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GATE CS 2021 : Full Syllabus Rapid Mock 2 (App update required to attempt this test)

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Question 1

Select the most appropriate option to fill in the blank.

How much money ___________ on your clothes so far?

Question 2

Select the most appropriate option to fill in the blank.
You would scarcely expect her to know that, ______?

Question 3

Direction: Select the most appropriate synonym of the given word.
ENDORSE

Question 4

Select the most appropriate synonym of the given word.
RECTOR

Question 5

In a parking lot, 30 cars, 30 vans and 40 LCVs are parked. What is the probability that a car leaves after a van or LCV have left?

Question 6

There are 63 students in a class. Due to the admission of 14 more students, the expenses of the class are increased by Rs 77 per day while the average expenditure per head decreased by Re 1. What was the original expenditure of the class?

Question 7

There are four distinct numbers whose product are 35937000 and each of these four numbers is formed by product of 3 distinct prime numbers. The average of all the four numbers is:

Question 8

8 liters are drawn from a cask full of wine and is then filled with same quantity of water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is 16: 65 . How much wine the cask holds originally?

Question 9

If a man sells a car at 7% profit and a bike at 16% profit, he earns Rs. 3255 as profit. But if he sells the car at % loss and bike at 5% profit then he bears no profit no loss. Find the cost price of the car and the bike?

Question 10

Professor Caesar wishes to develop a matrix-multiplication algorithm that is asymptotically faster than Strassen’s algorithm. His algorithm will use the divide and- conquer method, dividing each matrix into pieces of size n/4 x n/4, and the divide and combine steps together will take Ɵ(n2) time. He needs to determine how many sub-problems his algorithm has to create in order to beat Strassen’s algorithm. If his algorithm creates 'a' sub-problems, then the recurrence for the running time T(n) becomes T(n) = aT(n/4) + Ɵ(n2) . What is the largest integer value of 'a' for which Professor Caesar’s algorithm would be asymptotically faster than Strassen’s algorithm ___________________.

Question 11

Consider the following graph

Find the number of articulation points in the above graph?

Question 12

Choose the correct option to fill the empty blanks in below statement :

If variables are declared previously, then __________ is responsible for generation of symbol table but if variables are not declared then symbol table will be generated by __________.

Question 13

Consider the following operator grammar
EAaBcD
AbA|e
BbB|e
DeD|g
Which of the following precedence relation is incorrect from the above grammar? Assume x<y is used to represent x is having less precedence than y and in the expression x appears first and then y appears next.

Question 14

Station a need to send a message consisting of 10 packets to station B using a sliding window of size 4. All packets are ready and can be transferred immediately. Selective repeat and GBN are used at 2 different times and every 5th packet get lost for both protocols. (ACK’s from B never gets lost). Let x and y be the number of transmissions that A has to make in selective repeat and GBN respectively to ensure safe delivery to B. Then x+y=?

Question 15

Identify the statements from the following.
I. In STOP and WAIT ARQ if the receiver replies with ACK 0, then the sender will send next frame with sequence number as 1.
II. Physical layer recognizes the frames sent by sender and arranges them in particular order and gives it to layer-2 (Data link layer)
III. ACK sent by receiver also contains CRC.
IV. Stop and wait flow control gives inefficient line utilization for very high data rates over long distance.
V. In sliding window protocol ACK includes number of next frame.

Question 16

Consider the following data for a computer system:

Main Memory size = 64MB

and tag bits in physical address are given as 10 bits.

If cache is direct mapped then which of the following is true?

Question 17

Consider a 2D array A[-5….5][10……15], the base address is 100 and word length 2B find the address of the element A[2][13] using Row major order?

Question 18

Consider we have a stack and a queue. For stack it takes 2 seconds to push and 1 second to pop an element and for queue it takes 4 seconds to insert a element and 2 seconds to delete an element. (All other delays are negligible)
We have 5 elements 1,2,3,4,5 and we perform following tasks:
1) Insert all the element in stack starting from 1
2) Pop top 3 element from the stack.
3) Push them in the queue.
4) Remove two elements from queue and push them into the stack.

What is the total time spent in performing all the operations?

Question 19

Which of the following is the correct implementation of max () function in SQL using relational algebra on a table Emp (Sid, Sname, Sal)?

Question 20

Consider, a four-variable Boolean function, which contains half the number of minterms with an odd number of 1's. Then the Boolean expression can be realized with variables A, B, C, D as?

Question 21

Aman was implementing 4X16 Decoder using minimum number of 2X4 Decoders with enable Input. The implementation of 4X16 Decoder is given in the following figure.

decod.jpg

Now this Decoder has to be converted to 2X4 Decoder. Aman drew the following diagram.

2x4.jpg

But he was confused what to place in place of W, X, Y, Z out of A, B, C, D. Choose the correct option to help Aman solve the problem correctly.

Question 22

Suppose that four applicants a1, a2, a3, and a4 are available to fill six vacant positions p1, p2, p3, p4, p5 and p6. Applicant a1 is qualified to fill position p2 or p5. Applicant a2 is qualified to fill position p2 or p5. Applicant a3 is qualified for p1, p2, p3, p4 or p6. Applicant a4 can fill jobs p2 or p5. What is the maximum number of positions that can be filled?

Question 23

The following system of equations
x1 + x2 + 2x3 = 1
x1 + 2x2 + 3x3 = 2
x1 + 4x2 + αx3 = 4
has a unique solution. The only possible value(s) for α is/are

Question 24

Let X be a random variable following normal distribution with mean +1 and variance 4. Let Y be another normal variable with mean –1 and variance unknown. If P(X ≤ -1) = P(Y ≥ 2), the standard deviation of Y is

Question 25

A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is

Question 26

The security system at an IT office is composed of 10 computers of which exactly four are working. To check whether the system is functional, the officials inspect four of the computers picked at random (without replacement). The system is deemed functional if at least three of the four computers inspected are working. Let the probability that the system is deemed functional be denoted by p Then 100p= ______.

Question 27

The coefficient of in is ____________.

Question 28

Consider the following B-Tree:

The number of nodes to be traversed in searching for 49 is ______

Question 29

Consider the following graph :

How many Breadth First Traversals are possible starting from vertex A ____________.

Question 30

The number of 3 x 8 decoders with enable line needed to construct a 64K x 16 RAM from 1k x 2 RAM?
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Jun 16GATE & PSU CS