GATE Solved Paper 2020 - GATE 2020

46. Let R be the set of all binary relations on the set {2, 3}. Suppose a relation chosen from R at random. The probability that the chosen relation is reflex (round off to 3 decimal places) is ________.

  • Option : A
  • Explanation :
    No. of relation on A = 29
    No. of reflexive relation on A = 2(n2-n) = 2(32-3) = 26
    ∴ Probability (reflexive) = 26 / 29 = 1/8 = 0.125
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47. A direct mapped cache memory of 1 MB has a block size of 256 bytes. The cache has an access time of 3 ns and a hit rate of 94%. During a cache miss, it takes 20 ns to bring the first word of a block from the main memory, while each subsequent word takes 5 ns. The word size is 64 bits. The average memory access time in ns (round off to 1 decimal place) is _______.

  • Option : B
  • Explanation :
    Cache Memory = 1 MB
    Word size = 64 bit = 8 B
    Block size = 256 B
    Hit rate, x = 0.94 miss rate= 1-x = 0.06
    Cache access time, Tc = 3ns
    Number of words / Block = 256/8 = 32
    Using Hierarchical Approach,
    Tavg= ( x.Tc ) + (1-x)[ Tc + 1st word access time + remaining word access time]
    Tavg = (0.94 × 3) + (1 – 0.94) [3 + 20 + (31 × 5)]
    Tavg = 13.5 ns
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48. Consider the following grammar.
S → aSB | d
B → b
The number of reduction steps taken by a bottom-up parser while accepting string aaadbbb is ______ .

  • Option : B
  • Explanation :
    S → aSB
    → aaSBB [S → aSB]
    → aaaSBBB [S → aSB]
    → aaadBBB [S → d]
    → aaadbBB [B → b]
    → aaadbbB [B → b]
    → aaadbbb [B → b]
    Total 7 steps require
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49. If there are m input lines and n output for a decoder that is used to unique address a byte-addressable 1 KB RAM, then the minimum value of m + n is _____

  • Option : D
  • Explanation :
    Byte addressable 1 KB RAM
    ⇒ 210 bytes
    m = 10
    n = 2m
    m = 10, n = 1024
    so, m+n= 1024+ 10 = 1034
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