GATE CSE area:engineering-mathematics PYQs & Answers — Page 7

Questions 61–70 of 109. Imported answers require independent review unless marked reviewed.

Consider the following expression.

The value of the above expression (rounded to 2 decimal places) is ________.

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For a given biased coin, the probability that the outcome of a toss is a head is 0.4. This coin is tossed 1,000 times. Let

denote the random variable whose value is the number of times that head appeared in these 1,000 tosses. The standard deviation of

(rounded to 2 decimal places) is ________.

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Suppose that

is a

matrix such that every solution of the equation

is a scalar multiple of

. The rank of

is ________.

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Suppose that

is a continuous function on the interval

and a differentiable function in the interval

such that for every

in the interval,

. If

, then

is at most ________.

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In an examination, a student can choose the order in which two questions (QuesA and QuesB) must be attempted.

If the first question is answered wrong, the student gets zero marks.

If the first question is answered correctly and the second question is not answered correctly, the student gets the marks only for the first question.

If both the questions are answered correctly, the student gets the sum of the marks of the two questions. The following table shows the probability of correctly answering a question and the marks of the question respectively.

question	probability of answering correctly	marks
QuesA	0.8	10
QuesB	0.5	20

Assuming that the student always wants to maximize her expected marks in the examination, in which order should she attempt the questions and what is the expected marks for that order (assume that the questions are independent)?

Your answerChoose one option.

First QuesA and then QuesB. Expected marks 14.

First QuesB and then QuesA. Expected marks 14.

First QuesB and then QuesA. Expected marks 22.

First QuesA and then QuesB. Expected marks 16.

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A bag has r red balls and b black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of balls in the bag will increase by one, after the trial. A sequence of four such trials is conducted. Which one of the following choices gives the probability of drawing a red ball in the fourth trial?

Your answerChoose one option.

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Consider the two statements.

There exist random variables

and

such that

For all random variables

and

Which one of the following choices is correct?

Your answerChoose one option.

Both

and

are true.

is true, but

is false.

is false, but

is true.

Both

and

are false.

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For two

-dimensional real vectors

and

, the operation

is defined as follows:

Let

be a set of 10-dimensional non-zero real vectors such that for every pair of distinct vectors

. What is the maximum cardinality possible for the set

Your answerChoose one option.

100

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Consider the following matrix.

The largest eigenvalue of the above matrix is __________.

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A sender (

) transmits a signal, which can be one of the two kinds:

and

with probabilities 0.1 and 0.9 respectively, to a receiver (

). In the graph below, the weight of edge

is the probability of receiving

when

is transmitted, where

. For example, the probability that the received signal is

given the transmitted signal was

, is 0.7.

Diagram for Computer Science and Information Technology question 54

If the received signal is

, the probability that the transmitted signal was

(rounded to 2 decimal places) is __________.

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GATE CSE area:engineering-mathematics PYQs

Question 20

Question 22

Question 24

Question 25

Question 29

Question 33

Question 35

Question 37

Question 52

Question 54