JEE MAINS TYPE 5 – Start Exam

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JEE MAINS TYPE 5

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1 / 75

1. For a reaction, ΔG° is related to equilibrium constant K by

1) ΔG° = R ln(K)/T

2) ΔG° = −RT ln K

3) ΔG° = RT ln K

4) ΔG° = −RT/K

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2. If vector v = 5i + 4j + 4k, then |v|^2 equals

1) 59

2) 55

3) 57

4) 13

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3. Number of atoms in 0.5 mol of He (use NA≈6.022×10^23) in scientific notation (×10^23) rounded to 3 decimals.

4 / 75

4. Equation of line with slope 4 passing through (5,3) is

1) y=4x+3

2) y−3 = 4(x−5)

3) y+3=4(x+5)

4) y−5=4(x−3)

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5. The focal length of a lens is 25 cm. The power (in dioptres) is

1) −4

2) 0.25

3) 4

4) 25

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6. Value of ∑_{r=1}^5 r is

1) 16

2) 15

3) 25

4) 14

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7. The SI unit of magnetic field B is

1) Tesla

2) Weber

3) Newton

4) Coulomb

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8. A force of 40 N acts on mass 8 kg. Find acceleration (m/s^2).

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9. The conjugate base of H2CO3 is

1) HCO3−

2) H3CO3+

3) H2CO3−

4) CO3^2−

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10. The shape of CO2 molecule is

1) Bent

2) Trigonal planar

3) Tetrahedral

4) Linear

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11. Coefficient of x^2 in (1+x)^9 is

1) 36

2) 9

3) 41

4) 84

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12. In coordination compounds, ligands donate

1) Neutrons

2) Protons

3) A pair of electrons

4) Only sigma bonds always

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13. Which quantum number determines the shape of an orbital?

1) Spin (s)

2) Principal (n)

3) Magnetic (m)

4) Azimuthal (l)

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14. In an AC circuit, the device that opposes change in current is

1) Resistor

2) Inductor

3) Capacitor

4) Ammeter

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15. lim_(x→0) (sin(8x))/x equals

1) 1

2) 0

3) 64

4) 8

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16. A body moving with constant speed in a circle has acceleration because

1) Mass changes

2) Time changes

3) Speed changes

4) Direction of velocity changes

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17. Derivative of sin x is

1) −sin x

2) −cos x

3) cos x

4) sin x

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18. If (x−2)(x−9)=0, find x^2 (when x is the larger root).

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19. A pure semiconductor at 0 K behaves as

1) Superconductor

2) Insulator

3) Conductor

4) Perfect resistor

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20. Sum of first 8 terms of AP with first term 6 and common difference 2 is

1) 104

2) 48

3) 102

4) 106

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21. Which quantity is scalar?

1) Acceleration

2) Velocity

3) Work

4) Force

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22. A body of mass 5 kg moves with speed 6 m/s. Find momentum (kg·m/s).

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23. Which is the correct increasing order of metallic character across period 3?

1) Mg < Na < Si < S < Cl

2) Cl < S < Si < Mg < Na

3) Si < S < Cl < Mg < Na

4) Na < Mg < Si < S < Cl

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24. The hybridization of central atom in SF6 is

1) sp3

2) sp3d2

3) dsp2

4) sp2

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25. If log_10(1000)=3, then log_10(10^5) equals

1) 15

2) 4

3) 5

4) 6

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26. For quadratic equation x^2 − 2x + 3 = 0, the discriminant (b^2−4ac) equals

1) -8

2) 8

3) -12

4) -4

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27. Evaluate: (15×14×13)/(3×2×1).

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28. A convex mirror always forms an image that is

1) Real and magnified

2) Virtual and magnified

3) Virtual and diminished

4) Real and inverted

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29. Which of the following is NOT a colligative property?

1) Freezing point depression

2) Boiling point elevation

3) Viscosity

4) Osmotic pressure

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30. Principal value of sin^{-1}(1) is

1) π/2

2) π

3) −π/2

4) 0

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31. If z = 5+1i, then conjugate of z is

1) −5+1i

2) 5+1i

3) −5−1i

4) 5−1i

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32. A capacitor C=5 μF is charged to V=20 V. Find energy stored in μJ.

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33. Oxidation state of N in NH4+ is

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34. Determinant of upper triangular matrix diag(3,3,5) is

1) 45

2) 14

3) 11

4) 9

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35. The de Broglie wavelength decreases when

1) Momentum increases

2) Mass decreases always

3) Momentum decreases

4) Speed decreases always

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36. Molarity when 0.75 mol solute is present in 1.5 L solution is

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37. If P(A)=0.6, P(B)=0.5 and A,B independent, then P(A|B) equals

1) 1.1

2) 0.5

3) 0.3

4) 0.6

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38. A wave has speed 340 m/s and wavelength 2 m. Find frequency (Hz).

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39. A fair coin is tossed 4 times. Number of outcomes is

1) 8

2) Option 3

3) Option 4

4) 16

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40. In SHM, total energy is proportional to

1) 1/Amplitude

2) Amplitude^2

3) Amplitude

4) Frequency only

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41. For an endothermic reaction, increasing temperature shifts equilibrium

1) Towards products

2) Stops reaction

3) Towards reactants

4) No effect

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42. Which of the following is a biodegradable polymer?

1) Polystyrene

2) PHBV

3) PVC

4) Teflon

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43. If a vector has components (3,4,12), find its magnitude (nearest integer).

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44. ∫ 9x^8 dx equals

1) 9x^9+C

2) x^8+C

3) x^9 + C

4) ln x + C

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45. The oxidation state of Cr in K2Cr2O7 is

1) +3

2) +2

3) +7

4) +6

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46. The correct order of bond strength is

1) Double > Single > Triple

2) All equal

3) Single > Double > Triple

4) Triple > Double > Single

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47. If y = x^3, find dy/dx at x=2.

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48. Circle x^2 + y^2 = 36 has radius

1) 6

2) 12

3) 5

4) 36

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49. Number of permutations of letters in word ‘LEVEL’ is

1) 30

2) Option 4

3) 120

4) 10

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50. The refractive index of a medium is maximum when speed of light in it is

1) Minimum

2) Maximum

3) Equal to c

4) Zero

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51. For parabola y^2 = 4ax, the directrix is

1) y = a

2) y = −a

3) x = a

4) x = −a

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52. If current through a wire doubles, the heat produced in same time (Joule’s law) becomes

1) Two times

2) Half

3) Four times

4) Eight times

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53. For a body in free fall (neglect air resistance), mechanical energy is

1) Always increases

2) Conserved

3) Always decreases

4) Not conserved

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54. Evaluate: ∫_1^2 (1/x) dx (rounded to 3 decimals).

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55. The strongest intermolecular force among the following is

1) London forces

2) Hydrogen bonding

3) Ion-induced dipole

4) Dipole-dipole

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56. In Young’s double slit experiment, fringe width is directly proportional to

1) Slit separation

2) Wavelength

3) 1/Screen distance

4) Refractive index

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57. Which of the following is an example of a buffer solution?

1) H2SO4 + Na2SO4

2) CH3COOH + CH3COONa

3) NaOH + NaCl

4) HCl + NaCl

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58. Which of the following is a Lewis base?

1) H+

2) BF3

3) NH3

4) AlCl3

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59. The work done by friction is generally

1) Negative

2) Depends only on mass

3) Positive always

4) Zero always

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60. SI unit of electric charge is

1) Ohm

2) Volt

3) Ampere

4) Coulomb

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61. For ideal gas, if n=2 mol, T=300 K, R=0.082 L·atm/mol·K, then PV (L·atm) is

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62. A 9 V battery is connected to a 3 Ω resistor. Find current (A).

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63. Trace of matrix [[4,1],[2,6]] is

1) 10

2) -2

3) 24

4) 2

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64. The order of reaction is equal to sum of

1) Powers of concentration terms in rate law

2) Activation energies

3) Moles of products

4) Stoichiometric coefficients

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65. If two forces act on a body and the net force is zero, the body must be

1) In equilibrium

2) Accelerating always

3) At rest only

4) Moving in circle always

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66. The equivalent capacitance of capacitors in series is

1) Less than smallest capacitance

2) Greater than largest

3) Sum of capacitances

4) Equal to average

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67. Midpoint of (4,6) and (8,10) is

1) (6.0,8.0)

2) (4,10)

3) (8,6)

4) (6.0,6)

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68. The momentum of a photon of energy E is

1) c/E

2) Ec

3) E^2/c

4) E/c

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69. pH of 1×10^-3 M HNO3 (strong acid, ideal) is

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70. The number of sigma bonds in benzene is

1) 6

2) 12

3) 15

4) 9

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71. The magnetic field lines inside a bar magnet are directed

1) Circular around north only

2) From north to south

3) From south to north

4) Random

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72. In electrolysis of molten NaCl, product at cathode is

1) Cl2

2) H2

3) NaCl

4) Na

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73. Which device measures potential difference?

1) Galvanometer only

2) Wattmeter

3) Voltmeter

4) Ammeter

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74. Which of the following is an example of SN1 reaction?

1) Tertiary alkyl halide hydrolysis

2) Addition to alkene

3) Primary alkyl halide with strong nucleophile

4) Elimination always

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75. Which of the following is a reducing agent?

1) H2

2) KMnO4

3) K2Cr2O7

4) O2

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