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(#M40029664) GATE QUESTION GATE-Aptitude Keep an EYE

The cost function for a product in a firm is given by 5q^2, where q is the amount of production. The firm can sell the product at a market price of 50 per unit. The number of units to be produced by the firm such that the profit is maximized is
option
(A) 5
(B) 10
(C) 15
(D) 25

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(#M40029663) GATE QUESTION GATE-CS Keep an EYE

Consider an instance of TCP’s Additive Increase Multiplicative Decrease (AIMD) algorithm where the window size at the start of the slow start phase is 2 MSS and the threshold at the start of the first transmission is 8 MSS. Assume that a timeout occurs during the fifth transmission. Find the congestion window size at the end of the tenth transmission.
option
(A) 8 MSS
(B) 14 MSS
(C) 7 MSS
(D) 12 MSS

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(#M40029662) GATE QUESTION GATE-CS Keep an EYE

Consider a source computer (S) transmitting a file of size 10^6 bits to a destination computer (D)
over a network of two routers (R1 and R2) and three links (L1, L2, and L3). L1 connects S to R1; L2 connects R1 to R2; and L3 connects R2 to D. Let each link be of length 100 km. Assume signals travel over each link at a speed of 10^8 meters per second. Assume that the link bandwidth on each link is 1Mbps. Let the file be broken down into 1000 packets each of size 1000 bits. Find the total sum of transmission and propagation delays in transmitting the file from S to D?
option
(A) 1005 ms
(B) 1010 ms
(C) 3000 ms
(D) 3003 ms

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(#M40029661) GATE QUESTION GATE-CS Keep an EYE

Consider the virtual page reference string
1, 2, 3, 2, 4, 1, 3, 2, 4, 1
on a demand paged virtual memory system running on a computer system that has main memory size of 3 page frames which are initially empty. Let LRU, FIFO and OPTIMAL denote the number of page faults under the corresponding page replacement policy. Then
(A) OPTIMAL < LRU < FIFO
(B) OPTIMAL < FIFO < LRU
(C) OPTIMAL = LRU
(D) OPTIMAL = FIFO

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(#M40029660) GATE QUESTION GATE-CS Keep an EYE

A file system with 300 GByte disk uses a file descriptor with 8 direct block addresses, 1 indirect
block address and 1 doubly indirect block address. The size of each disk block is 128 Bytes and the size of each disk block address is 8 Bytes. The maximum possible file size in this file system is
(A) 3 KBytes
(B) 35 KBytes
(C) 280 KBytes
(D) dependent on the size of the disk

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(#M40029659) GATE QUESTION GATE-CS Keep an EYE

Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to

option
(A) 15
(B) 30
(C) 90
(D) 360

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(#M40029658) GATE QUESTION GATE-CS Keep an EYE

Suppose a circular queue of capacity ( n-1) elements is implemented with an array of n elements.
Assume that the insertion and deletion operations are carried out using REAR and FRONT as array
index variables, respectively. Initially, REAR = FRONT = 0. The conditions to detect queue full
and queue empty are

option
(A) full: (REAR+1) mod n == FRONT
empty: REAR == FRONT

(B) full: (REAR+1) mod n == FRONT
empty: (FRONT+1) mod n == REAR

(C) full: REAR == FRONT
empty: (REAR+1) mod n == FRONT

(D) full: (FRONT+1) mod n == REAR
empty: REAR == FRONT

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(#M40029657) GATE QUESTION GATE-CS Keep an EYE

An Internet Service Provider (ISP) has the following chunk of CIDR -based IP addresses available with it: 245.248.128.0/20. The ISP wants to give half of this chunk of addresses to Organization A, and a quarter to Organization B, while retaining the remaining with itself. Which of the following is a valid allocation of addresses to A and B?

option
(A) 245.248.136.0/21 and 245.248.128.0/22
(B) 245.248.128.0/21 and 245.248.128.0/22
(C) 245.248.132.0/22 and 245.248.132.0/21
(D) 245.248.136.0/24 and 245.248.132.0/21

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(#M40029656) GATE QUESTION GATE-CS Keep an EYE

Suppose a fair six -sided die is rolled once. If the value on the die is 1, 2, or 3, the die is rolled a second time. What is the probability that the sum total of values that turn up is at least 6?

option
(A) 10/21
(B) 5/12
(C) 2/3
(D) 1/6

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(#M40029655) GATE QUESTION GATE-CS Keep an EYE

The bisection method is applied to comp ute a zero of the function f(x) = x^4-x^3-x^2-4 in the interval [1,9]. The method converges to a solution after iterations.

option
(A) 1
(B) 3
(C) 5
(D) 7

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