GATE CSE
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 :
I. S can launch a birthday attack to replace m with a fraudulent message.
II. A third party attacker can launch a birthday attack to replace m with a fraudulent
message.
III. R can launch a birthday attack to replace m with a fraudulent message.
Where $$A = \left[ {{a_1},.....,\,\,{a_n}} \right]$$ and $$b = \sum\limits_{i = 1}^n {{a_i}.} $$
The set of equations has
Consider the following statements.
$$(I)$$ One eigenvalue must be in $$\left[ { - 5,5} \right]$$
$$(II)$$ The eigenvalue with the largest magnitude must be strictly greater than $$5$$
Which of the above statements about engenvalues of $$A$$ is/are necessarily correct?
The statement $(\neg p) \Rightarrow(\neg q)$ is logically equivalent to which of the statements below?
I. $\quad p \Rightarrow q$
II. $q \Rightarrow p$
III. $(\neg q) \vee p$
IV. $(\neg p) \vee q$
Consider the first-order logic sentence $F: \forall x(\exists y R(x, y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$?
I. $\quad \exists y(\exists x R(x, y))$
II. $\quad \exists y(\forall x R(x, y))$
III. $\forall y(\exists x R(x, y))$
IV. $\neg \exists x(\forall y \neg R(x, y))$
General Aptitude
After Rajendra Chola returned from his voyage to Indonesia, he ______ to visit the temple in Thanjavur.
"The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history."
Which of the following statements best reflects the author's opinion?
