GATE CSE 2017 SET-1

 Question 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. $(\neg p)\vee q$
 A I only B I and IV only C II only D II and III only
Discrete Mathematics   Propositional Logic
Question 1 Explanation:
 Question 2
Consider the first-order logic sentence $F:\forall x(\exists yR(x,y))$. 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. $\neg \exists x(\forall y\neg R(x,y))$
 A IV only B I and IV only C II only D II and III only
Discrete Mathematics   Propositional Logic
Question 2 Explanation:

 Question 3
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
 A a unique solution at $x=J_{n}$ where $J_{n}$ denotes a n-dimensional vector of all 1 B no solution C infinitely many solutions D finitely many solutions
Engineering Mathematics   Linear Algebra
Question 3 Explanation:
 Question 4
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:
 A $log_{2}n,\frac{100}{n}, 10,\sqrt{n},n$ B $\frac{100}{n}, 10,log_{2}n, \sqrt{n}, n$ C $10, \frac{100}{n}, \sqrt{n}, log_{2}n, n$ D $\frac{100}{n}, log_{2}n, 10, \sqrt{n}, n$
Algorithm   Asymptotic Notation
Question 4 Explanation:
 Question 5
Consider the following table:

Match the algorithms to the design paradigms they are based on.
 A P-(ii), Q-(iii),R-(i) B P-(iii), Q-(i), R-(ii) C P-(ii), Q-(i), R-(iii) D P-(i), Q-(ii), R-(iii)
Algorithm   Greedy Technique
Question 5 Explanation:

There are 5 questions to complete.