JEE MAINS TYPE 3 - Start Exam

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JEE MAINS TYPE 3

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1 / 75

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

1) x^2 e^x

2) e^x(2x)

3) e^x(x^2−2x)

4) e^x(x^2+2x)

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2. 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) 40 m/s

4) 10 m/s

3 / 75

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

4 / 75

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

1) 8.5

2) 9

3) 10.5

4) 8

5 / 75

5. If a·b=0, then vectors a and b are

1) Perpendicular

2) Collinear but opposite

3) Parallel

4) Equal

6 / 75

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

7 / 75

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

1) 300 J

2) 30 J

3) 7 J

4) 13 J

8 / 75

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

1) 35

2) 28

3) 32

4) 30

9 / 75

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

1) 35

2) 21

3) 70

4) 28

10 / 75

10. The energy of a photon is given by

1) hf

2) h/f

3) hc

4) fc

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11. AlCl3 acts as a Lewis acid because it

1) Accepts an electron pair

2) Donates an electron pair

3) Donates H+

4) Accepts OH-

12 / 75

12. Value of (1+tan^2θ) equals

1) cos^2θ

2) cosec^2θ

3) sec^2θ

4) 1−tan^2θ

13 / 75

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

1) Everywhere same

2) Extreme position

3) Mean position

4) Only after one period

14 / 75

14. Which reagent distinguishes aldehyde from ketone?

1) NaCl

2) Tollens’ reagent

3) H2O

4) Conc. H2SO4

15 / 75

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

16 / 75

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

17 / 75

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

1) y = x^3 + C

2) y = 3x^3 + C

3) y = x^2 + C

4) y = 3x + C

18 / 75

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

19 / 75

19. Unit of rate constant for second order reaction is

1) s^-1

2) dimensionless

3) L mol^-1 s^-1

4) mol L^-1 s^-1

20 / 75

20. 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

21 / 75

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

1) NaCl

2) CH4

3) [Co(NH3)6]Cl3

4) H2O

22 / 75

22. A diode allows current mainly in

1) One direction

2) Both directions equally

3) No direction

4) Only AC

23 / 75

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

1) 120

2) 60

3) 720

4) 210

24 / 75

24. The gas that turns lime water milky is

1) N2

2) CO2

3) O2

4) H2

25 / 75

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

26 / 75

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

27 / 75

27. Hybridization of carbon in ethyne (C2H2) is

1) dsp2

2) sp

3) sp2

4) sp3

28 / 75

28. pH of 1×10^-2 M HCl is

1) 7

2) 1

3) 2

4) 12

29 / 75

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

1) 3 A

2) 0.33 A

3) 48 A

4) 16 A

30 / 75

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

1) 2

2) 1

3) 4

4) 3

31 / 75

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

1) 2

2) 4

3) 3

4) 1

32 / 75

32. Moment of force is also known as

1) Impulse

2) Torque

3) Energy

4) Power

33 / 75

33. If 3x−7=20, find x.

34 / 75

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

1) 22

2) 18

3) 14

4) 16

35 / 75

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

1) Path function

2) Vector quantity

3) State function

4) Intensive only

36 / 75

36. SI unit of power is

1) Newton

2) Joule

3) Watt

4) Pascal

37 / 75

37. Which is NOT a transition element?

1) Cu

2) Fe

3) Ni

4) Zn

38 / 75

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

1) Hysteresis loss

2) Magnetic flux

3) Copper loss

4) Eddy current loss

39 / 75

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

1) 7

2) 6

3) 5

4) 4

40 / 75

40. IUPAC name of CH3-CH2-CHO is

1) Ethanal

2) Propanol

3) Propanal

4) Propanone

41 / 75

41. Which compound shows cis-trans isomerism?

1) CH4

2) CHCl=CHCl

3) CH3-CH2-OH

4) CH3-CH3

42 / 75

42. Photoelectric effect supports the concept of

1) Newton's laws

2) Wave nature only

3) Photon nature of light

4) Sound waves

43 / 75

43. Bond angle in NH3 is approximately

1) 120°

2) 180°

3) 107°

4) 90°

44 / 75

44. Molarity of pure water is approximately

1) 1000

2) 1

3) 18

4) 55.5

45 / 75

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

46 / 75

46. lim_{x→0} (sin 5x)/(x) equals

1) 1

2) 5

3) 0

4) 10

47 / 75

47. For uniform circular motion, acceleration is directed

1) Along velocity

2) Towards the center

3) Away from center

4) Zero

48 / 75

48. For an ideal gas, PV is proportional to

1) Temperature

2) Pressure

3) Mass

4) Volume

49 / 75

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

1) qE

2) q+E

3) q/E

4) E/q

50 / 75

50. The major product of hydration of ethene is

1) Ethane

2) Ethanal

3) Ethanoic acid

4) Ethanol

51 / 75

51. Oxidation state of Mn in KMnO4 is

1) +4

2) +2

3) +6

4) +7

52 / 75

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

53 / 75

53. Inelastic collision conserves

1) Both momentum and KE

2) Kinetic energy

3) Momentum

4) Neither

54 / 75

54. In galvanic cell, oxidation occurs at

1) Anode

2) Electrolyte

3) Cathode

4) Salt bridge

55 / 75

55. Evaluate: 8! / (6!)

56 / 75

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

1) 1/12

2) 1/9

3) 1/3

4) 1/6

57 / 75

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

1) (a,0)

2) (0,−a)

3) (0,a)

4) (−a,0)

58 / 75

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

59 / 75

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

1) sin θ

2) tan θ

3) sec θ

4) cos θ

60 / 75

60. Which is a strong electrolyte?

1) Urea

2) NaCl

3) Glucose

4) Sucrose

61 / 75

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

1) Mass increases

2) Shielding increases

3) Valence electrons decrease

4) Effective nuclear charge increases

62 / 75

62. Oxidation state of O in H2O2 is

63 / 75

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

1) Becomes zero always

2) Decreases

3) Remains same

4) Increases

64 / 75

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

1) On same side always

2) No image formed

3) On the opposite side of lens

4) At focus always

65 / 75

65. Dimensional formula of electric potential (volt) is

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

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

3) MLT^-2

4) ML^2T^-2

66 / 75

66. ∫ 2x/(1+x^2) dx equals

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

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

3) arctan x + C

4) 1/(1+x^2)+C

67 / 75

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

1) -2

2) -1

3) 2

4) -4

68 / 75

68. Let z=1−2i. Then |z|² equals

1) 5

2) 9

3) 3

4) 4

69 / 75

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

1) 5 Ω

2) 6 Ω

3) 1.2 Ω

4) 0.5 Ω

70 / 75

70. The quadratic x²−6x+9=0 has

1) Two distinct complex roots

2) No real roots

3) Two equal real roots

4) Two distinct real roots

71 / 75

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

1) (x−1)^2 + (y−2)^2 = 3

2) (x+1)^2 + (y−2)^2 = 9

3) x^2+y^2=9

4) (x−1)^2 + (y+2)^2 = 9

72 / 75

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

73 / 75

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

74 / 75

74. Which is the correct order of bond length?

1) Double > Single > Triple

2) Triple > Double > Single

3) All equal

4) Single > Double > Triple

75 / 75

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

1) Second order

2) Third order

3) Zero order

4) First order

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