GATE CSE 2013


Question 1
A binary operation \oplus on a set of integers is defined as x \oplus y= x^{2}+y^{2}. Which one of the following statements is TRUE about \oplus ?
A
Commutative but not associative
B
Both commutative and associative
C
Associative but not commutative
D
Neither commutative nor associative
Discrete Mathematics   Set Theory
Question 2
Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?
A
8/(2e^{3})
B
9/(2e^{3})
C
17/(2e^{3})
D
26/(2e^{3})
Discrete Mathematics   Probability Theory


Question 3
Which one of the following does NOT equal
\begin{bmatrix} 1 & x&x^{2} \\ 1& y & y^{2}\\ 1&z & z^{2} \end{bmatrix}?
A
\begin{bmatrix} 1 & x(x+1)&x+1 \\ 1& y(y+1) & y+1\\ 1&z(z+1) & z+1 \end{bmatrix}
B
\begin{bmatrix} 1 & x(x+1)&x^{2}+1 \\ 1& y(y+1) & y^{2}+1\\ 1&z(z+1) & z^{2}+1 \end{bmatrix}
C
\begin{bmatrix} 0& x(x+1)&x^{2}+1 \\ 0& y(y+1) & y^{2}+1\\ 1&z & z^{2} \end{bmatrix}
D
\begin{bmatrix} 2& x(x+1)&x^{2}+1 \\ 2& y(y+1) & y^{2}+1\\ 1&z & z^{2} \end{bmatrix}
Engineering Mathematics   Linear Algebra
Question 4
The smallest integer that can be represented by an 8-bit number in 2's complement form is
A
-256
B
-128
C
-127
D
0
Digital Logic   Number System
Question 5
In the following truth table, V = 1 if and only if the input is valid.

What function does the truth table represent?
A
Priority encoder
B
Decoder
C
Multiplexer
D
Demultiplexer
Digital Logic   Combinational Circuit




There are 5 questions to complete.

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