PREVIOUS YEAR SOLVED PAPERS MCQ - GATE 2018

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 :

So ‘a’ + 2 will be ‘c’, so Our next node p = {‘1’, ‘0’, ‘c’} and output will be 0, c. So answer is C

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?

E1 entries > E2 entities

So Every entity in E1 is associated with exactly one entity in E2. So options A is correct options.

23 Which one of the following is a closed form expression for the generating function of the sequence {a_n}, where a_n = 2n + 3 for all n = 0, 1, 2,.....?

The Given functions is, a_n = 2n + 3
generating function for 1 is

and n is

, the generating function for a_n is

Which is option (D).

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

(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

25 Consider a matrix P whose only eigenvectors are the multiples of

.
Consider the following statements :
I. P does not have an inverse.
II. P has a repeated eigenvalue.
III. P cannot be diagonalized.
Which one of the following options is correct?

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.