# 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 1 Explanation:
 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 2 Explanation:

 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 3 Explanation:
 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 4 Explanation:
 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
Question 5 Explanation:

There are 5 questions to complete.

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1. Q13 Option D – Correction (decryption part of the option has X and Y interchangef)