KEAM 2016 Question Papers: Download Paper and Answer Key PDFs

KEAM 2016 Questions

• 1.

  Evaluate the integral: \[ \int \frac{2x^2 + 4x + 3}{x^2 + x + 1} \, dx \]

  • \( \frac{2}{3} x^3 + 2x + C \)
  • \( \frac{1}{3} x^3 + 3x + C \)
  • \( \frac{1}{3} x^3 + x + C \)
  • \( \frac{2}{3} x^3 + 3x + C \)
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• 2.

  Find the frequency of the waveform shown in the graph.
  

  • 0.5 Hz
    
  • 1 Hz
    
  • 2 Hz
    
  • 5 Hz
    
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• 3.

  A wire of length 1m is clamped at half of its length. If the fundamental frequency is 3kHz, then find the velocity.
  

  • \(6 \, \text{m/s}\)
    
  • \(12 \, \text{m/s}\)
    
  • \(3 \, \text{m/s}\)
    
  • \(1.5 \, \text{m/s}\)
    
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• 4.

  To have the same RMS value as that of hydrogen at 30K, what will be the temperature of the oxygen molecule?
  

  • 60K
    
  • 90K
    
  • 180K
    
  • 45K
    
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• 5.

  Solve for \( a \) and \( b \) given the equations: \[ \sin x + \sin y = a, \quad \cos x + \cos y = b, \quad x + y = \frac{2\pi}{3} \]

  • \( a = \frac{1}{2}, \quad b = \frac{1}{2} \)
  • \( a = \frac{1}{2}, \quad b = \frac{1}{\sqrt{2}} \)
  • \( a = 0, \quad b = 1 \)
  • \( a = 1, \quad b = 1 \)
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