1
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Let, $${x_1} \oplus {x_2} \oplus {x_3} \oplus {x_4} = 0$$ where $${x_1},\,{x_2},\,{x_3},\,{x_4}$$ are Boolean Variables, and $$ \oplus $$ is the $$XOR$$ operator.

Which one of the following must always be TRUE?

A
$${x_1}{x_2}{x_3}{x_4} = 0$$
B
$${x_1}{x_3} + {x_2} = 0$$
C
$${\overline x _1} \oplus {\overline x _3} = {\overline x _2} \oplus {\overline x _4}$$
D
$${x_1} + {x_2} + {x_3} + {x_4} = 0$$
2
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Let $$ \ne $$ be a binary operator defined as $$X \ne Y = X' + Y'$$ where $$𝑋$$ and $$𝑌$$ are Boolean variables. Consider the following two statements. $$$\eqalign{ & \left( {S1} \right)\,\,\,\,\,\,\,\left( {P \ne Q} \right) \ne R = P \ne \left( {Q \ne R} \right) \cr & \left( {S2} \right)\,\,\,\,\,\,\,Q \ne R = R \ne Q \cr} $$$

Which of the following is/are true for the Boolean variables $$𝑃, 𝑄$$ and $$𝑅$$?

A
Only $$S1$$ is true
B
Only $$S2$$ is true
C
Both $$S1$$ and $$S2$$ are true
D
Neither $$S1$$ nor $$S2$$ are true
3
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Consider the following combinational function block involving four Boolean variables $$x, y, a,$$
$$b$$ where $$x, a, b$$ are inputs and $$y$$ is the output. GATE CSE 2014 Set 3 Digital Logic - Boolean Algebra Question 44 English
Which one of the following digital logic blocks is the most suitable for implementing this function?
A
Full adder
B
Priority encoder
C
Multiplexer
D
Flip-flop
4
GATE CSE 2014 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Consider the following Boolean expression for $$F:$$
$$F\left( {P,\,Q,\,R,\,S} \right) = PQ + \overline P QR + \overline P Q\overline R S.$$
The minimal sum-of-products form of $$F$$ is
A
$${PQ} + QR + QS$$
B
$$P + Q + R + S$$
C
$$\overline P + \overline Q + \overline R + \overline S $$
D
$$\overline P R + \overline P \overline R S + P$$
GATE CSE Subjects
Software Engineering
Web Technologies
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