KEAM 2023 Physics and Chemistry Question Paper: Download Answer Key and Solutions PDF

KEAM Questions

• 1.

  Evaluate the integral: \[ \int_0^1 \frac{t}{(t + 1)^3} \, dt \]

  • \( \frac{1}{8} \)
    
  • \( \frac{1}{4} \)
    
  • \( \frac{1}{2} \)
    
  • \( \frac{1}{16} \)
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• 2.

  Solve the equation: \[ \frac{(3x - 4)^2}{9} - \frac{(4x - 3)^2}{8} = 1 \quad \text{(length of the latus rectum)} \]

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• 3.

  Find the number of combinations of 3-lettered numbers that can be created by 3, 4, 5, and 7 with repeating. The three digits cannot be equal to zero.

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• 4.

  The equation of perpendicular bisector of the line segment joining the points (10, 0) and (0, -4) is

  • \( 5x + 2y = 21 \)
    
  • \( 5x + 2y = 0 \)
    
  • \( 2x - 5y = 21 \)
    
  • \( 5x - 2y = 21 \)
    
  • \( 2x + 3y = 21 \)
    
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• 5.

  The end-points of a diameter of a circle are \( (-1, 4) \) and \( (5, 4) \). Then the equation of the circle is

  • \( (x - 3)^2 + y^2 = 9 \)
    
  • \( (x - 3)^2 + (y + 4)^2 = 3 \)
    
  • \( (x - 2)^2 + (y - 4)^2 = 9 \)
    
  • \( (x + 3)^2 + (y + 4)^2 = 9 \)
    
  • \( (x - 3)^2 + (y - 4)^2 = 4 \)
    
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• 6.

  Benzene diazonium salt in the presence of Cu/HBr will give bromobenzene (C\(_6\)H\(_5\)Br) and release nitrogen gas (N\(_2\)). This reaction is known as:

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