KEAM 2012 Physics and Chemistry Question Paper with Answer Key PDF (April 23)

KEAM 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.

  Given that \( \mathbf{a} \times (2\hat{i} + 3\hat{j} + 4\hat{k}) = (2\hat{i} + 3\hat{j} + 4\hat{k}) \times \mathbf{b} \), \( |\mathbf{a} + \mathbf{b}| = \sqrt{29} \), \( \mathbf{a} \cdot \mathbf{b} = ? \)

  • 0
    
  • 5
    
  • 10
    
  • 15
    
  View Solution

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• 3.

  Methyl fluoride is prepared by heating methyl bromide in the presence of AgF. This reaction is known as

  • Swarts reaction
    
  • Finkelstein reaction
    
  • Sandmeyer’s reaction
    
  • Wurtz reaction
    
  • Kolbe’s reaction
    
  View Solution

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• 4.

  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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• 5.

  Evaluate the following statement: \[ f(x) = \sin(|x|) - |x| \text{ is not differentiable at } x = \underline{\hspace{2cm}} \]

  • \( x = 0 \)
    
  • \( x = 1 \)
    
  • \( x = -1 \)
    
  • \( x = 2 \)
    
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• 6.

  Evaluate the following limit: $ \lim_{x \to 0} \frac{1 + \cos(4x)}{\tan(x)} $

  • 2
    
  • 1
    
  • 0
    
  • 4
    
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