GATE Questions

Consider the following B+ tree with 5 nodes, in which a node can store at most 3 key values. The value 23 is now inserted in the B+ tree. Which of the following options(s) is/are CORRECT?

A shop has 4 distinct flavors of ice-cream. One can purchase any number of scoops of any flavor. The order in which the scoops are purchased is inconsequential. If one wants to purchase 3 scoops of ice-cream, in how many ways can one make that purchase?

Identify the ONE CORRECT matching between the OSI layers and their corresponding functionalities as shown.

OSI Layers
(a) Network layer
(b) Transport layer
(c) Datalink layer

Functionalities
(I) Packet routing
(II) Framing and error handling
(III) Host to host communication

A box contains 5 coins: 4 regular coins and 1 fake coin. When a regular coin is tossed, the probability $P(head)=0.5$ and for a fake coin, $P(head)=1$. You pick a coin at random and toss it twice, and get two heads. The probability that the coin you have chosen is the fake coin is ______. (rounded off to two decimal places)

In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point P and line QR. What is the ratio of the area of the triangle PST to the area of the trapezium SQRT?

Note: The figure shown is representative.

“I put the brown paper in my pocket along with the chalks, and possibly other things. I suppose every one must have reflected how primeval and how poetical are the things that one carries in one's pocket: the pocket-knife, for instance the type of all human tools, the infant of the sword. Once I planned to write a book of poems entirely about the things in my pocket. But I found it would be too long: and the age of the great epics is past.”

(From G.K. Chesterton’s “A Piece of Chalk”)

Based only on the information provided in the above passage, which one of the following statements is true?

Ravi had ______ younger brother who taught at ______ university. He was widely regarded as ______ honorable man.

Select the option with the correct sequence of articles to fill in the blanks.

#include < stdio.h>  
void foo(int *p, int x){  
    *p=x;  
}  
int main(){  
    int *z;  
    int a = 20, b = 25;  
    z = &a;  
    foo(z,b);  
    printf("%d",a);  
    return 0;  
}  

The output of the given C program is ________. (Answer in integer)

Despite his initial hesitation, Rehman's _________ to contribute to the success of the project never wavered.

Select the most appropriate option to complete the above sentence.

According to the map shown in the figure, which one of the following statements is correct?

Note: The figure shown is representative.

The CEO’s decision to downsize the workforce was considered myopic because it sacrificed long-term stability to accommodate short-term gains.

Select the most appropriate option that can replace the word “myopic” without changing the meaning of the sentence.

Suppose we are transmitting frames between two nodes using Stop-and-Wait protocol. The frame size is 3000 bits. The transmission rate of the channel is 2000 bps (bits/second) and the propagation delay between the two nodes is 100 milliseconds. Assume that the processing times at the source and destination are negligible. Also, assume that the size of the acknowledgement packet is negligible. Which ONE of the following most accurately gives the channel utilization for the above scenario in percentage?

Consider a probability distribution given by the density function $P(x)$.

$P(x)=\{\begin{array}{ll}C{x}^2,& \text{for }1\le x\le 4\\ 0,& \text{for }x<1\text{ or }x>4\end{array}$

The probability that $x$ lies between 2 and 3, i.e., $P(2\le x\le 3)$ is ________. (rounded off to three decimal places)

Consider the following statements:

(i) Address Resolution Protocol (ARP) provides a mapping from an IP address to the corresponding hardware (link-layer) address.
(ii) A single TCP segment from a sender S to a receiver R cannot carry both data from S to R and acknowledgement for a segment from R to S.

Which ONE of the following is CORRECT?

Let $p_1$ and $p_2$ denote two arbitrary prime numbers. Which one of the following statements is correct for all values of $p_1$ and $p_2$?

Suppose in a multiprogramming environment, the following C program segment is executed. A process goes into I/O queue whenever an I/O related operation is performed. Assume that there will always be a context switch whenever a process requests for an I/O, and also whenever the process returns from an I/O. The number of times the process will enter the ready queue during its lifetime (not counting the time the process enters the ready queue when it is run initially) is ______. (Answer in integer)

int main()  
{  
   int x=0, i=0;  
   scanf("%d",&x);  
   for(i=0; i<20; i++)  
   {  
       x = x+20;  
       printf("%d\n",x);  
   }  
   return 0;  
}   

Bird : Nest :: Bee : _______

Select the correct option to complete the analogy.

A fair six-faced dice, with the faces labelled 1, 2, 3, 4, 5, and 6, is rolled thrice. What is the probability of rolling 6 exactly once?

In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The corner L of the rectangle is on the side QR. Side MN of the rectangle passes through the corner S of the square.

What is the area (in cm^2) of the rectangle PLMN?

Note: The figure shown is representative.

Based only on the conversation below, identify the logically correct inference:

"Even if I had known that you were in the hospital, I would not have gone there to see you", Ramya told Josephine.