JEE MAINS TYPE 3

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JEE MAINS TYPE 3

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1 / 75

1. The quadratic x²−6x+9=0 has

1) Two distinct complex roots

2) Two equal real roots

3) No real roots

4) Two distinct real roots

2 / 75

2. Unit of rate constant for second order reaction is

1) dimensionless

2) mol L^-1 s^-1

3) L mol^-1 s^-1

4) s^-1

3 / 75

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

1) q+E

2) qE

3) E/q

4) q/E

4 / 75

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

1) Intensive only

2) Path function

3) Vector quantity

4) State function

5 / 75

5. The gas that turns lime water milky is

1) N2

2) CO2

3) H2

4) O2

6 / 75

6. A diode allows current mainly in

1) No direction

2) Both directions equally

3) Only AC

4) One direction

7 / 75

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

1) 18

2) 14

3) 16

4) 22

8 / 75

8. Bond angle in NH3 is approximately

1) 180°

2) 90°

3) 107°

4) 120°

9 / 75

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

10 / 75

10. Molarity of pure water is approximately

1) 1000

2) 18

3) 55.5

4) 1

11 / 75

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

1) Hysteresis loss

2) Copper loss

3) Eddy current loss

4) Magnetic flux

12 / 75

12. Hybridization of carbon in ethyne (C2H2) is

1) sp2

2) sp3

3) dsp2

4) sp

13 / 75

13. Which compound shows cis-trans isomerism?

1) CH3-CH2-OH

2) CHCl=CHCl

3) CH4

4) CH3-CH3

14 / 75

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).

15 / 75

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

1) H2O

2) NaCl

3) CH4

4) [Co(NH3)6]Cl3

16 / 75

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

17 / 75

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

1) Increases

2) Becomes zero always

3) Remains same

4) Decreases

18 / 75

18. ∫ 2x/(1+x^2) dx equals

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

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

3) arctan x + C

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

19 / 75

19. Moment of force is also known as

1) Power

2) Impulse

3) Energy

4) Torque

20 / 75

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

1) 1

2) 2

3) 4

4) 3

21 / 75

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

1) 32

2) 35

3) 30

4) 28

22 / 75

22. Evaluate: 8! / (6!)

23 / 75

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

1) 1/3

2) 1/6

3) 1/9

4) 1/12

24 / 75

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

1) 28

2) 21

3) 70

4) 35

25 / 75

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

1) 720

2) 120

3) 210

4) 60

26 / 75

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

27 / 75

27. Which is the correct order of bond length?

1) Double > Single > Triple

2) Single > Double > Triple

3) All equal

4) Triple > Double > Single

28 / 75

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

1) Extreme position

2) Everywhere same

3) Only after one period

4) Mean position

29 / 75

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

1) 300 J

2) 13 J

3) 7 J

4) 30 J

30 / 75

30. The major product of hydration of ethene is

1) Ethanoic acid

2) Ethane

3) Ethanol

4) Ethanal

31 / 75

31. Oxidation state of O in H2O2 is

32 / 75

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

1) sin θ

2) sec θ

3) cos θ

4) tan θ

33 / 75

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

1) Perpendicular

2) Collinear but opposite

3) Parallel

4) Equal

34 / 75

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

1) 1.2 Ω

2) 5 Ω

3) 6 Ω

4) 0.5 Ω

35 / 75

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

36 / 75

36. 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

37 / 75

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

38 / 75

38. Let z=1−2i. Then |z|² equals

1) 4

2) 9

3) 5

4) 3

39 / 75

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

1) e^x(x^2+2x)

2) e^x(2x)

3) x^2 e^x

4) e^x(x^2−2x)

40 / 75

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

41 / 75

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

1) Effective nuclear charge increases

2) Mass increases

3) Shielding increases

4) Valence electrons decrease

42 / 75

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

43 / 75

43. AlCl3 acts as a Lewis acid because it

1) Donates H+

2) Accepts an electron pair

3) Donates an electron pair

4) Accepts OH-

44 / 75

44. Oxidation state of Mn in KMnO4 is

1) +2

2) +6

3) +7

4) +4

45 / 75

45. pH of 1×10^-2 M HCl is

1) 2

2) 12

3) 1

4) 7

46 / 75

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

1) On same side always

2) At focus always

3) No image formed

4) On the opposite side of lens

47 / 75

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

1) Current decreases

2) Number of turns decreases

3) Radius increases

4) Current increases

48 / 75

48. The energy of a photon is given by

1) hf

2) h/f

3) fc

4) hc

49 / 75

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

50 / 75

50. SI unit of power is

1) Watt

2) Joule

3) Pascal

4) Newton

51 / 75

51. In galvanic cell, oxidation occurs at

1) Cathode

2) Anode

3) Electrolyte

4) Salt bridge

52 / 75

52. Value of (1+tan^2θ) equals

1) sec^2θ

2) cos^2θ

3) cosec^2θ

4) 1−tan^2θ

53 / 75

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

54 / 75

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

1) 3

2) 2

3) 4

4) 1

55 / 75

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

56 / 75

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

1) 0.33 A

2) 48 A

3) 3 A

4) 16 A

57 / 75

57. Which is NOT a transition element?

1) Zn

2) Ni

3) Fe

4) Cu

58 / 75

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

1) 10.5

2) 8

3) 9

4) 8.5

59 / 75

59. For uniform circular motion, acceleration is directed

1) Along velocity

2) Towards the center

3) Zero

4) Away from center

60 / 75

60. IUPAC name of CH3-CH2-CHO is

1) Propanol

2) Propanal

3) Ethanal

4) Propanone

61 / 75

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

1) Third order

2) First order

3) Zero order

4) Second order

62 / 75

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

1) (−a,0)

2) (0,a)

3) (a,0)

4) (0,−a)

63 / 75

63. If 3x−7=20, find x.

64 / 75

64. lim_{x→0} (sin 5x)/(x) equals

1) 0

2) 5

3) 1

4) 10

65 / 75

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

1) y = 3x^3 + C

2) y = x^3 + C

3) y = 3x + C

4) y = x^2 + C

66 / 75

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

1) 7

2) 5

3) 6

4) 4

67 / 75

67. Which reagent distinguishes aldehyde from ketone?

1) Conc. H2SO4

2) NaCl

3) H2O

4) Tollens’ reagent

68 / 75

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

69 / 75

69. Dimensional formula of electric potential (volt) is

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

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

3) ML^2T^-2

4) MLT^-2

70 / 75

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

1) x^2+y^2=9

2) (x+1)^2 + (y−2)^2 = 9

3) (x−1)^2 + (y+2)^2 = 9

4) (x−1)^2 + (y−2)^2 = 3

71 / 75

71. Photoelectric effect supports the concept of

1) Newton's laws

2) Sound waves

3) Photon nature of light

4) Wave nature only

72 / 75

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

1) -2

2) -1

3) 2

4) -4

73 / 75

73. Inelastic collision conserves

1) Kinetic energy

2) Momentum

3) Both momentum and KE

4) Neither

74 / 75

74. Which is a strong electrolyte?

1) Sucrose

2) Glucose

3) Urea

4) NaCl

75 / 75

75. For an ideal gas, PV is proportional to

1) Mass

2) Temperature

3) Pressure

4) Volume

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