JEE Main Question Paper 2022 (Available): Check Previous Year Question Paper with Solution PDF (2024-2014)

JEE Main 2022 Questions

• 1.

  The number of distinct real solutions of the equation \[ x|x + 4| + 3|x + 2| + 10 = 0 \] is

  • 2
    
  • 0
    
  • 3
    
  • 1
    
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• 2.

  Side of square is \( L \) and \( R \ll L \).
  Find mutual inductance of the system shown in the figure.
  

  

  • \( \frac{\sqrt{2 \mu_0} R^2}{L} \)
    
  • \( \frac{4 \sqrt{2 \mu_0} R^2}{L} \)
    
  • \( \frac{2 \mu_0 R^2}{L} \)
    
  • \( \frac{2 \sqrt{2 \mu_0} R^2}{L} \)
    
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• 3.

  A metal string A is suspended from a rigid support and its free end is attached to a block of mass M. Second block having mass 2M is suspended at the bottom of the first block using a string B. The area of cross sections of strings A and B are same. The ratio of lengths of strings of A to B is 2 and the ratio of their Young's moduli ($Y_A / Y_B$) is 0.5. The ratio of elongations in A to B is _______.
  

  • 1
    
  • 4
    
  • 8
    
  • 6
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• 4.

  The first term of an A.P. of 30 non-negative terms is \(\frac{10}{3}\). If the sum of this A.P. is the cube of its last term, then its common difference is:
  

  • \(\frac{5}{87}\)
    
  • \(\frac{25}{83}\)
    
  • \(\frac{15}{29}\)
    
  • \(\frac{5}{29}\)
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• 5.

  Two blocks ($P$ and $Q$) with respectively masses $2\text{ kg}$ and $1.5\text{ kg}$ are joined by a massless thread. These blocks are mounted on a frictionless pully which is fixed on the edge of a cube $(S)$, as shown in the figure below. Block $P$ is positioned on the top surface which has no friction and block $Q$ is in contact with side-surface, having coefficient friction $\mu$. The cube $(S)$ moves towards the right with acceleration of $\frac{g}{2}$, where $g$ is gravitational acceleration. During this movement the block $P$ and $Q$ remain stationary. The value of $\mu$ is ______. (take $g = 10\text{ m/s}^2$)

  

  • 0.33
  • 0.67
  • 1
  • 0.5
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