhysicsNumerical
The surface of water in a water tank of cross section area 750750750 cm2^22 on the top of a house is hhh m above the tap level. The speed of water coming out through the tap of cross section area 500500500 mm2^22 is 303030 cm/s. At that instant, dhdt\dfrac{dh}{dt}dtdh​ is x×10−3x\times10^{-3}x×10−3 m/s. The value of xxx is _________.

Correct answer: 2

Step-by-step solution →
Q29·PhysicsNumerical
In the given circuit, the value of ∣I1+I2I1∣\left|\dfrac{I_1+I_2}{I_1}\right|​I1​I1​+I2​​​ is _________.

Correct answer: 2

Step-by-step solution →
Q30·PhysicsNumerical
Nucleus A having Z=17Z=17Z=17 and equal number of protons and neutrons has 1.21.21.2 MeV binding energy per nucleon. Another nucleus B of Z=12Z=12Z=12 has total 262626 nucleons and 1.81.81.8 MeV binding energy per nucleons. The difference of binding energy of B and A will be _________ MeV.

Correct answer: 6

Step-by-step solution →

Chemistry — JEE Main 1 February 2023 Shift 2

Q31·ChemistrySingle correct
For electron gain enthalpies of the elements denoted as ΔegH\Delta_{eg}HΔeg​H, the incorrect option is:
  1. (A)ΔegH(Te)<ΔegH(Po)\Delta_{eg}H(Te)<\Delta_{eg}H(Po)Δeg​H(Te)<Δeg​H(Po)
  2. (B)ΔegH(Se)<ΔegH(S)\Delta_{eg}H(Se)<\Delta_{eg}H(S)Δeg​H(Se)<Δeg​H(S)
  3. (C)ΔegH(Cl)<ΔegH(F)\Delta_{eg}H(Cl)<\Delta_{eg}H(F)Δeg​H(Cl)<Δeg​H(F)
  4. (D)ΔegH(I)<ΔegH(At)\Delta_{eg}H(I)<\Delta_{eg}H(At)Δeg​H(I)<Δeg​H(At)

Correct answer: (B)

Step-by-step solution →
Q32·ChemistrySingle correct
All structures given below are of vitamin C. Most stable of them is:
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (A)

Step-by-step solution →
Q33·ChemistrySingle correct
A straight line is given for Freundlich Adsorption (y=3x+2.505y=3x+2.505y=3x+2.505). The value of 1n\dfrac1nn1​ and log⁡K\log KlogK are respectively.
  1. (A)0.30.30.3 and 0.70330.70330.7033
  2. (B)0.30.30.3 and log⁡2.505\log 2.505log2.505
  3. (C)333 and 0.70330.70330.7033
  4. (D)333 and 2.5052.5052.505

Correct answer: (D)

Step-by-step solution →
Q34·ChemistrySingle correct
The correct order of bond enthalpy (kJmol−1^{-1}−1) is:
  1. (A)C−C>Si−Si>Sn−Sn>Ge−GeC-C>Si-Si>Sn-Sn>Ge-GeC−C>Si−Si>Sn−Sn>Ge−Ge
  2. (B)C−C>Si−Si>Ge−Ge>Sn−SnC-C>Si-Si>Ge-Ge>Sn-SnC−C>Si−Si>Ge−Ge>Sn−Sn
  3. (C)Si−Si>C−C>Sn−Sn>Ge−GeSi-Si>C-C>Sn-Sn>Ge-GeSi−Si>C−C>Sn−Sn>Ge−Ge
  4. (D)Si−Si>C−C>Ge−Ge>Sn−SnSi-Si>C-C>Ge-Ge>Sn-SnSi−Si>C−C>Ge−Ge>Sn−Sn

Correct answer: (B)

Step-by-step solution →
Q35·ChemistrySingle correct
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): An aqueous solution of KOH when used for volumetric analysis, its concentration should be checked before the use. Reason (R): On aging, KOH solution absorbs atmospheric CO2CO_2CO2​. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)Both (A) and (R) are correct but (R) is not the correct explanation of (A)
  2. (B)(A) is correct but (R) is not correct
  3. (C)Both (A) and (R) are correct and (R) is the correct explanation of (A)
  4. (D)(A) is not correct but (R) is correct

Correct answer: (C)

Step-by-step solution →
Q36·ChemistrySingle correct
O−OO-OO−O bond length in H2O2H_2O_2H2​O2​ is X‾\underline{X}X​ than the O−OO-OO−O bond length in F2O2F_2O_2F2​O2​. The O−HO-HO−H bond length in H2O2H_2O_2H2​O2​ is Y‾\underline{Y}Y​ than the O−FO-FO−F bond in F2O2F_2O_2F2​O2​. Choose the correct option for X and Y from those given below
  1. (A)X-shorter, Y-longer
  2. (B)X-shorter, Y-shorter
  3. (C)X-longer, Y-shorter
  4. (D)X-longer, Y-longer

Correct answer: (C)

Step-by-step solution →
Q37·ChemistrySingle correct
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Cu2+Cu^{2+}Cu2+ in water is more stable than Cu+Cu^{+}Cu+. Reason (R): Enthalpy of hydration for Cu2+Cu^{2+}Cu2+ is much less than that of Cu+Cu^{+}Cu+. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)Both (A) and (R) are correct and (R) is the correct explanation of (A)
  2. (B)(A) is not correct but (R) is correct
  3. (C)(A) is correct but (R) is not correct
  4. (D)Both (A) and (R) are correct but (R) is not the correct explanation of (A)

Correct answer: (A)

Step-by-step solution →
Q38·ChemistrySingle correct
'X' in the given reaction is:
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (D)

Step-by-step solution →
Q39·ChemistrySingle correct
The complex cation which has two isomers is:
  1. (A)[Co(NH3)5NO2]2+[Co(NH_3)_5NO_2]^{2+}[Co(NH3​)5​NO2​]2+
  2. (B)[Co(H2O)6]3+[Co(H_2O)_6]^{3+}[Co(H2​O)6​]3+
  3. (C)[Co(NH3)5Cl]+[Co(NH_3)_5Cl]^{+}[Co(NH3​)5​Cl]+
  4. (D)[Co(NH3)5Cl]2+[Co(NH_3)_5Cl]^{2+}[Co(NH3​)5​Cl]2+

Correct answer: (A)

Step-by-step solution →
Q40·ChemistrySingle correct
The graph which represents the following reaction is: (C6H5)3C−Cl→PyridineOH−(C6H5)3C−OH(C_6H_5)_3C-Cl\xrightarrow[Pyridine]{OH^-}(C_6H_5)_3C-OH(C6​H5​)3​C−ClOH−Pyridine​(C6​H5​)3​C−OH
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (C)

Step-by-step solution →
Q41·Chemistry·AminesSingle correct
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): α\alphaα-halocarboxylic acid on reaction with dil NH3NH_3NH3​ gives good yield of α\alphaα-amino carboxylic acid whereas the yield of amines is very low when prepared from alkyl halides. Reason (R): Amino acids exist in zwitter ion form in aqueous medium. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)Both (A) and (R) are correct and (R) is the correct explanation of (A)
  2. (B)(A) is not correct but (R) is correct
  3. (C)Both (A) and (R) are correct but (R) is not the correct explanation of (A)
  4. (D)(A) is correct but (R) is not correct

Correct answer: (A)

Step-by-step solution →
Q42·ChemistrySingle correct
The industrial activity held least responsible for global warming is:
  1. (A)Industrial production of urea
  2. (B)Electricity generation in thermal power plants
  3. (C)steel manufacturing
  4. (D)manufacturing of cement

Correct answer: (A)

Step-by-step solution →
Q43·ChemistrySingle correct
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Gypsum is used for making fireproof wall boards. Reason (R): Gypsum is unstable at high temperatures. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)Both (A) and (R) are correct and (R) is the correct explanation of (A)
  2. (B)Both (A) and (R) are correct but (R) is not the correct explanation of (A)
  3. (C)(A) is correct but (R) is not correct
  4. (D)(A) is not correct but (R) is correct

Correct answer: (B)

Step-by-step solution →
Q44·ChemistrySingle correct
The starting material for convenient preparation of deuterated hydrogen peroxide (D2O2D_2O_2D2​O2​) in laboratory is:
  1. (A)BaO
  2. (B)K2S2O8K_2S_2O_8K2​S2​O8​
  3. (C)BaO2BaO_2BaO2​
  4. (D)2-ethylanthraquinol

Correct answer: (B)

Step-by-step solution →
Q45·ChemistrySingle correct
The effect of addition of helium gas to the following reaction in equilibrium state, is: PCl5(g)⇌PCl3(g)+Cl2(g)PCl_5(g)\rightleftharpoons PCl_3(g)+Cl_2(g)PCl5​(g)⇌PCl3​(g)+Cl2​(g)
  1. (A)helium will deactivate PCl5PCl_5PCl5​ and reaction will stop.
  2. (B)the equilibrium will shift in the forward direction and more of Cl2Cl_2Cl2​ and PCl3PCl_3PCl3​ gases will be produced.
  3. (C)the equilibrium will go backward due to suppression of dissociation of PCl5PCl_5PCl5​.
  4. (D)addition of helium will not affect the equilibrium.

Correct answer: (B)

Step-by-step solution →
Q46·ChemistrySingle correct
Which element is not present in Nessler's reagent?
  1. (A)Oxygen
  2. (B)Potassium
  3. (C)Mercury
  4. (D)Iodine

Correct answer: (A)

Step-by-step solution →
Q47·ChemistrySingle correct
The structures of major products A, B and C in the following reaction sequence are:
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (D)

Step-by-step solution →
Q48·ChemistrySingle correct
In the given reaction, reagents 'X' and 'Y' respectively are:
  1. (A)(CH3CO)2O/H+(CH_3CO)_2O/H^+(CH3​CO)2​O/H+ and (CH3CO)2O/H+(CH_3CO)_2O/H^+(CH3​CO)2​O/H+
  2. (B)CH3OH/H+, ΔCH_3OH/H^+,\ \DeltaCH3​OH/H+, Δ and (CH3CO)2O/H+(CH_3CO)_2O/H^+(CH3​CO)2​O/H+
  3. (C)CH3OH/H+, ΔCH_3OH/H^+,\ \DeltaCH3​OH/H+, Δ and CH3OH/H+, ΔCH_3OH/H^+,\ \DeltaCH3​OH/H+, Δ
  4. (D)(CH3CO)2O/H+(CH_3CO)_2O/H^+(CH3​CO)2​O/H+ and CH3OH/H+, ΔCH_3OH/H^+,\ \DeltaCH3​OH/H+, Δ

Correct answer: (D)

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Q49·ChemistrySingle correct
Which one of the following sets of ions represents a collection of isoelectronic species? (Given Atomic Number: F:9, Cl:17, Na=11, Mg=12, Al=13, K=19, Ca=20, Sc=21)
  1. (A)Ba2+,Sr2+,K+,Ca2+Ba^{2+},Sr^{2+},K^+,Ca^{2+}Ba2+,Sr2+,K+,Ca2+
  2. (B)Li+,Na+,Mg2+,Ca2+Li^+,Na^+,Mg^{2+},Ca^{2+}Li+,Na+,Mg2+,Ca2+
  3. (C)N3−,O2−,F−,S2−N^{3-},O^{2-},F^-,S^{2-}N3−,O2−,F−,S2−
  4. (D)K+,Cl−,Ca2+,Sc3+K^+,Cl^-,Ca^{2+},Sc^{3+}K+,Cl−,Ca2+,Sc3+

Correct answer: (D)

Step-by-step solution →
Q50·ChemistrySingle correct
Given below are two statements: Statement I: Sulphanilic acid gives esterification test for carboxyl group. Statement II: Sulphanilic acid gives red colour in Lassaigne's test for extra element detection. In the light of the above statements, choose most appropriate answer from the options given below:
  1. (A)Statement I is incorrect but Statement II is correct
  2. (B)Both Statement I and Statement II are incorrect
  3. (C)Statement I is correct but Statement II is incorrect
  4. (D)Both Statement I and Statement II are correct

Correct answer: (A)

Step-by-step solution →
Q51·ChemistryNumerical
0.30.30.3 g of ethane undergoes combustion at 27°C27°C27°C in a bomb calorimeter. The temperature of calorimeter system (including the water) is found to rise by 0.5°C0.5°C0.5°C. The heat evolved during combustion of ethane at constant pressure is _________ kJmol−1^{-1}−1. (Nearest integer) [Given: The heat capacity of the calorimeter system is 202020 kJ K−1^{-1}−1, R=8.3R=8.3R=8.3 JK−1^{-1}−1mol−1^{-1}−1. Assume ideal gas behaviour. Atomic mass of C and H are 121212 and 111 g mol−1^{-1}−1 respectively]

Correct answer: 1006

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Q52·ChemistryNumerical
Among the following, the number of tranquilizer/s is/are _________. A. Chlorodiazepoxide B. Veronal C. Valium D. Salvarsan

Correct answer: 3

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Q53·ChemistryNumerical
Among following compounds, the number of those present in copper matte is _________. A. CuCO3CuCO_3CuCO3​ B. Cu2SCu_2SCu2​S C. Cu2OCu_2OCu2​O D. FeO

Correct answer: 1

Step-by-step solution →
Q54·ChemistryNumerical
A metal M crystallizes into two lattices: face centred cubic (fcc) and body centred cubic (bcc) with unit cell edge length of 2.02.02.0 and 2.52.52.5 Å respectively. The ratio of densities of lattices fcc to bcc for the metal M is _________ (Nearest integer)

Correct answer: 4

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Q55·ChemistryNumerical
The spin only magnetic moment of [Mn(H2O)6]2+[Mn(H_2O)_6]^{2+}[Mn(H2​O)6​]2+ complexes is _________ B.M. (Nearest integer) (Given: Atomic no. of Mn is 25)

Correct answer: 6

Step-by-step solution →
Q56·ChemistryNumerical
1×10−51\times10^{-5}1×10−5 M AgNO3AgNO_3AgNO3​ is added to 111 L of saturated solution of AgBr. The conductivity of this solution at 298298298 K is _________ ×10−9\times10^{-9}×10−9 S m−1^{-1}−1. [Given: KSP(AgBr)=4.9×10−13K_{SP}(AgBr)=4.9\times10^{-13}KSP​(AgBr)=4.9×10−13 at 298298298 K, λAg+0=6×10−3\lambda^0_{Ag^+}=6\times10^{-3}λAg+0​=6×10−3, λBr−0=8×10−3\lambda^0_{Br^-}=8\times10^{-3}λBr−0​=8×10−3, λNO3−0=7×10−3\lambda^0_{NO_3^-}=7\times10^{-3}λNO3−​0​=7×10−3 S m2^22 mol−1^{-1}−1]

Correct answer: 14

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Q57·ChemistryNumerical
20%20\%20% of acetic acid is dissociated when its 555 g is added to 500500500 mL of water. The depression in freezing point of such water is _________ ×10−3\times10^{-3}×10−3 °C. Atomic mass of C, H and O are 12,112,112,1 and 161616 a.m.u. respectively. [Given: Molal depression constant and density of water are 1.861.861.86 K kg mol−1^{-1}−1 and 111 g cm−3^{-3}−3 respectively.]

Correct answer: 372

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Q58·ChemistryNumerical
A→BA\rightarrow BA→B. Above reaction is of zero order. Half life of this reaction is 505050 min. The time taken for the concentration of A to reduce to one-fourth of its initial value is _________ (Nearest integer) min.

Correct answer: 75

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Q59·ChemistryNumerical
Testosterone, which is a steroidal hormone, has the following structure. The total number of asymmetric carbon atom/s in testosterone is _________

Correct answer: 6

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Q60·ChemistryNumerical
The molality of a 10%10\%10%(v/v) solution of di-bromine solution in CCl4CCl_4CCl4​ (carbon tetrachloride) is 'x'. x=x=x= _________ ×10−2\times10^{-2}×10−2 M. (Nearest integer) [Given: molar mass of Br2=160Br_2=160Br2​=160 g mol−1^{-1}−1, atomic mass of C =12=12=12, Cl =35.5=35.5=35.5 g mol−1^{-1}−1, density of dibromine =3.2=3.2=3.2 g cm−3^{-3}−3, density of CCl4=1.6CCl_4=1.6CCl4​=1.6 g cm−3^{-3}−3]

Correct answer: 139

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Mathematics — JEE Main 1 February 2023 Shift 2

Q61·MathematicsSingle correct
Let αx=exp⁡(xβyγ)\alpha x=\exp(x^{\beta}y^{\gamma})αx=exp(xβyγ) be the solution of the differential equation 2x2y dy−(1−xy2)dx=02x^2y\,dy-(1-xy^2)dx=02x2ydy−(1−xy2)dx=0, x>0x>0x>0, y(2)=log⁡e2y(2)=\sqrt{\log_e 2}y(2)=loge​2​. Then α+β+γ\alpha+\beta+\gammaα+β+γ equals:
  1. (A)111
  2. (B)−1-1−1
  3. (C)333
  4. (D)000

Correct answer: (A)

Step-by-step solution →
Q62·MathematicsSingle correct
The sum ∑n=1∞2n2+3n+4(2n)!\sum_{n=1}^{\infty}\dfrac{2n^2+3n+4}{(2n)!}∑n=1∞​(2n)!2n2+3n+4​ is equal to:
  1. (A)13e4+54e\dfrac{13e}{4}+\dfrac{5}{4e}413e​+4e5​
  2. (B)11e2+72e−4\dfrac{11e}{2}+\dfrac{7}{2e}-4211e​+2e7​−4
  3. (C)11e2+72e\dfrac{11e}{2}+\dfrac{7}{2e}211e​+2e7​
  4. (D)13e4+54e−4\dfrac{13e}{4}+\dfrac{5}{4e}-4413e​+4e5​−4

Correct answer: (D)

Step-by-step solution →
Q63·MathematicsSingle correct
Let a⃗=5i^−j^−3k^\vec a=5\hat i-\hat j-3\hat ka=5i^−j^​−3k^ and b⃗=i^+3j^+5k^\vec b=\hat i+3\hat j+5\hat kb=i^+3j^​+5k^ be two vectors. Then which one of the following statements is TRUE?
  1. (A)Projection of a⃗\vec aa on b⃗\vec bb is 1335\dfrac{13}{\sqrt{35}}35​13​ and the direction of the projection vector is same as of b⃗\vec bb.
  2. (B)Projection of a⃗\vec aa on b⃗\vec bb is 1335\dfrac{13}{\sqrt{35}}35​13​ and the direction of the projection vector is opposite to the direction of b⃗\vec bb.
  3. (C)Projection of a⃗\vec aa on b⃗\vec bb is −1335\dfrac{-13}{\sqrt{35}}35​−13​ and the direction of the projection vector is same as of b⃗\vec bb.
  4. (D)Projection of a⃗\vec aa on b⃗\vec bb is −1335\dfrac{-13}{\sqrt{35}}35​−13​ and the direction of the projection vector is opposite to the direction of b⃗\vec bb.

Correct answer: (D)

Step-by-step solution →
Q64·MathematicsSingle correct
Let a⃗=2i^−7j^+5k^\vec a=2\hat i-7\hat j+5\hat ka=2i^−7j^​+5k^, b⃗=i^+k^\vec b=\hat i+\hat kb=i^+k^ and c⃗=i^+2j^−3k^\vec c=\hat i+2\hat j-3\hat kc=i^+2j^​−3k^ be three given vectors. If r⃗\vec rr is a vector such that r⃗×a⃗=c⃗×a⃗\vec r\times\vec a=\vec c\times\vec ar×a=c×a and r⃗⋅b⃗=0\vec r\cdot\vec b=0r⋅b=0, then ∣r⃗∣|\vec r|∣r∣ is equal to:
  1. (A)1152\dfrac{11}{5}\sqrt2511​2​
  2. (B)9147\dfrac{\sqrt{914}}{7}7914​​
  3. (C)1172\dfrac{11}{7}\sqrt2711​2​
  4. (D)117\dfrac{11}{7}711​

Correct answer: (C)

Step-by-step solution →
Q65·MathematicsSingle correct
Let f:R−{0,1}→Rf:\mathbb{R}-\{0,1\}\to\mathbb{R}f:R−{0,1}→R be a function such that f(x)+f(11−x)=1+xf(x)+f\left(\dfrac{1}{1-x}\right)=1+xf(x)+f(1−x1​)=1+x. Then f(2)f(2)f(2) is equal to
  1. (A)92\dfrac9229​
  2. (B)74\dfrac7447​
  3. (C)94\dfrac9449​
  4. (D)73\dfrac7337​

Correct answer: (C)

Step-by-step solution →
Q66·MathematicsSingle correct
Let P(S)P(S)P(S) denote the power set of S={1,2,3,…,10}S=\{1,2,3,\ldots,10\}S={1,2,3,…,10}. Define the relations R1R_1R1​ and R2R_2R2​ on P(S)P(S)P(S) as AR1BAR_1BAR1​B if (A∩Bc)∪(B∩Ac)=∅(A\cap B^c)\cup(B\cap A^c)=\varnothing(A∩Bc)∪(B∩Ac)=∅ and AR2BAR_2BAR2​B if A∪Bc=B∪AcA\cup B^c=B\cup A^cA∪Bc=B∪Ac, ∀A,B∈P(S)\forall A,B\in P(S)∀A,B∈P(S). Then:
  1. (A)only R1R_1R1​ is an equivalence relation
  2. (B)only R2R_2R2​ is an equivalence relation
  3. (C)both R1R_1R1​ and R2R_2R2​ are equivalence relations
  4. (D)both R1R_1R1​ and R2R_2R2​ are not equivalence relations

Correct answer: (C)

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Q67·MathematicsSingle correct
The area of the region given by {(x,y):xy≤8, 1≤y≤x2}\{(x,y):xy\leq 8,\,1\leq y\leq x^2\}{(x,y):xy≤8,1≤y≤x2} is:
  1. (A)16log⁡e2+7316\log_e 2+\dfrac7316loge​2+37​
  2. (B)16log⁡e2−14316\log_e 2-\dfrac{14}{3}16loge​2−314​
  3. (C)8log⁡e2−1338\log_e 2-\dfrac{13}{3}8loge​2−313​
  4. (D)8log⁡e2+768\log_e 2+\dfrac768loge​2+67​

Correct answer: (B)

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Q68·MathematicsSingle correct
If A=12[13−31]A=\dfrac12\begin{bmatrix}1&\sqrt3\\-\sqrt3&1\end{bmatrix}A=21​[1−3​​3​1​], then:
  1. (A)A30+A25+A=IA^{30}+A^{25}+A=IA30+A25+A=I
  2. (B)A30=A25A^{30}=A^{25}A30=A25
  3. (C)A30+A25−A=IA^{30}+A^{25}-A=IA30+A25−A=I
  4. (D)A30−A25=2IA^{30}-A^{25}=2IA30−A25=2I

Correct answer: (C)

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Q69·MathematicsSingle correct
Which of the following statements is a tautology?
  1. (A)p∨(p∧q)p\vee(p\wedge q)p∨(p∧q)
  2. (B)(p∧(p→q))→∼q(p\wedge(p\to q))\to\sim q(p∧(p→q))→∼q
  3. (C)(p∧q)→(∼(p)→q)(p\wedge q)\to(\sim(p)\to q)(p∧q)→(∼(p)→q)
  4. (D)p→(p∧(p→q))p\to(p\wedge(p\to q))p→(p∧(p→q))

Correct answer: (C)

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Q70·MathematicsSingle correct
The sum of the absolute maximum and minimum values of the function f(x)=∣x2−5x+6∣−3x+2f(x)=|x^2-5x+6|-3x+2f(x)=∣x2−5x+6∣−3x+2 in the interval [−1,3][-1,3][−1,3] is equal to:
  1. (A)121212
  2. (B)131313
  3. (C)101010
  4. (D)242424

Correct answer: (D)

Step-by-step solution →
Q71·MathematicsSingle correct
Let the plane P pass through the intersection of the planes x+3y−z=2x+3y-z=2x+3y−z=2 and x+2y+3z=6x+2y+3z=6x+2y+3z=6 and be perpendicular to the plane 2x+y−z=02x+y-z=02x+y−z=0. If d is the distance of P from the point (−7,1,1)(-7,1,1)(−7,1,1), then d2d^2d2 is equal to:
  1. (A)25083\dfrac{250}{83}83250​
  2. (B)25082\dfrac{250}{82}82250​
  3. (C)1553\dfrac{15}{53}5315​
  4. (D)2583\dfrac{25}{83}8325​

Correct answer: (A)

Step-by-step solution →
Q72·MathematicsSingle correct
The number of integral values of k, for which one root of the equation 2x2−8x+k=02x^2-8x+k=02x2−8x+k=0 lies in the interval (1,2)(1,2)(1,2) and its other root lies in the interval (2,3)(2,3)(2,3), is:
  1. (A)333
  2. (B)000
  3. (C)222
  4. (D)111

Correct answer: (D)

Step-by-step solution →
Q73·MathematicsSingle correct
Let P(x0,y0)P(x_0,y_0)P(x0​,y0​) be the point on the hyperbola 3x2−4y2=363x^2-4y^2=363x2−4y2=36, which is nearest to the line 3x+2y=13x+2y=13x+2y=1. Then 2(y0−x0)\sqrt2(y_0-x_0)2​(y0​−x0​) is equal to:
  1. (A)−9-9−9
  2. (B)−3-3−3
  3. (C)333
  4. (D)999

Correct answer: (A)

Step-by-step solution →
Q74·MathematicsSingle correct
Two dice are thrown independently. Let A be the event that the number appeared on the 1st1^{st}1st die is less than the number appeared on the 2nd2^{nd}2nd die, B be the event that the number appeared on the 1st1^{st}1st die is even and that on the second die is odd, and C be the event that the number appeared on the 1st1^{st}1st die is odd and that on the 2nd2^{nd}2nd die is even. Then:
  1. (A)the number of favourable cases of the events A, B and C are 15, 6 and 6 respectively
  2. (B)the number of favourable cases of the event (A∪B)∩C(A\cup B)\cap C(A∪B)∩C is 6
  3. (C)B and C are independent
  4. (D)A and B are mutually exclusive

Correct answer: (B)

Step-by-step solution →
Q75·Mathematics·DifferentiabilitySingle correct
If y(x)=xx, x>0y(x)=x^x,\ x>0y(x)=xx, x>0, then y′′(2)−2y′(2)y''(2)-2y'(2)y′′(2)−2y′(2) is equal to
  1. (A)4log⁡e2+24\log_e 2+24loge​2+2
  2. (B)8log⁡e2−28\log_e 2-28loge​2−2
  3. (C)4(log⁡e2)2+24(\log_e 2)^2+24(loge​2)2+2
  4. (D)4(log⁡e2)2−24(\log_e 2)^2-24(loge​2)2−2

Correct answer: (D)

Step-by-step solution →
Q76·MathematicsSingle correct
Let S={x∈R:0<x<1 and 2tan⁡−1(1−x1+x)=cos⁡−1(1−x21+x2)}S=\left\{x\in\mathbb{R}:0<x<1\text{ and }2\tan^{-1}\left(\dfrac{1-x}{1+x}\right)=\cos^{-1}\left(\dfrac{1-x^2}{1+x^2}\right)\right\}S={x∈R:0<x<1 and 2tan−1(1+x1−x​)=cos−1(1+x21−x2​)}. If n(S)n(S)n(S) denotes the number of elements in S then:
  1. (A)n(S)=2n(S)=2n(S)=2 and only one element in S is less than 12\dfrac1221​.
  2. (B)n(S)=1n(S)=1n(S)=1 and the element in S is more than 12\dfrac1221​.
  3. (C)n(S)=0n(S)=0n(S)=0
  4. (D)n(S)=1n(S)=1n(S)=1 and the element in S is less than 12\dfrac1221​.

Correct answer: (A)

Step-by-step solution →
Q77·MathematicsSingle correct
The value of the integral ∫−π4π4x+π42−cos⁡2xdx\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\dfrac{x+\frac{\pi}{4}}{2-\cos 2x}dx∫−4π​4π​​2−cos2xx+4π​​dx is:
  1. (A)π2123\dfrac{\pi^2}{12\sqrt3}123​π2​
  2. (B)π263\dfrac{\pi^2}{6\sqrt3}63​π2​
  3. (C)π26\dfrac{\pi^2}{6}6π2​
  4. (D)π233\dfrac{\pi^2}{3\sqrt3}33​π2​

Correct answer: (B)

Step-by-step solution →
Q78·MathematicsSingle correct
For the system of linear equations αx+y+z=1\alpha x+y+z=1αx+y+z=1, x+αy+z=1x+\alpha y+z=1x+αy+z=1, x+y+αz=βx+y+\alpha z=\betax+y+αz=β, which one of the following statements is NOT correct?
  1. (A)It has infinitely many solutions if α=2\alpha=2α=2 and β=−1\beta=-1β=−1
  2. (B)It has no solution if α=−2\alpha=-2α=−2 and β=1\beta=1β=1
  3. (C)x+y+z=34x+y+z=\dfrac34x+y+z=43​ if α=2\alpha=2α=2 and β=1\beta=1β=1
  4. (D)It has infinitely many solutions if α=1\alpha=1α=1 and β=1\beta=1β=1

Correct answer: (A)

Step-by-step solution →
Q79·MathematicsSingle correct
Let 9=x1<x2<…<x79=x_1<x_2<\ldots<x_79=x1​<x2​<…<x7​ be in an A.P. with common difference d. If the standard deviation of x1,x2,…,x7x_1,x_2,\ldots,x_7x1​,x2​,…,x7​ is 4 and mean is xˉ\bar xxˉ, then xˉ+x6\bar x+x_6xˉ+x6​ is equal to:
  1. (A)2(9+87)2\left(9+\dfrac{8}{\sqrt7}\right)2(9+7​8​)
  2. (B)18(1+13)18\left(1+\dfrac{1}{\sqrt3}\right)18(1+3​1​)
  3. (C)252525
  4. (D)343434

Correct answer: (D)

Step-by-step solution →
Q80·MathematicsNumerical
Let αx+βy+γz=1\alpha x+\beta y+\gamma z=1αx+βy+γz=1 be the equation of a plane through the point (3,−2,5)(3,-2,5)(3,−2,5) and perpendicular to the line joining the points (1,2,3)(1,2,3)(1,2,3) and (−2,3,5)(-2,3,5)(−2,3,5). Then the value of αβγ\alpha\beta\gammaαβγ is equal to

Correct answer: 6

Step-by-step solution →
Q81·MathematicsNumerical
If the term without x in the expansion of (x23+αx3)22\left(x^{\frac23}+\dfrac{\alpha}{x^3}\right)^{22}(x32​+x3α​)22 is 7315, then ∣α∣|\alpha|∣α∣ is equal to

Correct answer: 1

Step-by-step solution →
Q82·MathematicsNumerical
If the x-intercept of a focal chord of the parabola y2=8x+4y+4y^2=8x+4y+4y2=8x+4y+4 is 3, then the length of this chord is equal to

Correct answer: 16

Step-by-step solution →
Q83·MathematicsNumerical
Let the sixth term in the binomial expansion of (2log⁡2(10−3x)+2(x−2)log⁡235)m\left(\sqrt{2^{\log_2(10-3^x)}}+\sqrt[5]{2^{(x-2)\log_2 3}}\right)^m(2log2​(10−3x)​+52(x−2)log2​3​)m, in the increasing powers of 2(x−2)log⁡232^{(x-2)\log_2 3}2(x−2)log2​3, be 21. If the binomial coefficients of the second, third and fourth terms in the expansion are respectively the first, third and fifth terms of an A.P., then the sum of the squares of all possible values of x is

Correct answer: 4

Step-by-step solution →
Q84·MathematicsNumerical
The point of intersection C of the plane 8x+y+2z=08x+y+2z=08x+y+2z=0 and the line joining the points A(−3,−6,1)A(-3,-6,1)A(−3,−6,1) and B(2,−4,−3)B(2,-4,-3)B(2,−4,−3) divides the line segment AB internally in the ratio k:1. If a, b, c ([a],[b],[c][a],[b],[c][a],[b],[c] are coprime) are the direction ratios of the perpendicular from the point C on the line 1−x1=y+42=z+23\dfrac{1-x}{1}=\dfrac{y+4}{2}=\dfrac{z+2}{3}11−x​=2y+4​=3z+2​, then ∣a+b+c∣|a+b+c|∣a+b+c∣ is equal to

Correct answer: 10

Step-by-step solution →
Q85·MathematicsNumerical
The line x=8x=8x=8 is the directrix of the ellipse E:x2a2+y2b2=1E:\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1E:a2x2​+b2y2​=1 with the corresponding focus (2,0)(2,0)(2,0). If the tangent to E at the point P in the first quadrant passes through the point (0,43)(0,4\sqrt3)(0,43​) and intersects the x-axis at Q, then (3PQ)2(3PQ)^2(3PQ)2 equal to

Correct answer: 39

Step-by-step solution →
Q86·MathematicsNumerical
The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6, is

Correct answer: 81

Step-by-step solution →
Q87·MathematicsNumerical
Number of integral solutions to the equation x+y+z=21x+y+z=21x+y+z=21, where x≥1x\geq 1x≥1, y≥3y\geq 3y≥3, z≥4z\geq 4z≥4, is equal to

Correct answer: 105

Step-by-step solution →
Q88·MathematicsNumerical
The sum of the common terms of the following three arithmetic progressions: 3,7,11,15,…,3993,7,11,15,\ldots,3993,7,11,15,…,399; 2,5,8,11,…,3592,5,8,11,\ldots,3592,5,8,11,…,359 and 2,7,12,17,…,1972,7,12,17,\ldots,1972,7,12,17,…,197 is equal to

Correct answer: 321

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Q89·MathematicsNumerical
If ∫−π2π25cos⁡x(1+cos⁡xcos⁡3x+cos⁡2x+cos⁡3xcos⁡3x)1+5cos⁡xdx=kπ16\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\dfrac{5^{\cos x}\left(1+\cos x\cos 3x+\cos^2 x+\cos^3 x\cos 3x\right)}{1+5^{\cos x}}dx=\dfrac{k\pi}{16}∫−2π​2π​​1+5cosx5cosx(1+cosxcos3x+cos2x+cos3xcos3x)​dx=16kπ​, then k is equal to

Correct answer: 13

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Chapters tested in this paper

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  • 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
  • Definite Integration 168/186
  • Rotational Motion 172/186
  • Redox Reactions and Electrochemistry 177/186
  • Geometrical Optics 172/186
  • Kinematics 156/186
  • Vector Algebra 173/186
  • Differential Equations 167/186
  • Probability 176/186
  • Permutations and Combinations 162/186
  • Magnetic Field of Current 147/186
  • Binomial Theorem and Its Simple Applications 158/186
  • Electromagnetic Waves 144/186
  • Application of Derivatives 139/186
  • d- and f-Block Elements 126/186
  • Thermodynamics 154/186
  • Aldehydes and Ketones 135/186
  • Equilibrium 163/186
  • Solutions 158/186
  • Laws of Motion 130/186
  • Chemical Thermodynamics 165/186
  • Units and Measurements 149/186
  • Hydrocarbons 126/186
  • Biomolecules 162/186
  • Chemical Kinetics 169/186
  • Gravitation 152/186
  • Electric Field and Coulomb's Law 133/186
  • Atomic Structure 161/186
  • Electronic Devices 145/186
  • Dual Nature of Matter and Radiation 155/186
  • Amines 133/186
  • Quadratic Equations 148/186
  • Work, Energy and Power 132/186
  • Electromagnetic Induction 120/186
  • Wave Optics 130/186
  • Area Under Curves 139/186
  • Kinetic Theory of Gases 135/186
  • Purification and Characterisation of Organic Compounds 116/186
  • Oscillations 117/186
  • Nuclei 116/186
  • Capacitors and Dielectrics 115/186
  • Atoms 112/186
  • Classification of Elements and Periodicity in Properties 113/186
  • Parabola 101/186
  • Statistics 118/186
  • Ellipse 103/186
  • Isolation of Metals 106/186
  • Differentiability 91/186
  • s-Block Elements 88/186
  • Surface Chemistry 98/186
  • Inverse Trigonometric Functions 93/186
  • Environmental Chemistry 83/186
  • Hydrogen 81/186
  • Hyperbola 77/186
  • Carboxylic Acids and Derivatives 54/186
  • Solid State 63/186
  • Principles of Qualitative Analysis 58/186
  • Chemistry in Everyday Life 60/186
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