GATE CSE 2017 Set 1 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2017 Set 1

MCQ (Single Correct Answer)

-0.6

Let $$A$$ be $$n\,\, \times \,\,n$$ real valued square symmetric matrix of rank $$2$$ with $$\sum\limits_{i = 1}^n {\sum\limits_{j = 1}^n {A_{ij}^2 = 50.} } $$
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?

Both $$(I)$$ and $$(II)$$

$$(I)$$ only

$$(II)$$ only

Neither $$(I)$$ nor $$(II)$$

GATE CSE 2017 Set 1

MCQ (Single Correct Answer)

-0.33

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. $(\neg p) \vee q$

I only

I and IV only

II only

II and III only

GATE CSE 2017 Set 1

MCQ (Single Correct Answer)

-0.33

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. $\neg \exists x(\forall y \neg R(x, y))$

IV only

I and IV only

II only

II and III only

GATE CSE 2017 Set 1

MCQ (Single Correct Answer)

-0.33

After Rajendra Chola returned from his voyage to Indonesia, he ______ to visit the temple in Thanjavur.

was wishing

is wishing

wished

had wished

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