GATE Solved Paper 2017-19 - GATE 2018

43. Consider a matrix A = UVT

The largest eigenvalue of A is ________.

Note – Numerical Type question

  • Option : D
  • Explanation :
    Gate2018 cs
    A = UVT
    Gate2018 cs
    (1 - λ)(2 - λ) - 2 = 0
    λ2 - 3λ = 0
    λ(λ - 3) = 0
    λ = 0
    or, λ = 3
    The largest eigen value is 3.
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44. Consider a system with 3 processes that share 4 instances of the same resource type. Each process can request a maximum of K instances. Resource instances can be requested and released only one at a time. The largest value of K that will always avoid deadlock is ___________.

Note – Numerical Type question

  • Option : A
  • Explanation :
    Given,
    Number of processes (P) = 3
    Number of resources (R) = 4

    Since deadlock-free condition is:

    R ≥ P(N − 1) + 1
    Where R is total number of resources,
    P is the number of processes, and
    N is the max need for each resource.

    4 ≥ 3(N − 1) + 1
    3 ≥ 3(N − 1)
    1 ≥ (N − 1)
    N ≤ 2
    Therefore, the largest value of K that will always avoid deadlock is 2.
    Option (A) is correct.
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45. Let G be a finite group on 84 elements. The size of a largest possible proper subgroup of G is _________.

Note – Numerical Type question

  • Option : B
  • Explanation :
    Given |G| = 84
    Solutions:
    By Lagrang’s theorem any subgroup size is a divisior of 84.
    But a proper subgroup cannot have same size as group.
    So largest divisor of 84, other than 84 is 42.
    So, largest proper subgroup can have in size of 42.
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