MHT CET Question Paper 2017 (Available): Check Previous Year Question Paper with Solution PDF (2023-2015)

MHT CET 2017 Questions

• 1.

  The equation for the RMS velocity is given as \[ v_{\text{rms}} = \sqrt{\frac{3RT}{M_0}} \] where \( R \) is the gas constant, \( T \) is the temperature, and \( M_0 \) is the molecular mass. If the temperature is increased, find the new RMS velocity \( v_{\text{rms}} \) when the temperature is doubled.}
  

  • \( \sqrt{3} v_{\text{rms}} \)
    
  • \( 2 v_{\text{rms}} \)
    
  • \( \sqrt{2} v_{\text{rms}} \)
    
  • \( \frac{v_{\text{rms}}}{\sqrt{2}} \)
    
  View Solution

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• 2.

  If \( \tan^{-1} (\sqrt{\cos \alpha}) - \cot^{-1 (\cos \alpha) = x \), then what is \( \sin \alpha \)?}

  • \( \tan \left( \frac{x}{2} \right) \)
  • \( \cot \left( \frac{x}{2} \right) \)
  • \( \cot^2 \left( \frac{x}{2} \right) \)
  • \( \tan^2 \left( \frac{x}{2} \right) \)
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• 3.

  Evaluate the integral: \[ \int \frac{1}{\sin^2 2x \cdot \cos^2 2x} \, dx \]

  • \( \frac{1}{2} \tan 2x \)
  • \( \frac{1}{2} \cot 2x \)
  • \( \frac{1}{4} \cot 2x \)
  • \( \frac{1}{4} \tan 2x \)
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• 4.

  A body of mass 0.2 kg is attached to a light string of length 1 m and revolved in a vertical circle. What is the minimum speed at the lowest point so that the body can complete the circular motion? (Take \( g = 10 \, \text{m/s}^2 \))

  • 2 m/s
    
  • 3.16 m/s 
     

  • 5 m/s
    
  • 6.32 m/s
    
  View Solution

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• 5.

  Evaluate the integral: \[ \int \frac{\sqrt{\tan x}}{\sin x \cos x} \, dx \]

  • \( \frac{2}{\cos^2 x} \)
  • \( \frac{2}{\sin^2 x} \)
  • \( \frac{2}{\cos x} \)
  • \( \frac{2}{\sin x} \)
  View Solution