IIITH UGEE Question Paper 2026, Download Answer Key with Solutions PDF

IIITH UGEE 2026 Questions

• 1.

  Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is a prime number?

  • \(\frac{5}{12}\)
    
  • \(\frac{7}{12}\)
    
  • \(\frac{1}{2}\)
    
  • \(\frac{13}{36}\)
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• 2.

  If the \(n^{th}\) term of an A.P. is \(2n + 5\), find the sum of the first 10 terms.

  • \(110\)
    
  • \(155\)
    
  • \(160\)
    
  • \(165\)
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• 3.

  A pair of fair dice is rolled. What is the probability that the second die lands on a higher value than the first?

  • \(\frac{1}{36}\)
    
  • \(\frac{5}{36}\)
    
  • \(\frac{1}{6}\)
    
  • \(\frac{5}{12}\)
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• 4.

  What is the maximum number of electrons that can be accommodated in a subshell with orbital angular momentum quantum number \(l = 3\)?

  • \(6\)
    
  • \(10\)
    
  • \(14\)
    
  • \(18\)
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• 5.

  Let \(P\) be any point on the curve \(x^{2/3}+y^{2/3}=a^{2/3}\). Then, what would be the length of the segment of the tangent between the coordinate axes?

  • \(a\)
    
  • \(2a\)
    
  • \(3a\)
    
  • \(4a\)
    
  • \(5a\)
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