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 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 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 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 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




There are 5 questions to complete.

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