GATE-CS-2004

Question 21

How many 8-bit characters can be transmitted per second over a 9600 baud serial communication link using asynchronous mode of transmission with one start bit, eight data bits, two stop bits, and one parity bit ?

• 600
• 800
• 876
• 1200

Question 22

Identify the correct translation into logical notation of the following assertion.

"Some boys in the class are taller than all the girls" 

Note : taller(x,y) is true if x is taller than y.

• (∃x) (boy(x) → (∀y) (girl(y) ∧ taller(x,y)))
• (∃x) (boy(x) ∧ (∀y) (girl(y) ∧ taller(x,y)))
• (∃x) (boy(x) → (∀y) (girl(y) → taller(x,y)))
• (∃x) (boy(x) ∧ (∀y) (girl(y) → taller(x,y)))

Question 23

Consider the binary relation:

S = {(x, y) | y = x+1 and x, y ∈ {0, 1, 2, ...}}

The reflexive transitive closure of S is

• {(x, y) | y > x and x, y ∈ {0, 1, 2, ... }}
• {(x, y) | y ≥ x and x, y ∈ {0, 1, 2, ... }}
• {(x, y) | y < x and x, y ∈ {0, 1, 2, ... }}
• {(x, y) | y ≤ x and x, y ∈ {0, 1, 2, ... }}

Question 24

If a fair coin is tossed four times. What is the probability that two heads and two tails will result?

• 3/8
• 1/2
• 5/8
• 2/4

Question 25

The number of different n × n symmetric matrices with each element being either 0 or 1 is: (Note: power(2, x) is same as 2^x)

• power(2, n)
• power(2, n²)
• power(2, (n² + n)/2)
• power(2, (n² - n)/2)

Question 26

Let A, B, C, D be n × n matrices, each with non-­zero determinant. If ABCD = 1, then B^-1 is

• D^-1C^-1A^-1
  

• CDA
  

• ADC
  

• Does not necessarily exist
  

Question 27

What is the result of evaluating the following two expressions using three-digit floating point arithmetic with rounding?

(113. + -111.) + 7.51
113. + (-111. + 7.51) 

• 9.51 and 10.0 respectively
• 10.0 and 9.51 respectively
• 9.51 and 9.51 respectively
• 10.0 and 10.0 respectively

Question 28

The tightest lower bound on the number of comparisons, in the worst case, for comparison-based sorting is of the order of

• n
• n²
• n log n
• n log² n

Question 29

The problems 3-SAT and 2-SAT are

• both in P
• both NP-complete
• NP-complete and in P respectively
• undecidable and NP-complete respectively

Question 30

Consider the following C function: 

C

int f(int n)
{
   static int i = 1;
   if (n >= 5)
      return n;
   n = n+i;
   i++;
   return f(n);
}

The value returned by f(1) is

• 5

• 6

• 7

• 8