GATE DA format:nat PYQs & Answers

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Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.

Questions 1–10 of 46. Imported answers require independent review unless marked reviewed.

Topic practice 46 questionsPage 1 of 5

Consider that for a supervised learning task, the objective function being minimized is

, where

is the input and

is the parameter. Stochastic Gradient Descent with learning rate of 0.10 is used for parameter updates. Suppose that at the end of iteration

, the value of

becomes 10.00. Let

be the input for iteration

. The value of

at the end of iteration

is __________ . (Rounded off to two decimal places)

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Consider the game tree for a two-player turn-taking minimax game as shown in the figure. The value of a terminal node represents the utility of the game state if the game ends there. The numbers written next to the edges denote the strategies. There are two players MAX and MIN. At any particular state of the game, MAX prefers to move to a state of maximum value. On the other hand, MIN prefers to move to a state of minimum value. Suppose MAX starts the game at the root and has three strategies: 1, 2 and 3. Next, MIN plays and also has three strategies: 1, 2 and 3. The game ends there. Both players always take optimal strategies throughout the game. At the root, the best strategy for MAX is __________ . (Answer in integer)

Diagram for Data Science and Artificial Intelligence question 30

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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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Consider that Linear Ridge Regression is being used to learn a prediction function

, where

and Mean Absolute Error (MAE) is used to measure the prediction error. A weight of 0.20 is associated with the regularizer.

At an intermediate step of the training process, assume that the parameter

. In the next step, for the input

, the predicted value of

is noted. Let the relation between

and the true value of

The value of the overall regularized loss function for this instance is _____. (Rounded off to two decimal places)

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Consider a fully-connected feed-forward multi-layer perceptron. It has 30 neurons in the input layer, followed by two hidden layers and an output layer. The first hidden layer has 4 neurons and the second hidden layer has 3 neurons. The output layer has only one neuron. Assume that no bias parameters are used.

The number of learnable parameters in the multi-layer perceptron is __________ . (Answer in integer)

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A clinic specializes in testing for a disease D. The result of the test can be either positive or negative.

A study revealed that if a person suffers from the disease D, the test result in that clinic comes out positive 80% of the time, and negative 20% of the time. If a person is not suffering from the disease D, the test comes out positive 10% of the time and negative 90% of the time. It is also known that among the general population, the disease D occurs in 30% of the individuals.

If a person tests positive for D in that clinic, the probability that he/she actually suffers from the disease D is ________ . (Rounded off to two decimal places)

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GATE DA format:nat PYQs

How to practice format:nat

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