GATE-CS-2005

Question 11

Let G be a simple graph with 20 vertices and 100 edges. The size of the minimum vertex cover of G is 8. Then, the size of the maximum indepen­dent set of G is

• 12
• 8
• Less than 8
• More than 12

Question 12

Let f(x) be the continuous probability density func­tion of a random variable X. The probability that a < X ≤ b, is

		 
A) f(b - a)
B) f(b) - f(a)
C)  
D) 

• A
• B
• C
• D

Question 13

The set {1, 2, 4, 7, 8, 11, 13, 14} is a group under multiplication modulo 15. The inverses of 4 and 7 are respectively

• 3 and 13
• 2 and 11
• 4 and 13
• 8 and 14

Question 14

The grammar A → AA | (A) | ε is not suitable for predictive-parsing because the grammar is

• ambiguous

• left-recursive

• right-recursive

• an operator-grammar

Question 15

Consider the following circuit. Which one of the following is TRUE?

• f is independent of X
• f is independent of Y
• f is independent of Z
• None of X, Y, Z is redundant

Question 16

The range of integers that can be represented by an n bit 2\'s complement number system is

• - 2^{n - 1} to (2^{n - 1} - 1)
• - (2^{n - 1} - 1) to (2^{n - 1} - 1)
• - 2^{n - 1} to 2^{n - 1}
• - (2^{n - 1} + 1) to (2^{n - 1} + 1)

Question 17

The hexadecimal representation of 657₈ is

• 1AF
• D78
• D71
• 32F

Question 18

The switching expression corresponding to f(A, B, C, D) = Σ (1, 4, 5, 9, 11, 12) is

• BC\'D\' + A\'C\'D + AB\'D
• ABC\' + ACD + B\'C\'D
• ACD\' + A\'BC\' + AC\'D\'
• A\'BD + ACD\' + BCD\'

Question 19

Which one of the following is true for a CPU having a single interrupt request line and a single interrupt grant line?

• Neither vectored interrupt nor multiple interrupting devices are possible.

• Vectored interrupts are not possible but multiple interrupting devices are possible.

• Vectored interrupts and multiple interrupting devices are both possible.

• Vectored interrupt is possible but multiple in­terrupting devices are not possible.

Question 20

Normally user programs are prevented from handling I/O directly by I/O instructions in them. For CPUs having explicit I/O instructions, such I/O protection is ensured by having the I/O instructions privileged. In a CPU with memory mapped I/O, there is no explicit I/O instruction. Which one of the following is true for a CPU with memory mapped I/O?

• I/O protection is ensured by operating system routine (s)
• I/O protection is ensured by a hardware trap
• I/O protection is ensured during system configuration
• I/O protection is not possible