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 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))

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.