### GATE CS 2009 Solved Paper | GATE Computer Science Solved Paper 2009

**Q. No. 1 – 20 Carry One Mark Each**

**1. Which one of the following in NOT necessarily a property of a Group?**

(A) Commutativity (B) Associativity

(C) Existence of inverse for every element (D) Existence of identity

**2.** What is the chromatic number of an n-vertex simple connected graph which does not contain any odd length cycle? Assume n³ 2.

(A) 2 (B) 3 (C) n-1 (D) n

**3. Which one of the following is TRUE for any simple connected undirected graph with more than 2 vertices?**

(A) No two vertices have the same degree.

(B) At least two vertices have the same degree.

(C) At least three vertices have the same degree.

(D) All vertices have the same degree.

**4. Consider the binary relation R = {(x,y), (x,z), (z,x), (z,y)} on the set {x,y,z}. Which one of the following is TRUE?**

(A) R is symmetric but NOT antisymmetric

(B) R is NOT symmetric but antisymmetric

(C) R is both symmetric and antisymmetric

(D) R is neither symmetric nor antisymmetric

**5. (1217)8 is equivalent to**

(A) (1217)16 (B) (028F)16 (C) (2297)10 (D) (0B17)16

**6. What is the minimum number of gates required to implement the Boolean**

function (AB+C) if we have to use only 2-input NOR gates?

(A) 2 (B) 3 (C) 4 (D) 5

**7. How many 32K x 1 RAM chips are needed to provide a memory capacity of 256Kbytes?**

(A) 8 (B) 32 (C) 64 (D) 128

**8. A CPU generally handles an interrupt by executing an interrupt service routine**

(A) As soon as an interrupt is raised

(B) By checking the interrupt register at the end of fetch cycle.

(C) By checking the interrupt register after finishing the execution of the current instruction.

(D) By checking the interrupt register at fixed time intervals.

**9. In which one of the following page replacement policies, Belady’s anomaly may occur?**

(A) FIFO (B) Optimal (C) LRU (D) MRU

10. The essential content(s) in each entry of a page table is / are

(A) Virtual page number

(B) Page frame number

(C) Both virtual page number and page frame number

(D) Access right information

11. What is the number of swaps required to sort n elements using selection sort, in the worst case?

(A) q(n) (B) q(n log n) (C) 2 q(n ) (D) 2 q(n log n)

**12. S ® aSa bSb a b ;The language generated by the above grammar over the alphabet {a,b} is the set of**

(A) All palindromes.

(B) All odd length palindromes.

(C) Strings that begin and end with the same symbol

(D) All even length palindromes.

**13. Which of the following statement(s) is / are correct regarding Bellman-Ford shortest path algorithm?**

P. Always finds a negative weighted cycle, if one exists.

Q. Finds whether any negative weighted cycle is reachable from the source.

(A) P only (B) Q only

(C) both P and Q (D) Neither P nor Q

**14. Let A p be a problem that belongs to the class NP. Then which one of the following is TRUE?**

(A) There is no polynomial time algorithm for A p .

(B) If A p can be solved deterministically in polynomial time, then P = NP.

(C) If A p is NP-hard, then it is NP-complete.

(D) A p may be undecidable.

**15. Which one of the following languages over the alphabet {0,1} is described by the regular expression: (0+1)*0(0+1)*0(0+1)*?**

(A) The set of all strings containing the substring 00.

(B) The set of all strings containing at most two 0’s.

(C) The set of all strings containing at least two 0’s.

(D) The set of all strings that begin and end with either 0 or 1.

**16. Which one of the following is FALSE?**

(A) There is unique minimal DFA for every regular language

(B) Every NFA can be converted to an equivalent PDA.

(C) Complement of every context-free language is recursive.

(D) Every nondeterministic PDA can be converted to an equivalent deterministic PDA.

17. Match all items in Group 1 with correct options from those given in Group 2

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