GATE DA purpose:exam-prep PYQs & Answers — Page 4

Questions 31–40 of 195. Imported answers require independent review unless marked reviewed.

Let

be a sorted array containing 1000 distinct integers. You perform a recursive binary search on

to find an element

. Suppose each comparison checks whether the middle element computed during the current recursive step is equal to, less than, or greater than

. The maximum number of comparisons that may have to be performed if

is not an element of

is ________ . (Answer in integer)

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In a relational database, a B+ Tree Index is to be constructed for a relation on a key field. In a B+ Tree, a Node Pointer points to a sub-tree and a Data Record Pointer points to a block of database records. Let, Node size = 4096 bytes, Node Pointer size = 10 bytes, Search Key Field size = 11 bytes and Data Record Pointer size = 12 bytes. The maximum number of Node Pointers that can be present in a non-leaf node of the B+ Tree is ________ . (Answer in integer)

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The number of bijections

from the set

to itself such that

, for all

, is ________ . (Answer in integer)

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Let

be an exponentially distributed random variable with mean

. If

, then the conditional probability

is ________ . (Rounded off to two decimal places)

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The value of

is ____________ . (Answer in integer)

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Let four points in three-dimensional space be: P1: [2, 3, −1], P2: [3, 1, 1], P3: [5, −2, 3] and P4: [3, 3, 3]. Hierarchical Agglomerative Clustering is used to cluster the above points. If Manhattan Distance is used as the distance metric during clustering, which of the following options indicates the two points that will be merged first?

Your answerChoose one option.

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Which of the following statements is true for Ridge Regression?

Your answerChoose one option.

The regularizer in the objective function of Ridge Regression is used to guard against scenarios where the model works well for the test data, but poorly for the training data.

The regularizer of Ridge Regression uses

norm.

Ridge Regression aims to reduce the number of parameters that have negative values.

The regularizer of Ridge Regression may increase the bias of the model, but it helps in reducing the variance in predictions.

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Assume that a Creative (

) person will Succeed (

) if the person is also Disciplined (

), but will not succeed otherwise. Now, consider the following statements:

(i)

(ii)

(iii)

Which of the following options is correct?

Your answerChoose one option.

Both (i) and (ii) are TRUE

Only (ii) is TRUE

Both (ii) and (iii) are TRUE

Only (iii) is TRUE

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A recursive function in Python is given.

def mystery(n):

if n <= 0:

return 1

else:

return mystery(n-1) + mystery(n-2)

Now, consider the following function call:

mystery(4)

Assume that a typical runtime stack is used to manage function calls. Each function call is pushed onto the stack and removed only after it finishes execution.

Which of the following options denotes the total number of function calls (i.e., the total number of stack activations), including the initial call, to compute mystery(4)?

Your answerChoose one option.

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Consider a directed graph

, where

is the finite set of vertices and

is the set of directed edges between the vertices.

may contain cycles but there is no self-loop. Further,

may not be strongly connected.

Let

be the graph obtained by reversing the directions of all the edges in

without changing the set of vertices.

Assume that Breadth First Search (BFS) or Depth First Search (DFS) from any given vertex

of a graph visits only the reachable vertices from

in that graph.

Which of the following statements must always be true, regardless of the structure of

Your answerChoose one option.

is a reachable vertex in the BFS of

from

, then

is also a reachable vertex in the DFS of

from

, the BFS traversal from

will visit exactly the same set of vertices as the DFS from

The order of vertices visited in the BFS of

from

is the reverse of the order of vertices visited in the DFS of

from

is a reachable vertex in the DFS of

from

, then

is also a reachable vertex in the BFS of

from

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GATE DA purpose:exam-prep PYQs

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40