WBJEE 2023 Mathematics Question Paper with Answer Key PDF Download

WBJEE Questions

• 1.

  Three different liquids are filled in a U-tube as shown. Their densities are \( \rho_1, \rho_2, \rho_3 \) respectively. From the figure we may conclude that 
  

  • \( \rho_3 = 4(\rho_2 - \rho_1) \)
    
  • \( \rho_3 = 4(\rho_1 - \rho_2) \)
    
  • \( \rho_3 = 2(\rho_2 - \rho_1) \)
    
  • \( \rho_3 = \frac{\rho_1+\rho_2}{2} \)
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• 2.

  The variation of density of a solid cylindrical rod of cross-sectional area \( a \) and length \( L \) is \( \rho=\rho_0 \frac{x^2}{L^2} \), where \( x \) is the distance from one end. The position of its centre of mass from \( x=0 \) is 
  

  • \( \frac{2L}{3} \)
    
  • \( \frac{L}{2} \)
    
  • \( \frac{L}{3} \)
    
  • \( \frac{3L}{4} \)
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• 3.

  Six vectors \( \vec{a},\vec{b},\vec{c},\vec{d},\vec{e},\vec{f} \) have magnitudes and directions shown. Which statement is true? 
  

  • \( \vec{b}+\vec{e}=\vec{f} \)
    
  • \( \vec{b}+\vec{c}=\vec{f} \)
    
  • \( \vec{d}+\vec{c}=\vec{f} \)
    
  • \( \vec{d}+\vec{e}=\vec{f} \)
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• 4.

  Manufacturers supply a zener diode with zener voltage \( V_z=5.6\,\text{V} \) and maximum power dissipation \( P_{\max}=\frac14\,\text{W} \). This zener diode is used in the circuit shown. Calculate the minimum value of the resistance \( R_s \) so that the zener diode will not burn when the input voltage is \( V_{in}=10\,\text{V} \). 
  

  • \( 98.56\,\Omega \)
    
  • \( 170.52\,\Omega \)
    
  • \( 306.21\,\Omega \)
    
  • \( 412.37\,\Omega \)
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• 5.

  What are the charges stored in the \( 1\,\mu\text{F} \) and \( 2\,\mu\text{F} \) capacitors in the circuit once current becomes steady? 
  

  • \( 8\,\mu C \) and \( 4\,\mu C \)
    
  • \( 4\,\mu C \) and \( 8\,\mu C \)
    
  • \( 3\,\mu C \) and \( 6\,\mu C \)
    
  • \( 6\,\mu C \) and \( 3\,\mu C \)
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• 6.

  Which one among the following compounds will most readily be dehydrated under acidic condition? 

  

  • Option a
    
  • Option b
    
  • Option c
    
  • Option d
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