GATE-CS-2016 (Set 1)

Question 11

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

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

  Note : This question was asked as Numerical Answer Type.

• 8
• 9
• 11
• 12

Question 12

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
• B
• C
• D

Question 13

  Note : This question was asked as Numerical Answer Type.

• 0
• 1
• 2
• 3

Question 14

A probability density function on the interval [a, 1] is given by 1 / x² and outside this interval the value of the function is zero. The value of a is :   Note : This question was asked as Numerical Answer Type.

• -1
• 0
• 1
• 0.5

Question 15

Two eigenvalues of a 3 x 3 real matrix P are (2 + √ -1) and 3. The determinant of P is _____   

• 0

• 1

• 15

• -1

Question 16

Consider the Boolean operator # with the following properties: x#0 = x, x#1 = x\', x#x = 0 and x#x\' = 1 Then x#y is equivalent to

• x\'y + xy\'
• xy\' + (xy)
• x\'y + xy
• xy + (xy)\'

Question 17

The 16-bit 2’s complement representation of an integer is 1111 1111 1111 0101; its decimal representation is   Note : This question was asked as Numerical Answer Type.

• 10
• 11
• -10
• -11

Question 18

We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then repeats. The minimum number of J-K flip-flops required to implement this counter is   Note : This question was asked as Numerical Answer Type.

• 1

• 2

• 4

• 5

Question 19

A processor can support a maximum memory of 4 GB, where the memory is word-addressable (a word consists of two bytes). The size of the address bus of the processor is at ____ least bits.   Note : This question was asked as Numerical Answer Type.

• 16
• 31
• 32
• None

Question 20

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)?

• Both operations can be performed in O(1) time

• At most one operation can be performed in O(1) time but the worst case time for the other operation will be Ω(n)

• The worst case time complexity for both operations will be Ω(n)

• Worst case time complexity for both operations will be Ω(log n)