GATE CSE 2016 SET-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 ________.

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}?

\lim_{x\rightarrow 4}\frac{sin(x-4)}{x-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 __________.

Two eigen values of a 3x3 real matrix P are (2+\sqrt{-1}) and 3.The determinantof P is __________.

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

The 16 bit 2's complement representation of an integer is 1111 1111 1111 0101; its decimal representation is__________ .

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 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 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)?