**JEE MAIN 1st February 2023 Shift 2**

**Physics**

**SECTION-A**

**IMPORTANT INSTRUCTIONS:**

(1) The test is of **3 hours** duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of **Physics**, **Chemistry** and **Mathematics** having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) **Section-A:** This section contains 20 multiple choice questions which have only one correct answer. each question carries **4 marks** for correct answer and **−****1** mark for wrong answer.

(ii) **Section-B:** This section contains 10 questions. In Section-B, attempt any **five questions out of 10.** The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and **−****1 mark** for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. 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) −273°C

(2) −100°C

(3) −40°C

(4) −373°C

2. 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 600Ω, the voltmeter with resistance 1000Ω will be preferred over voltmeter with resistance 4000Ω.

**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) Both 𝐀 and 𝐑 are correct and 𝐑 is the correct explanation of 𝐀

(2) Both 𝐀 and 𝐑 are correct but 𝐑 is not the correct explanation of 𝐀

(3) 𝐀 is not correct but 𝐑 is correct

(4) 𝐀 is correct but 𝐑 is not correct

3. Figures (a), (b), (c) and (d) show variation of force with time.

The impulse is highest in figure.

(1) Fig (c)

(2) Fig (b)

(3) Fig (d)

(4) Fig (a)

4. An electron of a hydrogen like atom, having Z = 4, jumps from 4th energy state to 2nd energy state. The energy released in this process, will be :

(Given Rch=13.6eV)

Where R = Rydberg constant

c = Speed of light in vacuum

h = Planck’s constant

(1) 40.8eV

(2) 3.4eV

(3) 10.5eV

(4) 13.6eV

5. The ratio of average electric energy density and total average energy density of electromagnetic wave is :

(1) 3

(2) 1/2

(3) 1

(4) 2

6. Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is _______.

(1) 100 cm

(2) 60 cm

(3) 160 cm

(4) 40 cm

7. Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of resistance R would be:

8. A Carnot engine operating between two reservoirs has efficiency 1/3. When the temperature of cold reservoir raised by x, its efficiency decreases to 1/6. The value of x, if the temperature of hot reservoir is 99°C, will be:

(1) 66 K

(2) 62 K

(3) 33 K

(4) 16.5 K

9. 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) Both 𝐀 and 𝐑 are true and 𝐑 is the correct explanation of 𝐀

(2) 𝐀 is true but 𝐑 is false

(3) 𝐀 is false but 𝐑 is true 4.

(4) Both 𝐀 and 𝐑 are true but 𝐑 is not the correct explanation of 𝐀

10. 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) [h^{1/2}c^{−}^{1/2}G^{1}]

(2) [h^{−}^{1/2}c^{1/2}G^{1/2}]

(3) [n^{1/2}c^{1/2}G^{−}^{1/2}]

(4) [h^{1}c^{1}G^{−}^{1}]

11. Choose the correct statement about Zener diode :

(1) It works as a voltage regulator in forward bias and behaves like simple pn junction diode in reverse bias.

(2) It works as a voltage regulator only in forward bias.

(3) It works as a voltage regulator in both forward and reverse bias.

(4) It works as a voltage regulator in reverse bias and behaves like simple pn junction diode in forward bias.

12. The Young’s modulus of a steel wire of length 6 m and cross-sectional area 3 mm^{2}, is 2 × 10^{11} N/m^{2}. The wire is suspended from its support on a given planet. A block of mass 4 kg is attached to the free end of the wire. The acceleration due to gravity on the planet is 1/4 of its value on the earth. The elongation of wire is (Take g on the earth =10 m/s^{2}) :

(1) 0.1 cm

(2) 0.1 mm

(3) 1 cm

(4) 1 mm

13. 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) 2 : 1

(2) 1 : 2

(3) 4 : 1

(4) 1 : 1

14. The threshold frequency of a metal is f_{0}. When the light of frequency 2f_{0} is incident on the metal plate, the maximum velocity of photoelectrons is 𝑣_{1}. When the frequency of incident radiation is increased to 5f0, the maximum velocity of photoelectrons emitted is 𝑣_{2}. The ratio of 𝑣_{1} to 𝑣_{2} is:

15. A coil is placed 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 and B only

(2) A, B and D only

(3) A, B and C only

(4) A and C only

16. Choose the correct length (L) versus square of time period (T^{2}) graph for a simple pendulum executing simple harmonic motion.

17. As shown in the figure, a long straight conductor with semicircular arc of radius π/10 m is carrying current I=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})

(1) 1 μT

(2) 3 μT

(3) 4 μT

(4) 6 μT

18. As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle 30∘, with horizontal. For μ_{s} = 0.25, the block will just start to move for the value of F : [Given g = 10 ms^{−2}]

(1) 20 N

(2) 33.3 N

(3) 25.2 N

(4) 35.7 N

19. The escape velocities of two planets A and B are in the ratio 1:2. If the ratio of their radii respectively is 1:3, then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be :

(1) 3/2

(2) 2/3

(3) 3/4

(4) 4/3

20. For a body projected at an angle with the horizontal from the ground, choose the correct statement.

(1) The vertical component of momentum is maximum at the highest point.

(2) The Kinetic Energy (K.E.) is zero at the highest point of projectile motion.

(3) The horizontal component of velocity is zero at the highest point.

(4) Gravitational potential energy is maximum at the highest point.

**SECTION-B**

21. A block is fastened to a horizontal spring. The block is pulled to a distance x = 10 cm from its equilibrium position (at x = 0 ) on a frictionless surface from rest. The energy of the block at x = 5 cm is 0.25 J. The spring constant of the spring is ________ Nm^{−1}

22. A square shaped coil of area 70 cm^{2} having 600 turns rotates in a magnetic field of 0.4 wbm^{−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 500 revolution in a minute, the instantaneous emf when the plane of the coil is inclined at 60° with the field, will be ________ V. (Take π = 22/7)

23. As shown in the figure, in Young’s double slit experiment, a thin plate of thickness t = 10μm and refractive index μ = 1.2 is inserted infront of slit S1. The experiment is conducted in air (μ = 1) and uses a monochromatic light of wavelength λ = 500 nm. Due to the insertion of the plate, central maxima is shifted by a distance of xβ_{0}.β_{0} is the fringe-width before the insertion of the plate. The value of the x is ________.

24. Moment of inertia of a disc of mass 𝑀 and radius ‘R’ about any of its diameter is MR^{2}/4. The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, The value of x is ______.

25. For a train engine moving with speed of 20 ms^{−1}, the driver must apply brakes at a distance of 500 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 ms^{−1}. The value of x is ________. (Assuming same retardation is produced by brakes)

26. A cubical volume is bounded by the surfaces x = 0, x = a, y = 0, y = a, z = 0, z = a. The electric field in the region is given by Where E_{0} = 4 × 10^{4} NC^{−}^{1} m^{−}^{1}. If a = 2 cm, the charge contained in the cubical volume is Q × 10^{−}^{14} The value of Q is _______. (Take ϵ_{0} = 9 × 10^{−}^{12} C^{2}/Nm^{2})

27. A force F = (5 + 3y^{2}) acts on a particle in the 𝑦-direction, where F is in newton and y is in meter. The work done by the force during a displacement from y = 2 m to y = 5 m is ________ J.

28. The surface of water in a water tank of cross section area 750 cm2 on the top of a house is h m above the tap level. The speed of water coming out through the tap of cross section area 500 mm^{2} is 30 cm/s. At that instant, dh/dt is x × 10^{−}^{3} m/s. The value of x will be _______.

- In the given circuit, the value of is ________.

30. Nucleus A having Z = 17 and equal number of protons and neutrons has 1.2MeV binding energy per nucleon. Another nucleus B of Z = 12 has total 26 nucleons and 1.8MeV binding energy per nucleons. The difference of binding energy of B and A will be _______ MeV.

**Chemistry**

31. For electron gain enthalpies of the elements denoted as Δ_{eg}H, the incorrect option is :

1) Δ_{eg} H(Te) < Δ_{eg}H(PO)

(2) 2. Δ_{eg}H(Se) < Δ_{eg}H(S)

(3) Δ_{eg}H(Cl) < Δ_{eg}H(F)

(4) Δ_{eg}H(I) < Δ_{eg}H(At)

32. All structures given below are of vitamin C. Most stable of them is :

33. In figure, a straight line is given for Freundrich Adsorption (y = 3x + 2.505). The value of 1/n and log K are respectively.

(1) 0.3 and 0.7033

(2) 0.3 and log 2.505

(3) 3 and 0.7033

(4) 3 and 2.505

34. The correct order of bond enthalpy (kJmol^{−1}) is :

(1) C – C > Si – Si > Sn – Sn > Ge − Ge

(2) C − C > Si − Si > Ge − Ge > Sn − Sn

(3) Si – Si > C – C > Sn – Sn > Ge − Ge

(4) Si – Si > C – C > Ge – Ge > Sn − Sn

35. 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 CO_{2}.

In the light of the above statements, choose the correct answer from the options given below :

(1) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

(2) (A) is correct but (R) is not correct

(3) Both (A) and (R) are correct and (R) is the correct explanation of (A)

(4) (A) is not correct but (R) is correct

36. O − O bond length in H_{2}O_{2} is __X__ than the O − O bond length in F_{2}O_{2}. The O − H bond length in H_{2}O_{2} is __Y__ than that of the O − F bond in F_{2}O_{2}.

Choose the correct option for X and Y from those given below

(1) X-shorter, Y-longer

(2) X-shorter, Y-shorter

(3) X-longer, Y-shorter

(4) X-longer, Y-longer

37. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

**Assertion (A):** Cu^{2+} in water is more stable than Cu^{+}.

**Reason (R) :** Enthalpy of hydration for Cu^{2+} is much less than that of Cu^{+}.

(1) Both (A) and (R) are correct and (R) is the correct explanation of (A)

(2) (A) is not correct but (R) is correct

(3) (A) is correct but (R) is not correct

(4) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

38.

39. The complex cation which has two isomers is :

(1) [Co(NH_{3})_{5}NO_{2}]^{2+}

(2) [Co(H_{2}O)_{6}]^{3+}

(3) [Co(NH_{3})_{5}Cl]^{+}

(4) [Co(NH_{3})_{5}Cl]^{2+}

40. The graph which represents the following reaction is :

41. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

**Assertion (A) :** α-halocarboxylic acid on reaction with dil NH_{3} gives good yield of 𝛼-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) Both (A) and (R) are correct and (R) is the correct explanation of (A)

(2) (A) is not correct but (R) is correct

(3) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

(4) (A) is correct but (R) is not correct

42. The industrial activity held least responsible for global warming is :

(1) Industrial production of urea

(2) Electricity generation in thermal power plants

(3) steel manufacturing

(4) manufacturing of cement

43. 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) Both (A) and (R) are correct and (R) is the correct explanation of (A)

(2) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

(3) (A) is correct but (R) is not correct

(4) (A) is not correct but (R) is correct

44. The starting material for convenient preparation of deuterated hydrogen peroxide (D_{2}O_{2}) in laboratory is :

(1) BaO

(2) K_{2}S_{2}O_{8}

(3) BaO_{2}

(4) 2-ethylanthraquinol

45. The effect of addition of helium gas to the following reaction in equilibrium state, is :

PCl_{5}( g) ⇌ PCl_{3}( g) + Cl_{2}( g)

(1) helium will deactivate PCl_{5} and reaction will stop.

(2) the equilibrium will shift in the forward direction and more of Cl_{2} and PCl_{3} gases will be produced.

(3) the equilibrium will go backward due to suppression of dissociation of PCl_{5}.

(4) addition of helium will not affect the equilibrium.

46. Which element is not present in Nessler’s reagent ?

(1) Oxygen

(2) Potassium

(3) Mercury

(4) Iodine

47. The structures of major products A,B and C in the following reaction are sequence.

48. In a reaction,

Reagents ‘X’ and ‘Y’ respectively are:

(1) (CH_{3}CO)_{2}O/H^{+} and (CH_{3}CO)_{2}O/H^{+}

(2) CH_{3}OH/H^{+}, Δ and (CH_{3}CO)_{2}O/H^{+}

(3) CH_{3}OH/H^{+}, Δ and CH_{3}OH/H^{+}, Δ

(4) (CH_{3}CO)_{2}O/H^{+} and CH_{3}OH/H^{+}, Δ

49. 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) Ba^{2+}, Sr^{2+}, K^{+}, Ca^{2+}

(2) Li^{+}, Na^{+}, Mg^{2+}, Ca^{2+}

(3) N^{3}^{−}, O^{2}^{−}, F^{−}, S^{2}^{−}

(4) K^{+}, Cl^{−}, Ca^{2+}, Sc^{3+}

50. Given below are two statements :

**Statement I :** Sulphanilic acid gives esterification test for carboxyl group.

Statement II : Sulphanilic acid gives red colour in Lassigne’s test for extra element detection.

In the light of the above statements, choose the most appropriate answer from the options given below:

(1) Statement I is incorrect but Statement II is correct

(2) Both Statement I and Statement II are incorrect

(3) Statement I is correct but Statement II is incorrect

(4) Both Statement I and Statement II are correct

**SECTION B**

51. 0.3 g of ethane undergoes combustion at 27°C in a bomb calorimeter. The temperature of calorimeter system (including the water) is found to rise by 0.5∘C. The heat evolved during combustion of ethane at constant pressure is_____________ kJmol^{−1}. (Nearest integer)

[Given : The heat capacity of the calorimeter system is 20 kJ K^{−}^{1}, R = 8.3JK^{−}^{1} mol^{−}^{1}.

Assume ideal gas behavior.

Atomic mass of C and H are 12 and 1 g mol^{−1} respectively]

52. Among the following, the number of tranquilizer/s is/are _______

(A) Chloroliazepoxide (B) Veronal

(C) Valium (D) Salvarsan

53. Among the following, the number of tranquilizer/s is/are

(A) CuCO_{3} (B) Cu_{2}S (C) Cu_{2}O (D) FeO

54. A metal M crystallizes into two lattices :- face centred cubic (fcc) and body centred cubic (bcc) with unit cell edge length of 2.0 and 2.5Å respectively. The ratio of densities of lattices fcc to bcc for the metal M is___________ (Nearest integer)

55. The spin only magnetic moment of [Mn(H_{2}O)_{6}]^{2+} complexes is__________ B.M. (Nearest integer) (Given: Atomic no. of Mn is 25)

56. 1 × 10^{−5}M AgNO_{3} is added to 1 L of saturated solution of AgBr. The conductivity of this solution at 298 K is__________ × 10^{−8} S m^{−1}

[Given : K_{SP}(AgBr) = 4.9 × 10^{−}^{13} at 298 K

57. 20% of acetic acid is dissociated when its 5 g is added to 500 mL of water. The depression in freezing point of such water is___________ × 10^{−3}°C Atomic mass of C,H and O are 12,1 and 16 a.m.u. respectively.

[Given : Molal depression constant and density of water are 1.86 K kg mol^{−1} and 1 g cm^{−3} respectively.

58. A → B

20% of acetic acid is dissociated when its 5 g is added to 500 mL of water. The depression in freezing point of such water is___________ × 10^{−3}°C Atomic mass of C,H and O are 12, 1 and 16 a.m.u. respectively. [Given : Molal depression constant and density of water are 1.86 K kg mol^{−1} and 1 g cm^{−3} respectively.

59. Testosterone, which is a steroidal hormone, has the following structure.

The total number of asymmetric carbon atom /s in testosterone is___________

60. The molality of a 10%(v/v) solution of di-bromine solution in CCl_{4} (carbon tetrachloride) is ‘x’. x =_________ × 10^{−2} (Nearest integer)

[Given : molar mass of Br_{2} = 160 g mol^{−}^{1}

atomic mass of C = 12 g mol^{−}^{1}

atomic mass of Cl = 35.5 g mol^{−}^{1}

density of dibromine = 3.2 g cm^{−}^{3}

density of CCl_{4} = 1.6 g cm^{−}^{3}]

**Mathematics**

**SECTION-A**

61. Let αx = exp(x^{β}y^{γ}) be the solution of the differential equation 2x^{2}y dy – (1 – xy^{2}) dx = 0, x > 0, y(2) = √log_{e} 2. Then α + β + γ equals :

(1) 1

(2) −1

(3) 3

(4) 0

62. The sum

63. Let be two vectors. Then which one of the following statements is TRUE?

(1) Projection of and the direction of the projection vector is same as of

(2) Projection of and the direction of the projection vector is opposite to the direction of

(3) Projection of and the direction of the projection vector is same as of

(4) Projection of and the direction of the projection vector is opposite to the direction of

64. Let and be three given vectors. If is a vector such that then is equal to :

(1)

(2) √914/7

(3)

(4) 11/7

65. Let f : ℝ − 0, 1 → ℝ be a function such that Then f(2) is equal to

(1) 9/2

(2) 7/4

(3) 9/4

(4) 7/3

66. Let P(S) denote the power set of S = {1, 2, 3, ………., 10}. Define the relations R1 and R_{2} on P(S) as AR_{1}B if (A ∩ B^{C}) ∪ (B ∩ A^{C}) = ∅ and AR_{2}B if A ∪ B^{C} = B ∪ A^{C}, ∀ A, B ∈ P(S). Then :

(1) only R_{1} is an equivalence relation

(2) only R_{2} is an equivalence relation

(3) both R_{1} and R_{2} are equivalence relations

(4) both R_{1} and R_{2} are not equivalence relations

67. The area of the region given by {(x, y) : xy ≤ 8, 1 ≤ y ≤ x^{2}} is :

68. If then :

(1) A^{30} + A^{25} + A = I

(2) A^{30} = A^{25}

(3) A^{30} + A^{25} –A = I

(4) A^{30} – A^{25} = 2I

69. Which of the following statements is a tautology ?

(1) p ⋁ (p ⋀ q)

(2) (p ⋀ (p → q)) → ~q

(3) (p ⋀ q) → (~(p) → q)

(4) p → (p ⋀ (p → q))

70. The sum of the absolute maximum and minimum values of the function f (x) = |x^{2} – 5x + 6| − 3x + 2 in the interval [–1,3] is equal to :

(1) 12

(2) 13

(3) 10

(4) 24

71. Let the plane P pass through the intersection of the planes 2x + 3y – z = 2 and x + 2y + 3z = 6 and be perpendicular to the plane 2x + y – z = 0. If d is the distance of P form the point (–7, 1, 1,) then d^{2} is equal to :

(1) 250/83

(2) 250/82

(3) 15/53

(4) 25/83

72. The number of integral values of k, for which one root of the equation 2x^{2} – 8x + k = 0 lies in the interval (1,2) and its other root lies in the interval (2, 3), is :

(1) 3

(2) 0

(3) 2

(4) 1

73. Let P(x_{0}, y_{0}) be the point on the hyperbola 3x^{2} – 4y^{2} = 36, which is nearest to the line 3x + 2y = 1. Then √2(y_{0} – x_{0}) is equal to:

(1) −9

(2) −3

(3) 3

(4) 9

74. Two dice are thrown independently. Let A be the event that the number appeared on the 1st die is less than the number appeared on the 2nd die, B be the event that the number appeared on the 1st die is even and that on the second die is odd, and C be the event that the number appeared on the 1st die is odd and that on the 2nd is even. Then :

(1) the number of favourable cases of the events A,B and C are 15,6 and 6 respectively

(2) the number of favourable cases of the event (A ∪ B) ∩ C is 6

(3) B and C are independent

(4) A and B are mutually exclusive

75. If y(x) = x^{x}, x > 0, then y”(2) – 2yʹ(2) is equal to :

(1) 4log_{e} 2 + 2

(2) 8log_{e} 2 – 2

(3) 4(log_{e} 2)^{2} + 2

(4) 4(log_{e} 2)^{2} – 2

76. Let

If n(S) denotes the number of elements in S then :

(1) n(S) = 2 and only one element in S is less then 1/2.

(2) n(S) = 1 and the element in S is more than 1/2.

(3) n(S) = 0

(4) n(S) = 1 and the element in S is less than 1/2.

77. The value of the integral is :

(1) π^{2}/12√3

(2) π^{2}/6√3

(3) π^{2}/6

(4) π^{2}/3√3

78. For the system of linear equations αx + y + z = 1, x + αy + z = 1, x + y + αz = β, which one of the following statements is NOT correct?

(1) It has infinitely many solutions if α = 2 and β = −1

(2) It has no solution if α = −2 and β = 1

(3) if α = 2 and β = 1

(4) It has infinitely many solutions if α = 1 and β = 1

79. Let 9 = x_{1}< x_{2} < ….. < x_{7} …….., x_{7} be in an A.P. with common difference d. If the standard deviation of x_{1} ∙ x_{2} ………, x_{7} is 4 and mean is is equal to

(1)

(2)

(3) 25

(4) 34

80. Let a, b be two real numbers such that ab < 0. IF the complex number is of unit modulus and a + ib lies on the circle |z – 1| = |2z|, then a possible value of where [t] is greatest integer function, is :

(1) −1/2

(2) −1

(3) 1

(4) 1/2

**SECTION-B**

81. Let αx + βy + yz = 1 be the equation of a plane through the point (3, –2, 5)and perpendicular to the line joning the points (1, 2, 3) and (–2, 3, 5). Then the value of αβy is equal to

82. If the term without x in the expansion of is 7315, then |α| is equal to

83. If the x – intercept of a focal chord of the parabola y^{2 }= 8x + 4y + 4 is 3, then the length of this chord is equal to

84. Let the sixth term in the binomial expansion of in the increasing powers of 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 A.P., then the sum of the squares of all possible values of x is

85. The point of intersection C of the plane 8x + y + 2z = 0 and the line joining the point A(–3, –61) and B(2, –4, –3) divides the line segment AB internally in the ratio k:. If a, b, c (|a|, |b|, |c|) are coprime are the direction ratios of the perpendicular form the point C on the line then |a + b + c| is equal to

86. The line x = 8 is the directrix of the ellipse with the corresponding focus (2, 0). If the tangent to E at the point P in the first quadrant passes through the point (0, 4√3) and intersects that x-axis at Q then (3PQ)^{2} equal to

87. The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6 , is

88. Number of integral solutions to the equation x + y + z = 21, where x ≥ 1, y ≥ 3, z ≥ 4, is equal to

89. The sum of the common terms of the following three arithmetic progressions.

3, 7, 11, 15, ……., 399

2, 5, 8, 11, ……., 359 and

2, 7, 12, 17, …….., 197

is equal to

90. If

Then k is equal to

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