GATE Solved Paper 2017-19 - GATE 2018

23. Which one of the following is a closed form expression for the generating function of the sequence {an}, where an = 2n + 3 for all n = 0, 1, 2,.....?

  • Option : D
  • Explanation : The Given functions is, an = 2n + 3
    generating function for 1 is and n is , the generating function for an is

    Which is option (D).
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24. Let ⊕ and ⊙ denote the Exclusive OR and Exclusive NOR operations, respectively. Which one of the following is NOT CORRECT?

  • Option : D
  • Explanation :
    (P ⊕ P) ⊕ Q = (P ⊙P) ⊕ Q false
    (P ⊕ P) ⊕ Q = 1 ⊕ Q = Q
    (P ⊙ P) ⊕ Q = 0 ⊕ Q = Q
    (P ⊕ P) ⊕ Q ≠ (P ⊙ P) ⊕ Q
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25. Consider a matrix P whose only eigenvectors are the multiples of

  • Option : D
  • Explanation : Only Eigen vector is multiples means that eigen value is repeated since if eigen values were distinct we will get one more independent eigen vector. So, II P has repeated eigen value is true. I need not be true since has repeated eigen values and yet it is invertible. III is true since if matrix has repeated eigen values then it cannot be diagonalizable.
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