JEE ADVANCED TYPE 3 – Start Exam

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JEE ADVANCED TYPE 3

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1 / 108

1. Work done by centripetal force in uniform circular motion over any displacement is

1) Positive

2) Negative

3) Depends on mass

4) Zero

2 / 108

2. A parallel-plate capacitor remains connected to a battery. On inserting a dielectric fully, the charge on capacitor

1) Becomes zero

2) Increases

3) Decreases

4) Remains same

3 / 108

3. Select all correct statements about matrices (Set-03):

1) det(AB)=det(A)det(B)

2) det(A)≠0 implies invertible

3) AB=BA implies A=B

4) det(I)=1

4 / 108

4. Select all correct statements about probability (Set-03):

1) P(A∪B)=P(A)+P(B)+P(A∩B)

2) P(∅)=0

3) P(A∩B)≤P(A)

4) If A⊆B then P(A)≤P(B)

5 / 108

5. Select all correct statements about periodicity (Set-03):

1) Ionization energy decreases down a group.

2) Effective nuclear charge increases across a period.

3) Atomic radius increases down a group.

4) Electronegativity increases down a group.

6 / 108

6. Match colligative property with effect.

1. Boiling point elevation

2. Osmotic pressure

3. Freezing point depression

7 / 108

7. Match geometry item with formula.

1. Rectangle area

2. Triangle area

3. Circle area

8 / 108

8. Match test with compound class.

1. Iodoform

2. Bromine water

3. Tollens

9 / 108

9. If u=−20 cm and v=40 cm, focal length f (cm) from 1/f=1/v−1/u

10 / 108

10. In uniform circular motion with constant speed, which statement is correct?

1) Acceleration is non-zero and directed toward center

2) Acceleration is zero

3) Velocity is constant

4) Speed necessarily changes

11 / 108

11. Oxidizing agent is the species that

1) Gets reduced

2) Gets oxidized

3) Always has oxygen

4) Loses electrons

12 / 108

12. If N=150, ΔΦ=0.06 Wb in 0.02 s, induced emf (V)

13 / 108

13. Select all correct statements about permutations (Set-03):

1) nC0=1

2) Permutations of n objects is n!.

3) nPr=n!/(n−r)!

4) nPr=nCr always.

14 / 108

14. Highest lattice energy among the following is

1) NaCl

2) KBr

3) CsI

4) MgO

15 / 108

15. Strong electrolyte in water is

1) NaNO3

2) CH3COOH

3) NH4OH

4) Glucose

16 / 108

16. Derivative of (sin x) is

1) −cos x

2) sin x

3) −sin x

4) cos x

17 / 108

17. A loop of area 0.08 m² is in a magnetic field increasing at 1.1 T/s. Induced emf (V) is

1) 0.044

2) 13.75

3) 0.088

4) 0.176

18 / 108

18. A circuit draws current 3.2 A from a 24 V source. Equivalent resistance (Ω) is

1) 0.133

2) 9.5

3) 76.8

4) 7.5

19 / 108

19. Select all correct statements about gases (Set-03):

1) At constant T, P inversely proportional to V.

2) At constant P, V inversely proportional to T.

3) PV=nRT

4) At constant V, P proportional to T.

20 / 108

20. Select all correct statements about coordination compounds (Set-03):

1) Square planar often involves dsp2 hybridization.

2) Ligands may be neutral/anionic.

3) Coordination number equals donor atoms bonded.

4) Octahedral complexes cannot show geometrical isomerism.

21 / 108

21. A projectile is fired with speed 28 m/s at angle 40°. (g=9.8 m/s²). Find its range (m).

1) 78.78

2) 39.39

3) 157.56

4) 80.0

22 / 108

22. Sum of first 15 terms of AP with a=3 and d=2 is

1) 30

2) 240

3) 210

4) 255

23 / 108

23. If x=3, evaluate 4x^2.

24 / 108

24. When light enters a medium with higher refractive index, its

1) Frequency decreases

2) Speed increases and wavelength increases

3) Frequency increases

4) Speed decreases and wavelength decreases; frequency unchanged

25 / 108

25. Which acts as a Lewis acid?

1) Cl−

2) BF3

3) OH−

4) NH3

26 / 108

26. Magnitude of vector (2,1,2) is

27 / 108

27. Match acid-base term with definition.

1. Lewis base

2. Lewis acid

3. Brønsted acid

28 / 108

28. For ideal solutions, Raoult’s law states

1) p_i = x_i p_i°

2) ΔHmix always positive

3) p_i independent of x_i

4) Applies only to solids

29 / 108

29. Area of triangle with vertices (0,0),(6,0),(0,4) is

1) 12

2) 8

3) 6

4) 24

30 / 108

30. Match lattice with atoms per unit cell.

1. BCC

2. FCC

3. SC

31 / 108

31. If two resistors 6Ω and 3Ω are in parallel, equivalent resistance is

1) 2 Ω

2) 4.5 Ω

3) 9 Ω

4) 1 Ω

32 / 108

32. 0.75 mol of substance with molar mass 80 g/mol has mass (g)

1) 60

2) 6

3) 600

4) 80

33 / 108

33. Match probability term with meaning.

1. Complement

2. Independent events

3. Mutually exclusive

34 / 108

34. Moles in 22 g CO2 (M=44 g/mol) is

35 / 108

35. In an isolated system, during any collision, which quantity is always conserved?

1) Kinetic energy

2) Speed of each body

3) Linear momentum

4) Mechanical energy always

36 / 108

36. In photoelectric effect, maximum kinetic energy of photoelectrons depends on

1) Intensity only

2) Surface area only

3) Frequency of incident light

4) Temperature only

37 / 108

37. Total internal reflection occurs when light goes from denser to rarer medium and

1) Angle of incidence is greater than critical angle

2) Angle of incidence is less than critical angle

3) Angle of refraction is zero always

4) Refractive index of denser medium is smaller

38 / 108

38. If det(A)=0 for a square matrix A, then A is

1) Singular

2) Identity

3) Diagonal

4) Orthogonal

39 / 108

39. Select all correct statements about aromaticity (Set-03):

1) Aromatic systems follow (4n+2)π rule.

2) Cyclobutadiene is aromatic.

3) Aromatic species are necessarily neutral.

4) Aromatic systems are planar.

40 / 108

40. Select all correct statements about trigonometry (Set-03):

1) sin2θ=sinθ+cosθ

2) sin^2θ+cos^2θ=1

3) tanθ=sinθ/cosθ

4) cos2θ=cos^2θ−sin^2θ

41 / 108

41. A resistor 10 Ω carries 2 A. Voltage (V) is

42 / 108

42. A wave of frequency 250 Hz and wavelength 1.2 m has speed (m/s)

43 / 108

43. Select all correct statements about vectors (Set-03):

1) a×b=b×a.

2) If a ∥ b then a×b=0

3) Dot product is scalar.

4) Cross product is vector.

44 / 108

44. If z=5−12i, then |z| equals

1) 7

2) 144

3) 17

4) 13

45 / 108

45. determinant of [[2,1],[5,3]] is

46 / 108

46. Number of real roots of x^2+4x+5=0 is

1) 0

2) 1

3) 2

4) Infinite

47 / 108

47. An LC circuit has L=0.15 H and C=4 μF. Resonant frequency (Hz) is closest to

1) 0

2) 205.5

3) 102.8

4) 411.0

48 / 108

48. A charge 2 μC at potential 50 V has potential energy (in μJ)

49 / 108

49. [Fallback-8] Evaluate (2+8)^2.

50 / 108

50. Select all correct statements about continuity (Set-03):

1) Continuity implies differentiability.

2) If LHL=RHL, limit exists.

3) Polynomials are continuous everywhere.

4) Continuity implies limit equals function value.

51 / 108

51. A mass 5 kg moves at 4 m/s. Kinetic energy (J) is

52 / 108

52. Match condition with statement.

1. Centripetal acceleration

2. TIR

3. Resonance (LC)

53 / 108

53. log10(10^5)=x, then x is

1) 5

2) 0

3) 10

4) 1

54 / 108

54. If f(x)=2x+1, then f(−4) equals

1) 9

2) −7

3) 7

4) −9

55 / 108

55. Remainder when 37^2 is divided by 9 is

1) 2

2) 1

3) 4

4) 3

56 / 108

56. Number of subsets of a set with 6 elements is

1) 36

2) 64

3) 12

4) 32

57 / 108

57. If P(A)=0.7, then P(A^c) equals

1) 1.7

2) 0.3

3) 0.7

4) 0

58 / 108

58. Match (List-I) with dimensional formula (List-II).

1. Charge

2. Pressure

3. Energy

59 / 108

59. pH of 1×10^-3 M HCl (strong acid) is

60 / 108

60. If P(A)=0.25, then P(A^c) is

61 / 108

61. Select all correct statements about magnetic force (Set-03):

1) Magnetic force is q(v×B).

2) Magnetic force can do work and change speed always.

3) If v ⟂ B, force magnitude is qvB.

4) If v ∥ B, force is zero.

62 / 108

62. Tollens’ test is positive for

1) Benzene

2) CH3COOH

3) HCHO

4) CH3COCH3

63 / 108

63. Molarity for 1 mol solute in 4 L is

64 / 108

64. Match function with inverse (domain restricted).

1. 3x

2. x^2 (x≥0)

3. x+5

65 / 108

65. Work done in lifting 80 N weight by 1.5 m (J)

66 / 108

66. Atoms per unit cell in BCC is

67 / 108

67. Ozonolysis of alkenes uses

1) H2/Pd

2) O3 then Zn/H2O

3) NaBH4

4) LiAlH4

68 / 108

68. If t1/2=200 s (first order), k=0.693/t1/2 (s^-1) is

69 / 108

69. If Kc=9 for A⇌B, then Kc for B⇌A is

70 / 108

70. lim_{x→0} (sin x)/x is

71 / 108

71. A mass 2 kg attached to a spring of constant 320 N/m performs SHM. Time period (s) is

1) 0.248

2) 79.477

3) 0.994

4) 0.497

72 / 108

72. Conjugate base of H2CO3 is

1) H3CO3+

2) CO3^2−

3) HCO3−

4) H2CO3−

73 / 108

73. Value of 6! is

1) 1440

2) 120

3) 360

4) 720

74 / 108

74. Select all correct statements about optics (Set-03):

1) Critical angle exists only when light goes from denser to rarer.

2) Refractive index n=c/v.

3) TIR can occur for any incidence angle.

4) Frequency of light remains unchanged during refraction.

75 / 108

75. ∫ 3x^2 dx equals

1) x^2 + C

2) 3x + C

3) x^3 + C

4) ln x + C

76 / 108

76. If cosθ=1, θ could be

1) π/4

2) 0

3) π/3

4) π/2

77 / 108

77. Select all correct statements about integration (Set-03):

1) ∫(cf)=c∫f

2) ∫1/x dx = 1/x + C

3) ∫0 dx = C

4) ∫(f+g)=∫f+∫g

78 / 108

78. Colligative properties depend on

1) Pressure only

2) Number of solute particles

3) Solvent identity only

4) Nature of solute only

79 / 108

79. Select all correct statements about EMI (Set-03):

1) Induced emf depends on rate of change of flux.

2) Lenz’s law gives direction of induced current.

3) Changing area of loop can induce emf.

4) Induced current supports the change in flux.

80 / 108

80. Match trig identity.

1. sin^2θ+cos^2θ

2. 1+tan^2θ

3. 1+cot^2θ

81 / 108

81. Geometry of XeF4 is

1) Square planar

2) Trigonal bipyramidal

3) Tetrahedral

4) Linear

82 / 108

82. For normal incidence on a plane mirror, the angle of reflection is

1) 0°

2) 45°

3) 90°

4) 180°

83 / 108

83. Distance between (1,2) and (7,10) is

84 / 108

84. Select all correct statements about electrostatics (Set-03):

1) Electric field is conservative in electrostatics.

2) For a capacitor, Q ∝ V.

3) Capacitance depends on charge stored only.

4) Potential difference is path independent.

85 / 108

85. Select all correct statements about waves (Set-03):

1) Wavelength changes when speed changes (frequency fixed).

2) Sound in air is longitudinal.

3) v=fλ

4) Frequency changes when wave enters another medium.

86 / 108

86. Select all correct statements about momentum (Set-03):

1) Impulse equals change in momentum.

2) Momentum is always conserved even with external forces.

3) Momentum is a vector.

4) In isolated system, momentum is conserved.

87 / 108

87. Sigma bonds in benzene (C6H6) are

1) 18

2) 6

3) 9

4) 12

88 / 108

88. For a first-order reaction, the unit of rate constant is

1) s^-1

2) mol L^-1 s^-1

3) dimensionless

4) L mol^-1 s^-1

89 / 108

89. Compute 10C3.

90 / 108

90. Select all correct statements about SHM (Set-03):

1) At extreme position acceleration magnitude is maximum.

2) At mean position acceleration is zero.

3) At extreme position speed is maximum.

4) a and x are opposite in direction in SHM.

91 / 108

91. Select all correct statements about buffers (Set-03):

1) Buffer contains weak acid and its conjugate base.

2) Buffer keeps pH constant for any amount of acid/base.

3) Buffer resists pH change for small additions.

4) Henderson equation relates pH, pKa and ratio.

92 / 108

92. Select all correct statements about redox (Set-03):

1) Oxidation is loss of electrons.

2) Oxidizing agent is reduced.

3) Reduction is gain of electrons.

4) Reducing agent is reduced.

93 / 108

93. For vectors a=(1,2,0), b=(2,0,1), the dot product a·b equals

1) 2

2) 1

3) 4

4) 3

94 / 108

94. For ideal gas at constant volume, pressure is directly proportional to

1) Absolute temperature

2) Molar mass

3) Density only

4) Volume

95 / 108

95. Select all correct statements about coordinate geometry (Set-03):

1) Distance formula uses √[(Δx)^2+(Δy)^2]

2) Slope of vertical line is 0

3) Slope of horizontal line is 0

4) Midpoint formula averages coordinates

96 / 108

96. Number of π bonds in benzene is

97 / 108

97. Aromatic species is

1) Cyclobutadiene

2) C5H5−

3) C5H5+

4) COT

98 / 108

98. Mechanism of CH3Br + OH− → CH3OH + Br− is

1) E2

2) E1

3) SN1

4) SN2

99 / 108

99. Slope of line 2x−y+3=0 is

1) 2

2) 1/2

3) −2

4) −1/2

100 / 108

100. Two capacitors 4 μF and 5 μF in parallel have equivalent (μF)

101 / 108

101. Complex showing cis-trans isomerism is

1) [Co(NH3)6]3+

2) [Ni(CO)4]

3) [Pt(NH3)2Cl2]

4) [Fe(CN)6]4−

102 / 108

102. If GP has a=2, r=3, the 4th term is

103 / 108

103. Select all correct statements about solutions (Set-03):

1) Vapour pressure lowering is colligative.

2) Molality is temperature independent.

3) Molarity depends on temperature.

4) Ideal solution has large ΔHmix.

104 / 108

104. Select all correct statements about circuits (Set-03):

1) Power dissipated in resistor is I^2R.

2) In series, current is same in each element.

3) Equivalent resistance of parallel is greater than each resistor.

4) In parallel, voltage is same across branches.

105 / 108

105. Match phenomenon with law.

1. Induction

2. Refraction

3. Reflection

106 / 108

106. A charged particle moves with velocity parallel to a uniform magnetic field. Magnetic force on it is

1) Zero

2) Depends on charge only

3) Maximum

4) Always non-zero

107 / 108

107. Select all correct statements about kinetics (Set-03):

1) Higher activation energy generally lowers rate at given T.

2) Molecularity can be fractional.

3) Rate law is experimental.

4) Order can be fractional.

108 / 108

108. Match quantity with SI unit.

1. Charge

2. Power

3. Magnetic flux

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