KEAM 2026 Engineering April 17 Answer Key- Download PDF

KEAM 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.

  The cubic polynomial \( 2x^3 - 3x^2 - 36x + 28 \) is increasing in the range of \( x \). Find the interval where the function is increasing.

  • \( x>2 \)
  • \( x<-2 \)
  • \( -2<x<2 \)
  • \( x<0 \)
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• 3.

  Find the vertex of the parabola \( 4y = x^2 - 6x + 17 \).

  • \( (3, 7) \)
  • \( (1, 4) \)
  • \( (3, 4) \)
  • \( (1, 7) \)
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• 4.

  Evaluate the integral: $ \int \frac{1}{x(x^4 + 1)} \, dx $

  • \( \frac{1}{2} \log |x| \)
    
  • \( \frac{1}{2} \log |x^4 + 1| \)
    
  • \( \frac{1}{x^4 + 1} \)
    
  • \( \frac{1}{2} \log |x^2 + 1| \)
    
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• 5.

  Which of the following is not a chiral molecule?

  • 2-Chlorobutane
    
  • 2,3-Dihydroxy propanal
    
  • 2-Bromo propionic acid
    
  • Butan-2-ol
    
  • 2-Bromo-2-methoxypropane
    
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• 6.

  Given the set $ S = \{ a, b, c, d, e, f \} $, find the total number of subsets with an odd number of elements.

  • \( 16 \)
    
  • \( 32 \)
    
  • \( 64 \)
    
  • \( 2^{6-1} = 32 \)
    
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