KEAM 2021 Question Papers: Download Previous Year Question Paper with Answer Key PDFs

KEAM 2021 Questions

• 1.

  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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• 2.

  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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• 3.

  The element that has the highest melting point in the 3d series is:
  

  • V
    
  • Cr
    
  • Mn
    
  • W
    
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• 4.

  10 g of (90 percent pure) \( \text{CaCO}_3 \), treated with excess of HCl, gives what mass of \( \text{CO}_2 \)?

  • 4.4 g
    
  • 5.6 g
    
  • 3.6 g
    
  • 6.4 g
    
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• 5.

  If \( 5 \sin^{-1} \alpha + 3 \cos^{-1} \alpha = \pi \), then \( \alpha = ? \)

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