GATE CSE 2021 SET-1

Q51.

Consider two hosts P and Q connected through a router R. The maximum transfer unit (MTU) value of the link between P and R is 1500 bytes, and between R and Q is 820 bytes. A TCP segment of size 1400 bytes was transferred from P to Q through R, with IP identification value as 0x1234. Assume that the IP header size is 20 bytes. Further, the packet is allowed to be fragmented, i.e., Don't Fragment (DF) flag in the IP header is not set by P. Which of the following statements is/are correct?[MSQ]
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Q52.

For a Turing machine M, < M > denotes an encoding of M. Consider the following two languages. \begin{array}{ll} L1 = \{ \langle M \rangle \mid M \text{ takes more than } 2021 \text{ steps on all inputs} \} \\ L2 = \{ \langle M \rangle \mid M\text{ takes more than } 2021 \text{ steps on some input} \} \end{array} Which one of the following options is correct?
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Q53.

A TCP server application is programmed to listen on port number P on host S. A TCP client is connected to the TCP server over the network. Consider that while the TCP connection was active, the server machine S crashed and rebooted. Assume that the client does not use the TCP keepalive timer. Which of the following behaviors is/are possible?[MSQ]
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Q54.

A relation r(A,B) in a relational database has 1200 tuples. The attribute A has integer values ranging from 6 to 20, and the attribute B has integer values ranging from 1 to 20. Assume that the attributes A and B are independently distributed. The estimated number of tuples in the output of \sigma _{(A > 10)\vee(B=18)}(r) is ____________
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Q55.

Consider a 3-bit counter, designed using T flip-flops, as shown below: Assuming the initial state of the counter given by PQR as 000, what are the next three states?
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