# GATE Solved Paper 2017-19 - GATE 2018

• A

0, c  • B

0, a + 2  • C

‘0’, ‘a + 2’  • D

‘0’, ‘c’  • 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

• 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.

• 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).

• A

P ⊕ Q = P ⊙ Q  • B

P ⊕ Q = P ⊙ Q  • C

PQ = P ⊕ Q  • D

(P ⊕ P) ⊕ Q ≠ (P ⊙P) ⊕ Q  • 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

• A

Only I and II are necessarily true  • B

Only II is necessarily true  • C

Only I and III are necessarily true  • D

Only II and III are necessarily true  • 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