Let c¹, cⁿ be scalars not all zero. Such that the following expression holds:

where a_i is column vectors in Rⁿ. Consider the set of linear equations.

where A = [a₁.......a_n] and

Then, Set of equations has

Consider the following functions from positives integers to real numbers

The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:

Consider the following table

Match the algorithm to design paradigms they are based on:

Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are:

The n-bit fixed-point representation of an unsigned real number X uses f bits for the fraction part. Let i = n-f. The range of decimal values for X in this representation is

Consider the C code fragment given below.

typedef struct node   {
    int data;
    node* next;
}   node;

void join(node* m, node* n)   {
    node*  p = n;
    while(p→next  !=NULL)    {
       p = p→next; 
    }
    p→next=m;
}

Assuming that m and n point to valid NULL-terminated linked lists, invocation of join will

When two 8-bit numbers A₇...A₀ and B₇...B₀ in 2’s complement representation (with A₀ and B₀ as the least significant bits) are added using a ripple-carry adder, the sum bits obtained are S₇...S₀ and the carry bits are C₇...C₀. An overflow is said to have occurred if

Consider the C struct defined below:

    struct data   {
        int marks [100];
        char grade;
        int cnumber;
    };
    struct data student;

The base address of student is available in register R1. The field student.grade can be accessed efficiently using

Consider the following intermediate program in three address code

           p = a - b
           q = p * c
           p = u * v
           q = p + q

Which of the following corresponds to a static single assignment form of the above code?

Consider the following C code:

             #include <stdio.h>
             int *assignval(int *x, int val)   {
                  *x = val;
                  return x;
             }

             void main ( )  {
                  int  *x = malloc(sizeof(int));
                  if(NULL == x)  return;
                     x = assignval(x, 0);
                     if(x)  {
                           x = (int *)malloc(size of(int));
                           if(NULL == x)  return;
                              x = assignval(x, 10);
                     }
                     printf("%dn",  *x);
                     free(x);
              }

The code suffers from which one of the following problems:

Consider a TCP client and a TCP server running on two different machines. After completing data transfer, the TCP client calls close to terminate the connection and a FIN segment is sent to the TCP server. Server-side TCP responds by sending an ACK, which is received by the client-side TCP. As per the TCP connection state diagram (RFC 793), in which state does the client-side TCP connection wait for the FIN from the server-side TCP?