GATE CSE 2017 SET-1

The statement (\neg p)\Rightarrow (\neg q) is logically equivalent to which of the statements below?
I. p\Rightarrow q
II. q \Rightarrow p
III. (\neg q)\vee p
IV. (\neg p)\vee q

Consider the first-order logic sentence F:\forall z(\exists yR(x,y)). Assuming non-empty logical domains, which of the sentences below are implied by F?
I. \exists y(\exists xR(x,y))
II. \exists y(\forall xR(x,y))
III. \forall y(\exists xR(x,y))
IV. \neg \exists x(\forall y\neg R(x,y))

Let c_{1}....c_{n} be scalars, not all zero, such that \sum_{i=1}^{n}c_{i}a_{i}=0
where a_{i} are column vectors in R^{n}. Consider the set of linear equations Ax = b
where A=a_{1}....a_{n} and b=\sum_{i=1}^{n}a_{i}. The set of equations has

Consider the following functions from positive integers to real numbers:

10,\sqrt{n},n, log_{2}n,\frac{100}{n}.

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

Consider the following table:

Match the algorithms to the 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 :
Note: The height of a tree with a single node is 0.

The n-bit fixed-point representation of an unsigned real number real 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 A_{7}....A_{0} and B_{7}....B_{0} in 2's complement representation (with A_{0} and B_{0} as the least significant bits ) are added using a ripple-carry Combinational Circuit, the sum bits obtained are S_{7}....S_{0} and the carry bits are C_{7}....C_{0}. An overflow is said to have occurred if

Consider the following context-free grammar over the alphabet \sum = {a,b,c} with S as the start symbol.

S\rightarrowabScT|abcT
T\rightarrowbT|b

Which one of the following represents the language generated by the above grammar ?