COMEDK UGET 2026 Question Paper: Download Answer Key with Solution PDF

COMEDK UGET 2026 Questions

• 1.

  A bag contains \(5\) red balls and \(3\) blue balls. Two balls are drawn at random without replacement. What is the probability that both balls are red?

  • \(\dfrac{5}{28}\)
  • \(\dfrac{10}{28}\)
  • \(\dfrac{15}{56}\)
  • \(\dfrac{5}{14}\)
  View Solution

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• 2.

  The number of relations, defined on the set {a, b, c, d which are both reflexive and symmetric, is equal to:}
  

  • 256
    
  • 16
    
  • 1024
    
  • 64
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• 3.

  A coach needs to select a \(4\)-player starting lineup from a pool of \(10\) players consisting of:
  • \(5\) guards
  • \(3\) forwards
  • \(2\) centres Find the number of different selections if the lineup must include:
  • At least \(1\) guard
  • At most \(1\) forward
  • Exactly \(1\) centre

  • \(70\)
    
  • \(60\)
    
  • \(80\)
    
  • \(20\)
    
  View Solution

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• 4.

  Evaluate: \[ \int \tan^{-1}\left( \sqrt{\frac{1-\sin x}{1+\sin x}} \right)\,dx \]

  • \(\dfrac{\pi x}{2}-\dfrac{x^2}{4}+C\)
  • \(\dfrac{\pi x}{4}-\dfrac{x^2}{2}+C\)
  • \(\dfrac{\pi x}{4}-\dfrac{x}{4}+C\)
  • \(\dfrac{\pi x}{4}-\dfrac{x^2}{4}+C\)
  View Solution

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• 5.

  If the projection of \[ \vec a = 5\hat i+\hat j+\lambda\hat k \] on \[ \vec b = 2\hat i+6\hat j+3\hat k \] is \(4\) units, then \(\lambda=\)

  • \(6\)
  • \(4\)
  • \(5\)
  • \(3\)
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