Gate Exam General Ability General Knowledge

The recurrence relation capturing the optimal execution time of the Towers of Hanoi problem with n discs is

option
(A) T(n) = 2T(n - 2) + 2
(B) T(n) = 2T(n - 1) + n
(C) T(n) = 2T(n/2) + 1
(D) T(n) = 2T(n - 1) + 1

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Gate Other Question
Which of the following statements are TRUE about an SQL query?
P : An SQL query can contain a HAVING clause even if it does not have a GROUP BY clause
Q : An SQL query can contain a HAVING clause only if it has a GROUP BY clause
R : All attributes used in the GROUP BY clause must appear in the SELECT clause
S : Not all attributes used in the GROUP BY clause need to appear in the SELECT clause

option
(A) P and R
(B) P and S
(C) Q and R
(D) Q and S
Le t G be a simple undirected planar graph on 10 vertices with 15 edges. If G is a connected graph, then the number of bounded faces in any embedding of G on the plane is equal to

option
(A) 3
(B) 4
(C) 5
(D) 6