CS and IT GATE 2024 SET-1 Questions with Answer

Ques 40 Computer Science

Let A be an n × m matrix with m > n. Which of the following statements is/are TRUE about the system Ax = 0?

There exist at least mn linearly independent solutions to this system

There exist m - n linearly independent vectors such that every solution is a linear combination of these vectors

There exists a non-zero solution in which at least m - n variables are 0

There exists a solution in which at least n variables are non-zero

Ques 41 Computer Science

Consider the 5-state DFA M accepting the language L(M) ⊂ (0 + 1)* shown below. For any string w ∈ (0 + 1)* let n₀(w) be the number of 0′s in w and n₁(w) be the number of 1′s in w.

Which of the following statements is/are FALSE?

States 2 and 4 are distinguishable in M

States 3 and 4 are distinguishable in M

States 2 and 5 are distinguishable in M

Any string w with n₀(w) = n₁(w) is in L(M)

Ques 42 Computer Science

The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let G be any graph with n vertices and chromatic number k. Which of the following statements is/are always TRUE?

G contains a complete subgraph with k vertices

G contains an independent set of size at least n/k

G contains at least k(k-1)/2 edges

G contains a vertex of degree at least k

Ques 43 Computer Science

Consider the operators ◊ and □ defined by a ◊ b = a + 2b, a □ b = ab. for positive integers. Which of the following statements is/are TRUE?

Operator ◊ obeys the commutative law

Operator ◊ obeys the associative law

Operator □ obeys the distributive law over the operator ◊

Operator ◊ obeys the distributive law over the operator □

Ques 44 Computer Science

Consider two set-associative cache memory architectures: WBC, which uses the write back policy, and WTC, which uses the write through policy. Both of them use the LRU (Least Recently Used) block replacement policy. The cache memory is connected to the main memory. Which of the following statements is/are TRUE?

A read miss in WBC never evicts a dirty block

A read miss in WTC never triggers a write back operation of a cache block to main memory

A write hit in WBC can modify the value of the dirty bit of a cache block

A write miss in WTC always writes the victim cache block to main memory before loading the missed block to the cache

Ques 45 Computer Science

Consider a 512 GB hard disk with 32 storage surfaces. There are 4096 sectors per track and each sector holds 1024 bytes of data. The number of cylinders in the hard disk is

256000 is the correct answer.

Ques 46 Computer Science

The baseline execution time of a program on a 2 GHz single core machine is 100 nanoseconds (ns). The code corresponding to 90% of the execution time can be fully parallelized. The overhead for using an additional core is 10 ns when running on a multicore system. Assume that all cores in the multicore system run their share of the parallelized code for an equal amount of time. The number of cores that minimize the execution time of the program is

10 is the correct answer.

Ques 47 Computer Science

A given program has 25% load/store instructions. Suppose the ideal CPI (cycles per instruction) without any memory stalls is 2. The program exhibits 2% miss rate on instruction cache and 8% miss rate on data cache. The miss penalty is 100 cycles. The speedup (rounded off to two decimal places) achieved with a perfect cache (i.e., with NO data or instruction cache misses) is

1.27 is the correct answer.

Ques 48 Computer Science

Consider the following code snippet using the fork() and wait() system calls. Assume that the code compiles and runs correctly, and that the system calls run successfully without any errors.

The total number of times the printf statement is executed is

14 is the correct answer.

Ques 49 Computer Science

Consider the entries shown below in the forwarding table of an IP router. Each entry consists of an IP prefix and the corresponding next hop router for packets whose destination IP address matches the prefix. The notation "/N" in a prefix indicates a subnet mask with the most significant N bits set to 1.

This router forwards 20 packets each to 5 hosts. The IP addresses of the hosts are 10.1.1.16, 10.1.1.72, 10.1.1.132, 10.1.1.191, and 10.1.1.205. The number of packets forwarded via the next hop router R2 is

40 is the correct answer.

Ques 50 Computer Science

Let G = (V, Σ, S, P) be a context-free grammar in Chomsky Normal Form with Σ = {a, b, c} and V containing 10 variable symbols including the start symbol S. The string w = a³⁰ b³⁰ c³⁰ is derivable from S. The number of steps (application of rules) in the derivation S →* w is

89 is the correct answer.

Ques 51 Computer Science

The number of edges present in the forest generated by the DFS traversal of an undirected graph G with 100 vertices is 40. The number of connected components in G is

60 is the correct answer.

Ques 52 Computer Science

A bag contains 5 red balls and 7 green balls. Two balls are drawn randomly without replacement. If it is known that the first ball drawn is red, the probability (rounded off to two decimal places) that both balls drawn are red is____________.

0.29 is the correct answer.

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CS and IT GATE 2024 SET-1 Questions with Answer