JEE MAINS TYPE 3 - Start Exam

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JEE MAINS TYPE 3

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1 / 75

1. Dimensional formula of electric potential (volt) is

1) ML^2T^-2

2) M^0L^2T^-3A^-1

3) ML^2T^-3A^-1

4) MLT^-2

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2. For reaction A→Products, if rate = k[A], order is

1) First order

2) Zero order

3) Third order

4) Second order

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3. Coefficient of x^3 in (1+x)^7 is

1) 21

2) 35

3) 70

4) 28

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4. If a_n = 3n+2, then a_10 equals

1) 30

2) 35

3) 28

4) 32

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5. Equation of circle centered at (1,−2) with radius 3 is

1) (x−1)^2 + (y+2)^2 = 9

2) x^2+y^2=9

3) (x−1)^2 + (y−2)^2 = 3

4) (x+1)^2 + (y−2)^2 = 9

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6. If a body starts from rest and moves with acceleration 4 m/s^2 for 5 s, its speed is

1) 25 m/s

2) 20 m/s

3) 10 m/s

4) 40 m/s

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7. Molarity of pure water is approximately

1) 1000

2) 18

3) 1

4) 55.5

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8. A diode allows current mainly in

1) Only AC

2) Both directions equally

3) One direction

4) No direction

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9. A 2 Ω and 3 Ω resistors are in series. Equivalent resistance is

1) 6 Ω

2) 0.5 Ω

3) 1.2 Ω

4) 5 Ω

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10. Which is the correct order of bond length?

1) Double > Single > Triple

2) All equal

3) Single > Double > Triple

4) Triple > Double > Single

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11. Magnetic field at the center of a circular current loop increases if

1) Radius increases

2) Number of turns decreases

3) Current decreases

4) Current increases

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12. SI unit of power is

1) Newton

2) Watt

3) Joule

4) Pascal

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13. Find the value of C(9,2).

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14. For ideal gas, PV=nRT. If n=1 mol, T=300 K, R=0.082 L·atm/mol·K, find PV (in L·atm).

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15. If y = x^2 * e^x, then dy/dx equals

1) x^2 e^x

2) e^x(x^2−2x)

3) e^x(x^2+2x)

4) e^x(2x)

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16. If f(x)=2x+1, then f^{-1}(5) equals

1) 4

2) 1

3) 2

4) 3

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17. Which is NOT a transition element?

1) Ni

2) Fe

3) Cu

4) Zn

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18. A lens has focal length 20 cm. Find its power (in dioptres). (Use f in metres)

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19. The quadratic x²−6x+9=0 has

1) Two distinct complex roots

2) Two distinct real roots

3) Two equal real roots

4) No real roots

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20. In galvanic cell, oxidation occurs at

1) Anode

2) Salt bridge

3) Electrolyte

4) Cathode

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21. lim_{x→0} (sin 5x)/(x) equals

1) 10

2) 1

3) 5

4) 0

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22. Which of the following is an example of a coordination compound?

1) [Co(NH3)6]Cl3

2) H2O

3) CH4

4) NaCl

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23. Number of ways to choose 3 students from 10 is

1) 720

2) 120

3) 210

4) 60

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24. General solution of dy/dx = 3x^2 is

1) y = 3x^3 + C

2) y = x^3 + C

3) y = x^2 + C

4) y = 3x + C

25 / 75

25. ∫ 2x/(1+x^2) dx equals

1) 2ln(1+x^2)+C

2) ln(1+x^2)+C

3) 1/(1+x^2)+C

4) arctan x + C

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26. If n(A)=8 and n(B)=11 with n(A∩B)=3, then n(A∪B) equals

1) 14

2) 22

3) 16

4) 18

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27. If a circle has radius 7, find its diameter.

28 / 75

28. Calculate molar mass of H2O (in g/mol).

29 / 75

29. Work done by a constant force 10 N in displacing 3 m along the force is

1) 7 J

2) 30 J

3) 13 J

4) 300 J

30 / 75

30. Probability of getting sum 7 when two fair dice are thrown is

1) 1/9

2) 1/3

3) 1/6

4) 1/12

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31. Number of neutrons in 23Na (atomic number 11) is

32 / 75

32. If 3x−7=20, find x.

33 / 75

33. pH of 1×10^-2 M HCl is

1) 2

2) 7

3) 1

4) 12

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34. In a transformer, the core is laminated to reduce

1) Hysteresis loss

2) Copper loss

3) Eddy current loss

4) Magnetic flux

35 / 75

35. Bond angle in NH3 is approximately

1) 90°

2) 120°

3) 107°

4) 180°

36 / 75

36. Unit of rate constant for second order reaction is

1) L mol^-1 s^-1

2) mol L^-1 s^-1

3) s^-1

4) dimensionless

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37. For an ideal gas, PV is proportional to

1) Temperature

2) Pressure

3) Mass

4) Volume

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38. Value of (1+tan^2θ) equals

1) cosec^2θ

2) 1−tan^2θ

3) cos^2θ

4) sec^2θ

39 / 75

39. The gas that turns lime water milky is

1) CO2

2) N2

3) H2

4) O2

40 / 75

40. Which reagent distinguishes aldehyde from ketone?

1) NaCl

2) Conc. H2SO4

3) H2O

4) Tollens’ reagent

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41. For parabola y^2 = 4ax, the focus is

1) (0,−a)

2) (−a,0)

3) (0,a)

4) (a,0)

42 / 75

42. The force on a charge q in electric field E is

1) E/q

2) qE

3) q+E

4) q/E

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43. Distance between points (1,2,3) and (4,6,3) equals

1) 5

2) 7

3) 4

4) 6

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44. Oxidation state of O in H2O2 is

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45. Slope of the line passing through (2,3) and (6,11) is

1) 1

2) 4

3) 2

4) 3

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46. The energy of a photon is given by

1) hf

2) fc

3) h/f

4) hc

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47. A charge of 2 C is moved through potential difference 6 V. Find work done (J).

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48. A projectile is launched at angle θ with speed u. Time of flight is proportional to

1) sec θ

2) sin θ

3) cos θ

4) tan θ

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49. A convex lens forms a real image of an object placed beyond focus. The image is formed

1) On the opposite side of lens

2) On same side always

3) At focus always

4) No image formed

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50. Inelastic collision conserves

1) Neither

2) Momentum

3) Kinetic energy

4) Both momentum and KE

51 / 75

51. The major product of hydration of ethene is

1) Ethanal

2) Ethane

3) Ethanol

4) Ethanoic acid

52 / 75

52. IUPAC name of CH3-CH2-CHO is

1) Ethanal

2) Propanol

3) Propanone

4) Propanal

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53. A body travels 60 m in 5 s with constant speed. Find speed (m/s).

54 / 75

54. Mean of numbers 4, 7, 10, 13 is

1) 10.5

2) 8.5

3) 8

4) 9

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55. If V=IR, then current in a 4 Ω resistor with 12 V across it is

1) 0.33 A

2) 48 A

3) 16 A

4) 3 A

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56. Hess’s law is based on the fact that enthalpy is a

1) Intensive only

2) Vector quantity

3) Path function

4) State function

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57. If a·b=0, then vectors a and b are

1) Perpendicular

2) Parallel

3) Equal

4) Collinear but opposite

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58. Moment of force is also known as

1) Energy

2) Impulse

3) Power

4) Torque

59 / 75

59. Let z=1−2i. Then |z|² equals

1) 5

2) 4

3) 3

4) 9

60 / 75

60. Photoelectric effect supports the concept of

1) Photon nature of light

2) Wave nature only

3) Newton's laws

4) Sound waves

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61. Oxidation state of Mn in KMnO4 is

1) +7

2) +6

3) +2

4) +4

62 / 75

62. Which compound shows cis-trans isomerism?

1) CH3-CH3

2) CH4

3) CH3-CH2-OH

4) CHCl=CHCl

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63. Determinant of [[2,3],[4,5]] equals

1) -1

2) -4

3) 2

4) -2

64 / 75

64. If 0.5 mol of NaCl is dissolved to make 1 L solution, find molarity.

65 / 75

65. For uniform circular motion, acceleration is directed

1) Towards the center

2) Away from center

3) Along velocity

4) Zero

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66. If frequency of a wave increases while speed stays same, wavelength

1) Remains same

2) Increases

3) Decreases

4) Becomes zero always

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67. A force of 12 N acts on mass 3 kg. Find acceleration (m/s^2).

68 / 75

68. In periodic table, atomic radius generally decreases across a period because

1) Effective nuclear charge increases

2) Shielding increases

3) Valence electrons decrease

4) Mass increases

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69. For a simple harmonic oscillator, maximum speed occurs at

1) Mean position

2) Extreme position

3) Everywhere same

4) Only after one period

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70. A 5 Ω resistor is connected to 10 V. Find current (in A).

71 / 75

71. Which is a strong electrolyte?

1) Sucrose

2) Urea

3) Glucose

4) NaCl

72 / 75

72. Evaluate: 8! / (6!)

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73. AlCl3 acts as a Lewis acid because it

1) Accepts OH-

2) Donates an electron pair

3) Accepts an electron pair

4) Donates H+

74 / 75

74. Hybridization of carbon in ethyne (C2H2) is

1) sp2

2) sp3

3) sp

4) dsp2

75 / 75

75. If the arithmetic mean of 5 numbers is 18, find their sum.

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