GATE DA format:nat PYQs & Answers — Page 4

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Questions 31–40 of 46. Imported answers require independent review unless marked reviewed.

Topic practice 46 questionsPage 4 of 5

Consider sorting the following array of integers in ascending order using an in-place Quicksort algorithm that uses the last element as the pivot.

60 70 80 90 100

The minimum number of swaps performed during this Quicksort is ______.

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Consider the following two tables named Raider and Team in a relational database maintained by a Kabadi league. The attribute ID in table Team references the primary key of the Raider table, ID.

Raider:

ID	Name	Raids	RaidPoints
1	Arjun	200	250
2	Ankush	190	219
3	Sunil	150	200
4	Reza	150	190
5	Pratam	175	220
6	Gopal	193	215

Team:

City	ID	BidPoints
Jaipur	2	200
Patna	3	195
Hyderabad	5	175
Jaipur	1	250
Patna	4	200
Jaipur	6	200

The SQL query described below is executed on this database:

SELECT * FROM Raider, Team WHERE Raider.ID=Team.ID AND City="Jaipur" AND RaidPoints > 200;

The number of rows returned by this query is _____.

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The fundamental operations in a double-ended queue D are:

insertFirst(e) – Insert a new element e at the beginning of D. insertLast(e) – Insert a new element e at the end of D. removeFirst() – Remove and return the first element of D. removeLast() – Remove and return the last element of D.

In an empty double-ended queue, the following operations are performed:

insertFirst(10)

insertLast(32)

a ← removeFirst()

insertLast(28)

insertLast(17)

a ← removeFirst()

a ← removeLast()

The value of a is _____.

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Let

be the function

The value of the derivative of

where

is _____ (rounded off to two decimal places).

Note:

denotes the set of real numbers.

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The sample average of 50 data points is 40. The updated sample average after including a new data point taking the value of 142 is _____.

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Consider the

matrix

The determinant of

is _____.

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Let

be a random variable uniformly distributed in the interval

and

be a random variable uniformly distributed in the interval

. If

and

are independent of each other, the probability

is _____ (rounded off to three decimal places).

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Let

be a random variable exponentially distributed with parameter

. The probability density function of

is given by:

, where

and

indicate the expectation and variance of

, respectively, the value of

is _____ (rounded off to one decimal place).

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Consider two events T and S. Let

denote the complement of the event T. The probability associated with different events are given as follows:

Then,

is _____ (rounded off to two decimal places).

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Consider a joint probability density function of two random variables X and Y

Then,

is _____.

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GATE DA format:nat PYQs

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