JEE ADVANCED TYPE 3

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JEE ADVANCED TYPE 3

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1 / 108

1. Tollens’ test is positive for

1) CH3COCH3

2) CH3COOH

3) HCHO

4) Benzene

2 / 108

2. Compute 10C3.

3 / 108

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

4 / 108

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

1) PV=nRT

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

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

4) At constant V, P proportional to T.

5 / 108

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

1) AB=BA implies A=B

2) det(I)=1

3) det(AB)=det(A)det(B)

4) det(A)≠0 implies invertible

6 / 108

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

1) 24

2) 8

3) 12

4) 6

7 / 108

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

1) 2

2) 3

3) 1

4) 4

8 / 108

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

1) Order can be fractional.

2) Rate law is experimental.

3) Molecularity can be fractional.

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

9 / 108

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

10 / 108

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

1) Kinetic energy

2) Linear momentum

3) Speed of each body

4) Mechanical energy always

11 / 108

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

12 / 108

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

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

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

3) Induced current supports the change in flux.

4) Changing area of loop can induce emf.

13 / 108

13. Value of 6! is

1) 720

2) 1440

3) 120

4) 360

14 / 108

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

15 / 108

15. Aromatic species is

1) C5H5−

2) C5H5+

3) COT

4) Cyclobutadiene

16 / 108

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

1) E1

2) E2

3) SN1

4) SN2

17 / 108

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

18 / 108

18. lim_{x→0} (sin x)/x is

19 / 108

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

1) Speed necessarily changes

2) Acceleration is non-zero and directed toward center

3) Velocity is constant

4) Acceleration is zero

20 / 108

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

21 / 108

21. Match colligative property with effect.

1. Osmotic pressure

2. Freezing point depression

3. Boiling point elevation

22 / 108

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

23 / 108

23. Atoms per unit cell in BCC is

24 / 108

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

1) 9 Ω

2) 2 Ω

3) 4.5 Ω

4) 1 Ω

25 / 108

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

26 / 108

26. Match trig identity.

1. 1+cot^2θ

2. sin^2θ+cos^2θ

3. 1+tan^2θ

27 / 108

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

1) ∫1/x dx = 1/x + C

2) ∫0 dx = C

3) ∫(f+g)=∫f+∫g

4) ∫(cf)=c∫f

28 / 108

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

29 / 108

29. Molarity for 1 mol solute in 4 L is

30 / 108

30. Match geometry item with formula.

1. Rectangle area

2. Circle area

3. Triangle area

31 / 108

31. ∫ 3x^2 dx equals

1) x^3 + C

2) x^2 + C

3) ln x + C

4) 3x + C

32 / 108

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

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

2) If v ∥ B, force is zero.

3) If v ⟂ B, force magnitude is qvB.

4) Magnetic force is q(v×B).

33 / 108

33. 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.

34 / 108

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

1) 76.8

2) 0.133

3) 9.5

4) 7.5

35 / 108

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

1) Remains same

2) Increases

3) Decreases

4) Becomes zero

36 / 108

36. Oxidizing agent is the species that

1) Gets oxidized

2) Loses electrons

3) Gets reduced

4) Always has oxygen

37 / 108

37. Which acts as a Lewis acid?

1) OH−

2) Cl−

3) BF3

4) NH3

38 / 108

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

1) 30

2) 210

3) 240

4) 255

39 / 108

39. For ideal solutions, Raoult’s law states

1) p_i = x_i p_i°

2) Applies only to solids

3) p_i independent of x_i

4) ΔHmix always positive

40 / 108

40. Geometry of XeF4 is

1) Trigonal bipyramidal

2) Linear

3) Square planar

4) Tetrahedral

41 / 108

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

1) If LHL=RHL, limit exists.

2) Continuity implies limit equals function value.

3) Continuity implies differentiability.

4) Polynomials are continuous everywhere.

42 / 108

42. Derivative of (sin x) is

1) sin x

2) −cos x

3) cos x

4) −sin x

43 / 108

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

1) Positive

2) Negative

3) Zero

4) Depends on mass

44 / 108

44. Ozonolysis of alkenes uses

1) O3 then Zn/H2O

2) NaBH4

3) LiAlH4

4) H2/Pd

45 / 108

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

46 / 108

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

1) Molarity depends on temperature.

2) Molality is temperature independent.

3) Vapour pressure lowering is colligative.

4) Ideal solution has large ΔHmix.

47 / 108

47. Match condition with statement.

1. Centripetal acceleration

2. Resonance (LC)

3. TIR

48 / 108

48. Sigma bonds in benzene (C6H6) are

1) 18

2) 9

3) 6

4) 12

49 / 108

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

50 / 108

50. Complex showing cis-trans isomerism is

1) [Ni(CO)4]

2) [Pt(NH3)2Cl2]

3) [Co(NH3)6]3+

4) [Fe(CN)6]4−

51 / 108

51. Conjugate base of H2CO3 is

1) H3CO3+

2) H2CO3−

3) CO3^2−

4) HCO3−

52 / 108

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

1) Cyclobutadiene is aromatic.

2) Aromatic systems are planar.

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

4) Aromatic species are necessarily neutral.

53 / 108

53. If z=5−12i, then |z| equals

1) 17

2) 7

3) 144

4) 13

54 / 108

54. Match test with compound class.

1. Tollens

2. Iodoform

3. Bromine water

55 / 108

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

56 / 108

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

1) Zero

2) Maximum

3) Always non-zero

4) Depends on charge only

57 / 108

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

1) cos2θ=cos^2θ−sin^2θ

2) tanθ=sinθ/cosθ

3) sin2θ=sinθ+cosθ

4) sin^2θ+cos^2θ=1

58 / 108

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

59 / 108

59. Match probability term with meaning.

1. Independent events

2. Complement

3. Mutually exclusive

60 / 108

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

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

2) TIR can occur for any incidence angle.

3) Refractive index n=c/v.

4) Frequency of light remains unchanged during refraction.

61 / 108

61. Match acid-base term with definition.

1. Brønsted acid

2. Lewis base

3. Lewis acid

62 / 108

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

1) P(A∪B)=P(A)+P(B)+P(A∩B)

2) If A⊆B then P(A)≤P(B)

3) P(A∩B)≤P(A)

4) P(∅)=0

63 / 108

63. If cosθ=1, θ could be

1) 0

2) π/2

3) π/3

4) π/4

64 / 108

64. Strong electrolyte in water is

1) CH3COOH

2) Glucose

3) NH4OH

4) NaNO3

65 / 108

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

1) dimensionless

2) s^-1

3) mol L^-1 s^-1

4) L mol^-1 s^-1

66 / 108

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

1) Frequency increases

2) Speed decreases and wavelength decreases; frequency unchanged

3) Frequency decreases

4) Speed increases and wavelength increases

67 / 108

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

1) 180°

2) 45°

3) 0°

4) 90°

68 / 108

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

69 / 108

69. Slope of line 2x−y+3=0 is

1) −1/2

2) 1/2

3) 2

4) −2

70 / 108

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

1) Oxidizing agent is reduced.

2) Oxidation is loss of electrons.

3) Reducing agent is reduced.

4) Reduction is gain of electrons.

71 / 108

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

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

2) In parallel, voltage is same across branches.

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

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

72 / 108

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

1) nPr=n!/(n−r)!

2) Permutations of n objects is n!.

3) nC0=1

4) nPr=nCr always.

73 / 108

73. If f(x)=2x+1, then f(−4) equals

1) 9

2) −7

3) −9

4) 7

74 / 108

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

1) At extreme position acceleration magnitude is maximum.

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

3) At extreme position speed is maximum.

4) At mean position acceleration is zero.

75 / 108

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

76 / 108

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

1) Volume

2) Absolute temperature

3) Molar mass

4) Density only

77 / 108

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

1. Energy

2. Charge

3. Pressure

78 / 108

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

1) In isolated system, momentum is conserved.

2) Momentum is always conserved even with external forces.

3) Momentum is a vector.

4) Impulse equals change in momentum.

79 / 108

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

1) Electric field is conservative in electrostatics.

2) Capacitance depends on charge stored only.

3) Potential difference is path independent.

4) For a capacitor, Q ∝ V.

80 / 108

80. Colligative properties depend on

1) Pressure only

2) Solvent identity only

3) Nature of solute only

4) Number of solute particles

81 / 108

81. Highest lattice energy among the following is

1) MgO

2) KBr

3) NaCl

4) CsI

82 / 108

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

1) Temperature only

2) Intensity only

3) Surface area only

4) Frequency of incident light

83 / 108

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

1) Identity

2) Orthogonal

3) Singular

4) Diagonal

84 / 108

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

85 / 108

85. Match lattice with atoms per unit cell.

1. BCC

2. SC

3. FCC

86 / 108

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

1) 0

2) 411.0

3) 205.5

4) 102.8

87 / 108

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

1) 0.3

2) 1.7

3) 0

4) 0.7

88 / 108

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

1) Buffer contains weak acid and its conjugate base.

2) Buffer resists pH change for small additions.

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

4) Henderson equation relates pH, pKa and ratio.

89 / 108

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

1) Angle of incidence is less than critical angle

2) Refractive index of denser medium is smaller

3) Angle of incidence is greater than critical angle

4) Angle of refraction is zero always

90 / 108

90. 0.75 mol of substance with molar mass 80 g/mol has mass (g)

1) 80

2) 600

3) 6

4) 60

91 / 108

91. Match phenomenon with law.

1. Refraction

2. Reflection

3. Induction

92 / 108

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

1) 10

2) 5

3) 1

4) 0

93 / 108

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

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

2) Frequency changes when wave enters another medium.

3) Sound in air is longitudinal.

4) v=fλ

94 / 108

94. Match quantity with SI unit.

1. Magnetic flux

2. Power

3. Charge

95 / 108

95. Number of π bonds in benzene is

96 / 108

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

1) Infinite

2) 0

3) 1

4) 2

97 / 108

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

1) 4

2) 2

3) 3

4) 1

98 / 108

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

1) Slope of horizontal line is 0

2) Midpoint formula averages coordinates

3) Slope of vertical line is 0

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

99 / 108

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

1) 0.248

2) 0.497

3) 0.994

4) 79.477

100 / 108

100. Match function with inverse (domain restricted).

1. 3x

2. x^2 (x≥0)

3. x+5

101 / 108

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

1) 157.56

2) 39.39

3) 78.78

4) 80.0

102 / 108

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

1) Dot product is scalar.

2) a×b=b×a.

3) Cross product is vector.

4) If a ∥ b then a×b=0

103 / 108

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

104 / 108

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

105 / 108

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

106 / 108

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

1) Atomic radius increases down a group.

2) Effective nuclear charge increases across a period.

3) Ionization energy decreases down a group.

4) Electronegativity increases down a group.

107 / 108

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

1) 12

2) 36

3) 32

4) 64

108 / 108

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

1) 0.176

2) 0.088

3) 0.044

4) 13.75

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