JEE ADVANCED TYPE 2 – Start Exam

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JEE ADVANCED TYPE 2

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1 / 108

1. For light going from glass (n=1.50) to air (n=1.00), the critical angle is closest to

1) 75°

2) 30°

3) 60°

4) 41.81°

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2. Compute determinant of matrix [[2,3],[5,7]].

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3. Match (List-I) with (List-II).

1. d/dx (sin x)

2. ∫ x^n dx (n≠−1)

3. d/dx (ln x)

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4. Which of the following has maximum bond order?

1) F2

2) Ne2

3) N2

4) O2

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5. Which pair represents coordination isomerism?

1) linkage in [Co(NH3)5NO2]Cl2

2) optical in [Co(en)3]3+

3) cis/trans in [Pt(NH3)2Cl2]

4) [Co(NH3)5Br]SO4 and [Co(NH3)5SO4]Br

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6. Match (List-I) with the correct count formula (List-II).

1. Diagonals in n-gon

2. Permutations of n distinct items

3. Subsets of n-set

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7. Select all correct statements about heat transfer (Set-02):

1) Convection involves bulk motion of fluid.

2) Radiation can occur in vacuum.

3) Conduction requires a material medium.

4) Convection occurs only in solids.

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8. Select all correct statements about chemical equilibrium (Set-02):

1) At equilibrium, concentrations of reactants and products are necessarily equal.

2) A catalyst speeds up reaching equilibrium but does not change equilibrium composition.

3) At equilibrium, forward and reverse reaction rates are equal.

4) Equilibrium can be approached from either side (reactants/products).

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9. Match (List-I) with the correct hybridization (List-II).

1. BeCl2 (g)

2. BF3

3. CH4

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10. A charged particle moves in a circle of radius 0.4 m in uniform magnetic field B=0.5 T with speed 6×10^6 m/s. The magnitude of q/m equals (q/m = v/(Br))

1) 15000000.0 C/kg

2) 15000000.0 C/kg

3) 30000000.0 C/kg

4) 0.0 C/kg

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11. For first order reaction, if half-life t1/2=693 s, k (s^-1) equals (k=0.693/t1/2).

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12. Select all correct statements about periodic trends (Set-02):

1) Atomic radius generally decreases across a period.

2) Ionization energy generally increases across a period.

3) Electron affinity generally becomes more negative across a period (with exceptions).

4) Electronegativity generally decreases across a period.

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13. Match (List-I) with the correct dimension (List-II).

1. Pressure

2. Energy

3. Impulse

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14. Select all correct statements about coordination compounds (Set-02):

1) Geometrical isomerism is possible in square planar complexes.

2) Oxidation state of metal is always zero.

3) Ligands act as Lewis bases.

4) Coordination number equals number of donor atoms attached to metal.

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15. A 0.5 kg mass attached to spring executes SHM with k=200 N/m. Angular frequency ω (rad/s) is

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16. Match the wave phenomenon (List-I) with the key condition (List-II).

1. Constructive interference

2. Total internal reflection

3. Diffraction (single slit)

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17. If sinθ=3/5 (θ acute), then value of sin(2θ) is

1) 7/25

2) 12/25

3) 1

4) 24/25

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18. For the equilibrium N2(g)+3H2(g)⇌2NH3(g), increasing pressure at constant temperature shifts equilibrium

1) Towards N2 and H2

2) Depends only on catalyst

3) No change

4) Towards NH3

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19. A body starts from rest and accelerates uniformly at 4 m/s² for 5 s. Final speed (m/s) is

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20. Select all correct statements about vectors (Set-02):

1) a·b = |a||b|cosθ.

2) a×b is perpendicular to both a and b.

3) If a×b=0, then a and b are perpendicular.

4) If a·b=0, then a and b are perpendicular (or one is zero vector).

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21. A current 6 A passes through resistance 6 Ω. Power dissipated is

1) 36 W

2) 1.0 W

3) 216 W

4) 1.0 W

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22. A 2 Ω and 3 Ω resistors are connected in series across 10 V. Current (A) is

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23. Select all correct statements about induced emf (Set-02):

1) Direction of induced current opposes the change in flux producing it.

2) A changing flux can be due to changing B, area, or orientation.

3) Induced emf is proportional to rate of change of magnetic flux.

4) Induced emf exists even if flux is constant but magnetic field is present.

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24. In a galvanic cell, electrons flow in the external circuit from

1) Salt bridge to anode

2) Electrolyte to electrodes equally

3) Cathode to anode

4) Anode to cathode

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25. Select all correct statements about SN1 reactions (Set-02):

1) A stable carbocation intermediate is formed.

2) Racemization can occur for chiral centers.

3) Inversion of configuration always occurs.

4) Rate depends only on substrate concentration.

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26. Sum of infinite GP with first term 4 and common ratio 1/7 is

1) 3.5

2) 4.667

3) 3.429

4) 4

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27. The correct order of increasing electronegativity is

1) Na < Mg < Al < Si

2) Si < Al < Mg < Na

3) Na < Al < Mg < Si

4) Mg < Na < Al < Si

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28. Which reagent converts an aldehyde to a primary alcohol selectively?

1) HNO3

2) NaBH4

3) KMnO4

4) K2Cr2O7/H+

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29. Select all correct statements about probability (Set-02):

1) P(A^c)=1−P(A).

2) If A and B are independent, then P(A∩B)=P(A)+P(B).

3) 0 ≤ P(A) ≤ 1 for any event A.

4) P(A∪B)=P(A)+P(B) when A and B are mutually exclusive.

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30. A resistor R=3 Ω is in series with a capacitor C=2 μF. The time constant τ=RC is

1) 0.000006 s

2) 1500000.000000 s

3) 0.000001 s

4) 3.000002 s

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31. If vectors a and b are perpendicular, then a·b equals

1) 1

2) −|a||b|

3) |a||b|

4) 0

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32. A capacitor 3 μF is charged to 40 V. Energy stored in μJ is

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33. Select all correct statements about sequences (Set-02):

1) In a GP, nth term is ar^{n−1}.

2) Sum of first n natural numbers is n^2.

3) In an AP, nth term is a+(n−1)d.

4) Sum of first n natural numbers is n(n+1)/2.

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34. A wire carries current 3 A for 120 s. Charge passed (C) is

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35. Evaluate lim(x→0) (e^3x − 0)/x (note: expression is (e^a·x)/x)

1) 1

2) 20.086

3) 0

4) 3

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36. Select all correct statements about conic sections (Set-02):

1) For ellipse, sum of distances from two foci is constant.

2) Hyperbola has constant product of distances from foci.

3) Parabola is the locus of points equidistant from a fixed point and a fixed line.

4) Circle is a special case of ellipse.

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37. How many grams of NaCl are present in 0.5 mol? (M=58.5 g/mol)

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38. For y=ln x, the derivative dy/dx is

1) 1/x

2) e^x

3) x

4) ln x

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39. Oxidation state of S in H2SO4 is

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40. For an ideal solution, the enthalpy change of mixing (ΔHmix) is

1) 0

2) Negative

3) Always large

4) Positive

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41. ∫ x^4 dx equals

1) x^5/5 + C

2) x^4 + C

3) 4x^3+C

4) ln x + C

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42. Which compound gives iodoform test?

1) CH3CH2OH

2) CH3COCH3

3) HCHO

4) CH3COOH

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43. A sound wave of frequency 350 Hz travels in air at 340 m/s. Wavelength is

1) 0.971 m

2) 119000 m

3) 1.942 m

4) 1.0294 m

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44. Sum of roots of equation x^2 + 7x + 1 = 0 is

1) 1

2) 0

3) 7

4) -7

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45. Select all correct statements about determinants (Set-02):

1) Interchanging two rows changes sign of determinant.

2) If two rows of a determinant are identical, determinant is zero.

3) Adding a multiple of one row to another does not change determinant.

4) If determinant is non-zero, the matrix is singular.

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46. In interference, for two waves of equal amplitude, resultant intensity is maximum when phase difference is

1) π (or (2n+1)π)

2) 0 (or 2πn)

3) 3π/2

4) π/2

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47. Select all correct statements about polymers (Set-02):

1) Nylon-6,6 is a condensation polymer.

2) Condensation polymers often eliminate small molecules (like H2O).

3) Teflon is a condensation polymer.

4) Addition polymers generally do not eliminate small molecules during formation.

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48. An ideal gas at P=1.0×10^5 Pa and V=2.0×10^-3 m³ has temperature 300 K. Number of moles is (use PV=nRT, R=8.314)

1) 0.0802 mol

2) 0.00802 mol

3) 0.802 mol

4) 0.1604 mol

49 / 108

49. Coefficient of x^8 in (1+x)^10 is

1) 46

2) 9

3) 10

4) 45

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50. A block slides down a rough incline (angle 30°) with coefficient of friction μ=0.2. Take g=9.8 m/s². Acceleration down the plane is

1) 4.9 m/s²

2) 3.2 m/s²

3) 0 m/s²

4) 6.6 m/s²

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51. Evaluate: ∫_0^1 6x(1−x) dx.

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52. For a projectile (no air resistance), time of flight depends on

1) Initial speed only (independent of angle)

2) Initial speed and angle (and g)

3) Mass of projectile

4) Horizontal range only

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53. If a matrix A is singular, then

1) A^-1 exists

2) A is always diagonal

3) trace(A)=0

4) det(A)=0

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54. Match the conic (List-I) with the standard form (List-II).

1. Ellipse

2. Parabola

3. Circle

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55. Which oxide is amphoteric?

1) CO2

2) SO3

3) Na2O

4) Al2O3

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56. Which of the following is a stronger acid in aqueous solution?

1) H2CO3

2) CH3COOH

3) HClO

4) HClO4

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57. Select all correct statements about redox reactions (Set-02):

1) Oxidizing agent itself gets oxidized.

2) Oxidation involves increase in oxidation number.

3) Reduction involves gain of electrons.

4) Reducing agent itself gets oxidized.

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58. Find the remainder when (32^2 + 16) is divided by 14.

1) 5

2) 4

3) 7

4) 6

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59. Select all correct statements about capacitors in series (Set-02):

1) Equivalent capacitance is less than the smallest individual capacitance.

2) Charge on each capacitor is same in series combination.

3) Total potential difference is sum of individual potential differences.

4) Potential difference across each capacitor is same in series combination.

60 / 108

60. Select all correct statements about ideal transformers (Set-02):

1) Power input equals power output (no losses).

2) In ideal transformer, current ratio is inverse of turns ratio (Ip/Is = Ns/Np).

3) Voltage ratio equals turns ratio (Vp/Vs = Np/Ns).

4) Transformer works on electrostatic induction.

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61. In BCC lattice, number of atoms per unit cell is

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62. If a vector has components (2,3,6), find its magnitude (rounded to 2 decimals).

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63. Which statement best describes a catalyst?

1) It is consumed stoichiometrically

2) It increases equilibrium constant

3) It increases rate by lowering activation energy

4) It increases ΔH of reaction

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64. A wave travels with speed 360 m/s and frequency 120 Hz. Wavelength (m) is

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65. Match the physical situation (List-I) with the corresponding principle (List-II).

1. Closed path integral of electrostatic field

2. Induced current opposes change

3. No net external force on a system

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66. The pH of a 10^-3 M strong acid solution is closest to

1) 1

2) 3

3) 7

4) 11

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67. Select all correct statements for a body in SHM (Set-02):

1) Acceleration is proportional to displacement and opposite in direction.

2) Speed is maximum at equilibrium position.

3) Time period is independent of amplitude (for ideal SHM).

4) Total energy changes with time in ideal SHM.

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68. Match (List-I) with the correct trend (List-II).

1. Ionization energy down a group

2. Atomic radius across a period

3. Electronegativity down a group

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69. Select all correct statements about logarithms (Set-02):

1) log(a+b)=log a + log b always.

2) log(a^k)=k log a (a>0).

3) log 1 = 0 (any base).

4) log(ab)=log a + log b (same base).

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70. Number of onto functions from a set of 8 elements to a set of 2 elements is

1) 256

2) 256

3) 2

4) 254

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71. If P(A)=0.4 and P(B)=0.25 and independent, compute P(A∩B).

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72. Masses 2 kg and 3 kg move along a line with speeds 14 m/s and 8 m/s in same direction. They stick together. Final speed is

1) 10.4 m/s

2) 11.0 m/s

3) 22 m/s

4) 0.8 m/s

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73. For ideal gas: n=1 mol, T=300 K, R=0.082 L·atm/mol·K. Find PV (L·atm).

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74. Compute the value of 12C3.

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75. Number of diagonals in a convex polygon with 13 sides is

1) 65

2) 78

3) 10

4) 66

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76. Match the matrix property (List-I) with the implication (List-II).

1. A is identity

2. A is singular

3. det(A)≠0

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77. Match the quantity (List-I) with its SI unit (List-II).

1. Capacitance

2. Electric potential

3. Magnetic field B

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78. A mass 2.0 kg is raised vertically by 10 m (take g=9.8). Increase in potential energy is

1) 20.0 J

2) 20.0 J

3) 98.0 J

4) 196.0 J

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79. A lens has focal length 20 cm. Power (D) is

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80. Select all correct statements about projectile motion (Set-02):

1) At highest point, acceleration becomes zero.

2) Horizontal component of velocity remains constant.

3) Vertical acceleration is constant and equals g downward.

4) Time to reach highest point depends on initial vertical component.

81 / 108

81. Equation of the circle with center (5,7) and radius 5 is

1) (x−5)+(y−7)=25

2) (x−5)^2+(y−7)^2=25

3) (x−5)^2+(y−7)^2=5

4) (x+5)^2+(y+7)^2=25

82 / 108

82. Select all correct statements about limits (Set-02):

1) If lim x→a f(x) exists, then f(a) must be defined.

2) If lim x→a f(x)=L and lim x→a g(x)=M, then lim x→a (f(x)+g(x))=L+M.

3) If f is continuous at a, then lim x→a f(x)=f(a).

4) If lim x→a f(x) exists, left and right limits at a are equal.

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83. Calculate molarity when 0.25 mol solute is dissolved to make 0.50 L solution.

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84. Match (List-I) with the correct statement (List-II).

1. Equilibrium constant K

2. Rate constant k

3. Catalyst

85 / 108

85. Compute: lim_{x→0} (sin 5x)/x.

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86. Select all correct statements about functions (Set-02):

1) Every one-one function is onto.

2) Composition of two one-one functions is one-one.

3) If a function is onto, every element of codomain has a preimage.

4) If a function is one-one, distinct inputs give distinct outputs.

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87. Select all correct statements about electric field lines (Set-02):

1) Density of field lines indicates field strength.

2) Field lines are always closed loops in electrostatics.

3) Electric field lines start on positive charges and end on negative charges (or infinity).

4) Two electric field lines can never intersect.

88 / 108

88. If P(A)=0.3, P(B)=0.5 and A,B are independent, then P(A∪B) equals

1) 0.8

2) 0.65

3) 0.15

4) 0.2

89 / 108

89. The number of atoms per unit cell in a BCC lattice is

1) 4

2) 2

3) 1

4) 6

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90. An inductor of inductance 0.6 H carries current 6 A. Energy stored is

1) 0.1 J

2) 10.0 J

3) 10.8 J

4) 3.6 J

91 / 108

91. A circle has radius 7. Its area (in terms of π) equals

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92. Which statement is correct for a capacitor connected to a DC source after a long time?

1) It behaves as a short circuit

2) Voltage across it is zero

3) Charge on it is zero

4) It behaves as an open circuit (no steady current)

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93. A particle executes SHM with amplitude A=0.04 m and angular frequency ω=25 rad/s. Its maximum speed is

1) 25.0 m/s

2) 1.0 m/s

3) 625.0 m/s

4) 0.0016 m/s

94 / 108

94. Select all correct statements about colligative properties (Set-02):

1) Viscosity is a colligative property.

2) Osmotic pressure is a colligative property.

3) Freezing point depression depends on molality.

4) Boiling point elevation depends on number of solute particles.

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95. If the roots of x^2−7x+10=0 are α,β, compute α^2+β^2.

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96. Let f(x)=ax+b with a=2, b=3. If f(f(x)) = 4x + 9, then a equals

1) 3

2) 2

3) 1

4) 3

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97. In SN2 reactions, stereochemistry at the chiral center typically shows

1) Retention of configuration

2) Racemization always

3) No effect on stereochemistry

4) Inversion of configuration

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98. Which polymer is an addition polymer?

1) Polyethylene

2) Nylon-6,6

3) Bakelite

4) Terylene

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99. Value of determinant |1 1 1; 1 5 1; 1 1 5| is

1) 113

2) 25

3) 112

4) 64

100 / 108

100. Select all correct statements about photons (Set-02):

1) Photoelectric threshold depends on material.

2) Increasing intensity increases photon energy at fixed frequency.

3) Photon energy is proportional to frequency.

4) Photon momentum is p=E/c.

101 / 108

101. Monochromatic light of wavelength 450 nm has photon energy (use 1240 eV·nm).

1) 2.76 eV

2) 1.38 eV

3) 5.51 eV

4) 450 eV

102 / 108

102. If pOH=5, pH is

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103. Number of moles in 12 g of a substance with molar mass 98 g/mol (rounded to 3 decimals) is

1) 0.012

2) 0.122

3) 8.167

4) 1.220

104 / 108

104. A 2 kg block is pulled horizontally with force 14 N on a frictionless surface. Find acceleration (m/s²).

105 / 108

105. A conducting loop is moved out of a uniform magnetic field region with constant speed. The induced emf is non-zero because

1) Magnetic flux through the loop changes with time

2) Resistance of loop changes

3) Electric field outside is zero

4) Area of loop changes randomly

106 / 108

106. Match (List-I) with the correct test (List-II).

1. Aldehyde group

2. Methyl ketone

3. Unsaturation (C=C)

107 / 108

107. Select all correct statements about thermodynamics (Set-02):

1) ΔU = q + w (work done on system positive).

2) State functions depend only on initial and final states.

3) For an isothermal process of ideal gas, ΔU=0.

4) Entropy of the universe always decreases for a spontaneous process.

108 / 108

108. Number of σ-bonds in ethane (C2H6) is

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