JEE Mains 2026 April 7 Shift 2 B.Planning Question Paper with Solutions PDF

JEE Main Questions

• 1.

  A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field $\vec{E}_1 = E_0 \hat{x}$. If another electric field $\vec{E}_2 = 2E_0 (\hat{y} + \hat{z})$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?
  

  • 73%
    
  • 63%
    
  • 83%
    
  • 53%
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• 2.

  An unpolarised light is incident at an interface of two dielectric media having refractive indices of $2$ (incident medium) and $2\sqrt{3}$ (refracted medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is ___.
  

  • $45^\circ$
  • $30^\circ$
  • $10^\circ$
  • $60^\circ$ 

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• 3.

  19.5 g of fluoro acetic acid (molar mass = 78 g mol\(^{-1}\)) is dissolved in 500 g of water at 298 K. The depression in the freezing point of water was \(1^\circ C\). What is \(K_a\) of fluoro acetic acid? (For water, \(K_f = 1.86\, K\,kg\,mol^{-1}\)). Assume molarity and molality to have same values.

  • \(10^{-6}\)
    
  • \(4\times10^{-4}\)
    
  • \(3\times10^{-5}\)
    
  • \(3\times10^{-3}\)
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• 4.

  Let \(O\) be the vertex of the parabola \(y^2 = 4x\). Let \(P\) and \(Q\) be two points on parabola such that chords \(OP\) and \(OQ\) are perpendicular to each other. If the locus of mid-point of segment \(PQ\) is a conic \(C\), then latus rectum of \(C\) is
  

  • 1
    
  • 2
    
  • 3
    
  • 4
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• 5.

  The figure shows a pipe with cross-section area 10 \( cm^2 \). Water flows from one end with velocity 20 cm/s. The other end of the pipe is closed and consists of 10 holes each of area 30 \( mm^2 \). Find the velocity of water coming out from each hole: 
  
  

  • 66 cm/s
    
  • 0.66 cm/s
    
  • 6.6 cm/s
    
  • 66 mm/s
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• 6.

  When 300 J of heat is given to an ideal gas with \( C_p = \frac{7}{2}R \), its temperature rises from 20°C to 50°C keeping its volume constant. The mass of the gas is (approximately) ______ g. (R = 8.314 J/mol K)
  

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