KEAM 2016 Question Papers: Download Paper and Answer Key PDFs

KEAM 2016 Questions

• 1.

  Benzene when treated with Br\(_2\) in the presence of FeBr\(_3\), gives 1,4-dibromobenzene and 1,2-dibromobenzene. Which type of reaction is this?

  • Nucleophilic substitution
    
  • Nucleophilic addition
    
  • Electrophilic substitution
    
  • Electrophilic addition
    
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• 2.

  Given that \( \vec{a} \parallel \vec{b} \), \( \vec{a} \cdot \vec{b} = \frac{49}{2} \), and \( |\vec{a}| = 7 \), find \( |\vec{b}| \).

  • \( |\vec{b}| = 7 \)
  • \( |\vec{b}| = 14 \)
  • \( |\vec{b}| = \frac{49}{7} \)
  • \( |\vec{b}| = \frac{49}{14} \)
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• 3.

  Evaluate the integral: \[ \int \frac{\sin(2x)}{\sin(x)} \, dx \]

  • \( 2 \sin(x) + C \)
    
  • \( 2 \log \left| \tan \left( \frac{x}{2} \right) \right| + C \)
    
  • \( 2 \log \left| \cot \left( \frac{x}{2} \right) \right| + C \)
    
  • \( 2 \cos(x) + C \)
    
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• 4.

  If \( A \) is a \( 3 \times 3 \) matrix and \( |B| = 3|A| \) and \( |A| = 5 \), then find \( \left| \frac{\text{adj} B}{|A|} \right| \).

  • 3
  • 9
  • 1
  • 5
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• 5.

  If $ \cos^{-1}(x) - \sin^{-1}(x) = \frac{\pi}{6} $, then find } $ x $.

  • \( \frac{1}{2} \)
    
  • \( \frac{\sqrt{3}}{2} \)
    
  • \( \frac{1}{\sqrt{2}} \)
    
  • \( \frac{\sqrt{2}}{2} \)
    
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