1
GATE CSE 1990
+5
-1.5
For the synchronous counter shown in fig. write the truth table of $${Q_0},\,\,{Q_1}$$ and $${Q_2}$$ after each pulse starting from $${Q_0} = {Q_1} = {Q_2} = 0$$ and determine the counting sequenced also the modulus of the counter

What is the modules of the counter with initial state $${Q_2}\,{Q_1}\,{Q_0} = 000$$

A
$$3$$
B
$$4$$
C
$$5$$
D
$$6$$
2
GATE CSE 1990
+2
-0.6
Indicate which of the following well-formed formula are valid:
A
$$\left( {\left( {{\rm P} \Rightarrow Q} \right) \wedge \left( {Q \Rightarrow R} \right)} \right) \Rightarrow \left( {{\rm P} \Rightarrow R} \right).$$
B
$$\left( {{\rm P} \Rightarrow Q} \right) \Rightarrow \left( { \sim P \Rightarrow \sim Q} \right)$$
C
$$\left( {{\rm P}\, \wedge \,\left( { \sim {\rm P}\,\,V \sim Q} \right)} \right) \Rightarrow Q\left( { \sim {\rm P} \Rightarrow \sim Q} \right)$$
D
$$\left( {\left( {{\rm P} \Rightarrow R} \right) \vee \left( {Q \Rightarrow R} \right)} \right) \Rightarrow \left( {\left( {\left( {{\rm P} \vee Q} \right) \Rightarrow R} \right)} \right)$$
3
GATE CSE 1990
+2
-0.6
A graph is planar if and only if,
A
it does not contain subgraphs homeomorphic to K5 and K3, 3.
B
it does not contain subgraphs isomorphic to K5 or K3, 3.
C
it does not contain subgraphs isomorphic to K5 and K3, 3.
D
it does not contain subgraphs homeomorphic to K5 or K3, 3.
4
GATE CSE 1990
Fill in the Blanks
+2
-0
The highest-response ratio next scheduling policy favours $$.......$$ jobs, but it also limits the waiting time of $$.....$$ jobs.
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