JEE Main PYQs on Capacitance: JEE Main Questions for Practice with Solutions

JEE Main Questions

• 1.

  A body of mass \(4\) kg is placed at a point \(P\) having coordinates \( (3,4) \) m. Under the action of force \( \mathbf{F} = (2\hat{i} + 3\hat{j}) \) N, it moves to a new point \(Q\) having coordinates \( (6,10) \) m in \(4\) sec. The average power and instantaneous power at the end of \(4\) sec are in the ratio:

  • \( 1:2 \)
    
  • \( 6:13 \)
    
  • \( 4:3 \)
    
  • \( 13:6 \)
    
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• 2.

  Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). 

  Assertion (A): Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged. 

  Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \( \frac{R}{\sqrt{R^2 + \omega^2 L^2}} \), where \( \omega \) is the frequency of the supply across resistor \( R \) and inductor \( L \). If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.

  In light of the above statements, choose the most appropriate answer from the options given below:

  • Both (A) and (R) are true and (R) is the correct explanation of (A)
    
  • (A) is false but (R) is true
    
  • Both (A) and (R) are true but (R) is not the correct explanation of (A)
    
  • (A) is true but (R) is false
    
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• 3.

  The motion of an airplane is represented by the velocity-time graph as shown below. The distance covered by the airplane in the first 30.5 seconds is                km.

  

  • 9
    
  • 6
    
  • 3
    
  • 12
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• 4.

  An AC current is represented as: $ i = 5\sqrt{2} + 10 \cos\left(650\pi t + \frac{\pi}{6}\right) \text{ Amp} $ The RMS value of the current is:

  • 50 Amp
  • 100 Amp
  • 10 Amp
  • \( 5\sqrt{2} \) Amp
    
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• 5.

  A bar magnet has total length \( 2l = 20 \) units and the field point \( P \) is at a distance \( d = 10 \) units from the centre of the magnet. If the relative uncertainty of length measurement is 1%, then the uncertainty of the magnetic field at point P is:
  

  

  • 10%
    
  • 4%
    
  • 5%
    
  • 3%
    
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• 6.

  The increase in pressure required to decrease the volume of a water sample by 0.2percentage is \( P \times 10^5 \, \text{Nm}^{-2} \). Bulk modulus of water is \( 2.15 \times 10^9 \, \text{Nm}^{-2} \). The value of \( P \) is ________________.

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