PREVIOUS YEAR SOLVED PAPERS MCQ - GATE 2018

51 Consider the sequential circuit shown in the figure, where both flip-flops used are positive edge-triggered D flip-flops.

The number of states in the state transition diagram of the circuit that have a transition back to the same state on some value of “in” is __________.

Note – Numerical Type question

State Table:

P.S		Input	FF input		N.S
Q1	Q₀	x	D₁ = x	D₁ = Q₁	Q₁	Q₀	Out = Q₀
0	0	0	0	0	0	0	0
0	0	1	1	0	1	0	0
0	1	0	0	0	0	0	0
0	1	1	1	0	1	0	0
1	0	0	0	1	0	1	1
1	0	1	1	1	1	1	1
1	1	0	0	1	0	1	1
1	1	1	1	1	1	1	1

State Transition Diagram:

self-loop states are 00 and 11.
Hence answer is 2.

52 Consider a long-lived TCP session with an end-to-end bandwidth of 1 Gbps (= 109 bits-per-second). The session starts with a certain sequence number. The minimum time (in seconds, rounded to the closest integer) before this sequence number can be used again is _________.

Note – Numerical Type question

1 sec = 10⁹ bits
(2³² x 8)/10⁹ = bytes
⇒ 34.35 sec

53 Consider a storage disk with 4 platters (numbered as 0, 1, 2 and 3), 200 cylinders (numbered as 0, 1, …., 199) and 256 sectors per track (numbered as 0,1, ….., 255). The following 6 disk requests of the form [sector number, cylinder number, platter number] are received by the disk controller at the same time:
[120, 72, 2], [180, 134, 1], [60, 20, 0], [60, 20, 0], [212, 86, 3], [56, 116, 2], [118, 16, 1]
Currently the head is positioned at sector number 100 of cylinder 80 and is moving towards higher cylinder numbers. The average power dissipation in moving the head over 100 cylinders is 20 milliwatts and for reversing the direction of the head movement once is 15 milliwatts. Power dissipation associated with rotational latency and switching of head between different platters is negligible.
The total power consumption in milliwatts to satisfy all of the above disk requests using the Shortest Seek Time First disk scheduling algorithm is ____________.

Note – Numerical Type question

(86 - 80) + (86 - 72) + (134 - 72) + (134 - 16) + 62 + 118 + 14 = 200
100 → 20
200 → ?
(200/100) x 20 = 40
3 direction changes 3 x 15 = 45
40 + 45 = 85

54 A processor has 16 integer registers (R0, R1, …… R15) and 64 floating point registers (F0, F1, ……, F63). It uses a 2-byte instruction format. There are four categories of instructions. Type-1, Type-2, Type-3 and Type-Type-1 category consists of four instructions, each with 3 integer register operands (3Rs). Type-2 category consists of eight instructions, each with 2 floating point register operands (2Fs). Type-3 category consists of fourteen instructions, each with one integer register operand and one floating point register operand (1R + 1F). Type-4 category consists of N instructions, each with a floating point register operand (1F). The maximum value of N is _________.

Note – Numerical Type question

Given, size of instruction format is 2 byte (= 16 bits), therefore number of instruction encoding = 216
Also, total number of bits in integer operand = log2(16 integer registers) = 4
Total number of bits in floating point operand = log2(64 floating point registers) = 6
So, number of encoding consumed:

By type 1 instructions = 4×23×4 = 214
By type 2 instructions = 8×22×6 = 215
By type 3 instructions = 14×2(4+6) = 14336

Now, number of encoding left for type 4 instructions = 216 − (214 + 215 + 14336) = 2048
Therefore, total number of different instructions of type 4 instructions = 2048 /64 = 32 Please note that there is difference between number of different instructions and number of different encoding, a single instruction can have different encodings when the address part differs. So, answer is 32.

55 Consider the following undirected graph G:

Choose a value of x that will maximize the number of minimum weight spanning trees (MWSTs) of G. The number of MWSTs of G for this value of x is ___________.

Note – Numerical Type question

ü Edges with weights 1 and 3 will be selected first,
ü Now bottom edge with weight 4 will not be selected as will cause cycle on MST,
ü both corner vertices have two-two choices to select the vertices, so these corner edges with weights 4 and 5 will resultant 2*2 = 4 MSTs.
So, total number of MSTs are 2*2 = 4, which is answer.
Option (A) is correct.

PREVIOUS YEAR SOLVED PAPERS MCQ - GATE 2018

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