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# GATE 2001 : Computer Science And Information Technology

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SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives, A, B, C and D are provided. Choose the most appropriate alternative and darken its bubble on the Objective Response Sheet (ORS) against the corresponding sub-question number using a soft HB pencil. Do not darken more than one bubble for any sub-question. Do not use the ORS for any rough work. You may use the answer book for any rough work, if needed. 1.1 Consider the following statements: S1: The sum of two singular n n matrices may be non-singular S2: The sum of two n n non-singular matrices may be singular. Which of the following statements is correct? (a) S1 and S2 are both true (c) S1 is false, S2 is true 1.2 (b) S1 is true, S2 is false (d) S1 and S2 are both false Consider the following relations: R1 (a,b) iff (a+b) is even over the set of integers R2 (a,b) iff (a+b) is odd over the set of integers R3 (a,b) iff a.b > 0 over the set of non-zero rational numbers R4 (a,b) iff |a b| 2 over the set of natural numbers Which of the following statements is correct? (a) R1 and R2 are equivalence relations, R3 and R4 are not (b) R1 and R3 are equivalence relations, R2 and R4 are not (c) R1 and R4 are equivalence relations, R2 and R3 are not (d) R1, R2, R3 and R4 are all equivalence relations 1.3 Consider two well-formed formulas in prepositional logic F1: P P F2: (P P) ( P P) Which of the following statements is correct? (a) F1 is satisfiable, F2 is valid (c) F1 is unsatisfiable, F2 is valid 1.4 (b) F1 unsatisfiable, F2 is satisfiable (d) F1 and F2 are both satisfiable consider the following two statements: { S2: {0 } S1: 02n n 1 is a regular language m n m+ n 1 0 } m 1 and n 1 is a regular language Which of the following statements is correct? (a) Only S1 is correct (b) Only S2 is correct (c) Both S1 and S2 are correct (d) None of S1 and S2 is correct

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Additional Info : Solved GATE exam paper study guide - GATE 2001 : Computer Science And
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