GATE CS 2019

Question 41

Assume that in a certain computer, the virtual addresses are 64 bits long and the physical addresses are 48 bits long. The memory is word addressable. The page size is 8k Band the word size is 4 bytes. The Translation Look-aside Buffer (TLB) in the address translation path has 128 valid entries. At most how many distinct virtual addresses can be translated without any TLB miss?

• 16 x 2¹⁰
• 8 x 2²⁰
• 4 x 2²⁰
• 256 x 2¹⁰

Question 42

Consider the first order predicate formula:

∀x [( ∀z z|x ⇒ ((z = x) ∨ (z = 1))) ⇒ ∃w(w > x) ∧ (∀z z⏐w ⇒ ((w = z) ∨ (z = 1)))] 

Here ‘a⏐b’ denotes that ‘a divides b’, where a and b are integers. Consider the following sets:

• S₁: {1, 2, 3, ..., 100}
• S₂: Set of all positive integers
• S₃: Set of all integers

Which of the above sets satisfy φ ?

• S₁ and S₃
• S₂ and S₃
• S₁, S₂ and S₃
• S₁ and S₂

Question 43

Consider the following grammar and the semantic actions to support the inherited type declaration attributes. Let X₁, X₂, X₃, X₄, X₅ and X₆ be the placeholders for the non-terminals D, T, L or L₁ in the following table:

Which one of the following are the appropriate choices for X₁, X₂, X₃ and X₄?

• X₁ = L, X₂ = T, X₃ = L₁, X₄ = L
• X₁ = L, X₂ = L, X₃ = L₁, X₄ = T
• X₁ = T, X₂ = L, X₃ = L₁, X₄ = T
• X₁ = T, X₂ = L, X₃ = T, X₄ = L₁

Question 44

There are n unsorted arrays: A₁, A₂, ....,A_n. Assume that n is odd. Each of A₁, A₂, ...., A_n contains n distinct elements. There are no common elements between any two arrays. The worst-case time complexity of computing the median of the medians of A₁, A₂, ....,A_n is ________ . 

• Ο(n log n)
  

• Ο(n²)
  

• Ο(n)
  

• Ω(n²log n)
  

Question 45

Let G be any connection, weighted, undirected graph:

• I. G has a unique minimum spanning tree if no two edges of G have the same weight.
• II. G has a unique minimum spanning tree if, for every cut G, there is a unique minimum weight edge crossing the cut.

Which of the above two statements is/are TRUE?

• Neither I nor II
• I only
• II only
• Both I and II

Question 46

Consider the following snapshot of a system running n concurrent processes. Process i is holding X_i instances of a resource R, 1 ≤ i ≤ n. Assume that all instances of R arecurrently in use. Further, for all i, process i can place a request for at most Y_i additional instances of R while holding the X_t instances it already has. Of the n processes, there are exactly two processes p and q such that Y_p = Y_q = 0. Which one of the following conditions guarantees that no other process apart from p and q can complete execution?

• X_p + X_q < Min {Y_k ⏐ 1 ≤ k ≤ n, k ≠ p, k ≠ q}
• Min (X_p, X_q) ≥ Min {Y_k ⏐ 1 ≤ k≤ n, k ≠ p, k ≠ q}
• Min (X_p, X_q) ≤ Max {Y_k ⏐ 1 ≤ k ≤ n, k ≠ p, k ≠ q}
• X_p + X_q < Max {Y_k ⏐ 1 ≤ k ≤ n, k ≠ p, k ≠ q}

Question 47

Consider the following statements:

• I. The smallest element in a max-heap is always at a leaf node.
• II. The second largest element in a max-heap is always a child of the root node.
• III. A max-heap can be constructed from a binary search tree in Θ(n) time.
• IV. A binary search tree can be constructed from a max-heap in Θ(n) time.

Which of the above statements is/are TRUE?

• II, III and IV
• I, II and III
• I, III and IV
• I, II and IV

Question 48

Consider the following four processes with arrival times (in milliseconds) and their length of CPU burst (in milliseconds) as shown below:

These processes are run on a single processor using preemptive Shortest Remaining Time First scheduling algorithm. If the average waiting time of the processes is 1 millisecond, then the value of Z is __________. Note: This was Numerical Type question.

• 2
• 3
• 1
• 4

Question 49

The index node (inode) of a Unix-like file system has 12 direct, one single-indirect and one double-indirect pointer The disk block size is 4 kB and the disk block addresses 32-bits long. The maximum possible file size is (rounded off to 1 decimal place) __________ GB. Note: This was Numerical Type question.

• 4
• 2
• 1
• 0.50

Question 50

Consider the augmented grammar given below: S′ → S S → ⏐id L → L, S⏐S Let I₀ = CLOSURE ({[S′ → S]}). The number of items in the set GOTO (I₀, <) is __________.
Note: This was Numerical Type question.

• 5
• 4
• 3
• 1