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PREVIOUS YEAR SOLVED PAPERS - GATE 2018

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21. Consider the following C program:
#include
Struct ournode {
   Char x, y, z;
};
int main() {
   struct ournode p = {‘1’, ‘0’, ‘a’ + 2};
   struct ournode *p = &q;
   printf(“%c, %c”, *((char*) q + 1), *((char*) q + 2));
   return 0;
}
The output of this program is :

  • Option : A
  • Explanation :
    So ‘a’ + 2 will be ‘c’, so Our next node p = {‘1’, ‘0’, ‘c’} and output will be 0, c. So answer is C
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22. In an Entity-Relationship (ER) model, suppose R is a many-to-one relationship from entity set E1 to entity set E2. Assume that E1 and E2 participate totally in R and that the cardinality of E1 is greater than the cardinality of E2.
Which one of the following is true about R?

  • Option : A
  • Explanation :
    E1 entries > E2 entities

    So Every entity in E1 is associated with exactly one entity in E2. So options A is correct options.
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23. Which one of the following is a closed form expression for the generating function of the sequence {an}, where an = 2n + 3 for all n = 0, 1, 2,.....?

  • Option : D
  • Explanation : The Given functions is, an = 2n + 3
    generating function for 1 is and n is , the generating function for an is

    Which is option (D).
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24. Let ⊕ and ⊙ denote the Exclusive OR and Exclusive NOR operations, respectively. Which one of the following is NOT CORRECT?

  • Option : D
  • Explanation :
    (P ⊕ P) ⊕ Q = (P ⊙P) ⊕ Q false
    (P ⊕ P) ⊕ Q = 1 ⊕ Q = Q
    (P ⊙ P) ⊕ Q = 0 ⊕ Q = Q
    (P ⊕ P) ⊕ Q ≠ (P ⊙ P) ⊕ Q
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25. Consider a matrix P whose only eigenvectors are the multiples of

  • Option : D
  • Explanation : Only Eigen vector is multiples means that eigen value is repeated since if eigen values were distinct we will get one more independent eigen vector. So, II P has repeated eigen value is true. I need not be true since has repeated eigen values and yet it is invertible. III is true since if matrix has repeated eigen values then it cannot be diagonalizable.
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GATE 2018