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

JEE Main Questions

• 1.

  A monoatomic anion (A⁻) has 45 neutrons and 36 electrons. Atomic mass, group in the periodic table and physical state at room temperature of the element (A) respectively are
  

  • 80, 17, liquid
    
  • 81, 16, solid
    
  • 80, 16, gas
    
  • 81, 15, gas
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• 2.

  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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• 3.

  Let \( f(x) = \begin{cases} x^3 + 8 & x < 0 \\ x^2 - 4 & x \ge 0 \end{cases} \) and \( g(x) = \begin{cases} (x-8)^{1/3} & x < 0 \\ (x+4)^{1/2} & x \ge 0 \end{cases} \) then find number of points of discontinuity of \( g(f(x)) \).
  

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• 4.

  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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• 5.

  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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• 6.

  A river of width 200 m is flowing from west to east with a speed of 18 km/h. A boat, moving with speed of 36 km/h in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are _________ and _________} respectively.

  • 20 s and 100 m
  • 40 s and 100 m
  • 40 s and 0 m
  • 40 s and 200 m
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