JEE Main 2022 July 27 Shift 1 Question Paper with Solution PDF- Download Here

JEE Main Questions

• 1.

  Total number of non-bonded electrons present in \( \text{NO}_2 \); ion based on Lewis theory is:

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• 2.

  A body of mass 100 g is moving in a circular path of radius 2 m on a vertical plane as shown in the figure. The velocity of the body at point A is 10 m/s. The ratio of its kinetic energies at point B and C is: (Take acceleration due to gravity as 10 m/s\(^2\)) 
  

  • \( \frac{3 + \sqrt{3}}{2} \)
    
  • \( \frac{2 + \sqrt{3}}{3} \)
    
  • \( \frac{3 - \sqrt{2}}{2} \)
    
  • \( \frac{2 + \sqrt{2}}{3} \)
    
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• 3.

  If the equation \( a(b - c)x^2 + b(c - a)x + c(a - b) = 0 \) has equal roots, where \( a + c = 15 \) and \( b = \frac{36}{5} \), then \( a^2 + c^2 \) is equal to               .

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• 4.

  The value of \( (\sin 70^\circ)(\cot 10^\circ \cot 70^\circ - 1) \) is:

  • \( 1 \)
    
  • \( 0 \)
    
  • \( 3/2 \)
    
  • \( 2/3 \)
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• 5.

  Which of the following electronegativity order is incorrect?

  • Al \( <\) Mg \( <\) B \( <\) N
    
  • Al \( <\) Si \( <\) C \( <\) N
    
  • Mg \( <\) Be \( <\) B \( <\) N
    
  • S \( <\) Cl \( <\) O \( <\) F
    
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• 6.

  Let the area of a triangle \( \triangle PQR \) with vertices \( P(5, 4) \), \( Q(-2, 4) \), and \( R(a, b) \) be 35 square units. If its orthocenter and centroid are \( O(2, \frac{14}{5}) \) and \( C(c, d) \) respectively, then \( c + 2d \) is equal to:

  • \( \frac{7}{3} \)
    
  • \( 3 \)
    
  • \( 2 \)
    
  • \( \frac{8}{3} \)
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