GATE CSE 2014 Set 3 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

-0.3

Consider the following interm expression of $$F:$$
$$F\left( {P,\,Q,\,R,\,S} \right) = \sum {0,2,5,7,8,10,13,15} $$
The minterms $$2, 7, 8$$ and $$13$$ are 'do not care' terms. The minimal sum-of-products form for $$F$$ is _______

$$Q\overline S + \overline Q S$$

$$\overline Q \overline S + QS$$

$$\overline Q \overline R \overline S + \overline Q R\overline S + Q\overline R S + QRS$$

$$\overline P \overline Q \overline S + \overline P QS + PQS + P\overline Q \overline S $$

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

-0.6

GATE CSE 2014 Set 3 Digital Logic - Sequential Circuits Question 17 English

The above synchronous sequential circuit built using $$JK$$ flip-flops is initialized with $${Q_2}{Q_1}{Q_0} = 000.\,\,$$ The state sequence for this circuit for the next $$3$$ clock cycles is

$$001,010,011$$

$$111,110,101$$

$$100,110,111$$

$$100,011,001$$

GATE CSE 2014 Set 3

Numerical

-0

Let S be a sample space and two mutually exclusive events A and B be such that $$A\, \cup \,B = \,S$$. If P(.) denotes the probability of the event, the maximum value of P(A) P(B) is ________________.

Your input ____

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

-0.6

The CORRECT formula for the sentence, "not all rainy days are cold" is

$$\forall d\left( {Rainy\left( d \right) \wedge \sim Cold\left( d \right)} \right)$$

$$\forall d\left( { \sim Rainy\left( d \right) \to Cold\left( d \right)} \right)$$

$$\exists d\left( { \sim Rainy\left( d \right) \to Cold\left( d \right)} \right)$$

$$\exists d\left( {Rainy\left( d \right) \wedge \sim Cold\left( d \right)} \right)$$

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