GATE CSE 2016 Set 2 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2016 Set 2

MCQ (Single Correct Answer)

-0.6

Which one of the following well-formed formulae in predicate calculus is NOT valid?

$$\left( {\forall xp\left( x \right) \vee \forall xq\left( x \right)} \right) \Rightarrow \left( {\exists x\neg p\left( x \right) \vee \forall xq\left( x \right)} \right)$$

$$\left( {\exists xp\left( x \right) \vee \exists xq\left( x \right)} \right) \Rightarrow \exists x\left( {p\left( x \right) \vee q\left( x \right)} \right)$$

$$\exists x\left( {p\left( x \right) \wedge q\left( x \right)} \right) \Rightarrow \left( {\exists xp\left( x \right) \wedge \exists xq\left( x \right)} \right)$$

$$\forall x\left( {p\left( x \right) \vee q\left( x \right)} \right) \Rightarrow \left( {\forall xp\left( x \right) \vee \forall xq\left( x \right)} \right)$$

GATE CSE 2016 Set 2

Numerical

-0

The value of the expression $${13^{99}}$$ ($$mod$$ $$17$$), in the range $$0$$ to $$16,$$ is ______________ .

Your input ____

GATE CSE 2016 Set 2

MCQ (Single Correct Answer)

-0.3

Consider the system, each consisting of m linear equations in $$n$$ variables.
$$I.$$ $$\,\,\,$$ If $$m < n,$$ then all such system have a solution
$$II.$$ $$\,\,\,$$ If $$m > n,$$ then none of these systems has a solution
$$III.$$ $$\,\,\,$$ If $$m = n,$$ then there exists a system which has a solution

Which one of the following is CORRECT?

$$I$$ , $$II$$ and $$III$$ are true

Only $$II$$ and $$III$$ are true

Only $$III$$ is true

None of them is true

GATE CSE 2016 Set 2

Numerical

-0

Let $${A_1},\,{A_2},\,{A_3}$$ and $${A_4}$$ be four matrices of dimensions $$10 \times 5,\,5 \times 20,\,20 \times 10,$$ and $$10 \times 5,$$ respectively. The minimum number of scalar multiplications required to find the product $${A_1}{A_2}{A_3}{A_4}$$ using the basic matrix multiplication method is _________.

Your input ____

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