GATE CSE 2016 SET-1

Question 1
Let p,q, r, s represent the following propositions.

p: x\in{8,9,10,11,12}
q: x is a composite number
r: x is a perfect square
s: x is a prime number

The integer x\geq2 which satisfies \neg((p\Rightarrow q)\wedge (\neg r \vee \neg s)) is ________.
A
9
B
10
C
11
D
12
Discrete Mathematics   Propositional Logic
Question 2
Let a_{n} be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of the following is the recurrence relation for a_{n}?
A
a_{n}=a_{n-1}+2a_{n-2}
B
a_{n}=a_{n-1}+a_{n-2}
C
a_{n}=2a_{n-1}+a_{n-2}
D
a_{n}=2a_{n-1}+2a_{n-2}
Discrete Mathematics   Recurrence
Question 3
\lim_{x\rightarrow 4}\frac{sin(x-4)}{x-4}=_________.
A
0
B
1
C
2
D
4
Engineering Mathematics   Calculus
Question 4
A probability density function on the interval [a,1] is given by 1/x^{2} and outside this interval the value of the function is zero.The value of a is __________.
A
0.25
B
0.5
C
0.75
D
1
Discrete Mathematics   Probability Theory
Question 5
Two eigen values of a 3x3 real matrix P are (2+\sqrt{-1}) and 3.The determinantof P is __________.
A
9
B
15
C
6
D
30
Engineering Mathematics   Linear Algebra
Question 6
Consider the Boolean operator with the following properties:
x \# 0=x, x \# 1=\bar{x}, x \# x=0 and x \# \bar{x}=1. Then x \# y is equivalent to
A
x\bar{y}+\bar{x}y
B
x\bar{y}+\bar{x}\bar{y}
C
\bar{x}y+xy
D
xy+\bar{x}\bar{y}
Digital Logic   Boolean Algebra
Question 7
The 16 bit 2's complement representation of an integer is 1111 1111 1111 0101; its decimal representation is__________ .
A
-11
B
11
C
10
D
-10
Digital Logic   Number System
Question 8
We want to design a synchronous counter that counts these quence 0-1-0-2-0-3 and then repeats. The minimum number of J-K flip flop srequired to implement this counteris ________.
A
3
B
4
C
5
D
2
Digital Logic   Sequential Circuit
Question 9
A processor can support a maximum memory of 4GB, where the memory is word-addressable (a word consists of two bytes). The size of the address bus of the process or is at least bits________.
A
32
B
31
C
16
D
15
Operating System   Memory Management
Question 10
A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are performed efficiently. Which one of the following statements is CORRECT (n refers to the number of items in the queue)?
A
Both operations can be performed in O(1) time
B
At most one operation can be performed in O(1) time but the worst case time for the other operation will be \Omega(n)
C
The worst case time complexity for both operations will be \Omega(n)
D
Worst case time complexity for both operations will be \Omega(logn)
Data Structure   Queue
There are 10 questions to complete.

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