GATE CSE area:engineering-mathematics PYQs & Answers — Page 3

Questions 21–30 of 109. Imported answers require independent review unless marked reviewed.

Consider the given system of linear equations for variables

and

, where

is a real-valued constant. Which of the following option(s) is/are CORRECT?

Your answerSelect all correct options. You can choose more than one.

There is exactly one value of

for which the above system of equations has no solution.

There exist an infinite number of values of

for which the system of equations has no solution.

There exists exactly one value of

for which the system of equations has exactly one solution.

There exists exactly one value of

for which the system of equations has an infinite number of solutions.

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Consider the given function

If the function is differentiable everywhere, the value of

must be ______. (rounded off to one decimal place)

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A box contains 5 coins: 4 regular coins and 1 fake coin. When a regular coin is tossed, the probability

and for a fake coin,

. You pick a coin at random and toss it twice, and get two heads. The probability that the coin you have chosen is the fake coin is ______. (rounded off to two decimal places)

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Let

be a

matrix as given.

What are the eigenvalues of the matrix

Your answerChoose one option.

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Consider a system of linear equations

where

and

. Suppose

has an LU decomposition,

, where

Which of the following statement(s) is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

The system

can be solved by first solving

and then

is invertible, then both

and

are invertible.

is singular, then at least one of the diagonal elements of

is zero.

is symmetric, then both

and

are symmetric.

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Suppose a 5-bit message is transmitted from a source to a destination through a noisy channel. The probability that a bit of the message gets flipped during transmission is 0.01. Flipping of each bit is independent of one another. The probability that the message is delivered error-free to the destination is _____. (rounded off to three decimal places)

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Consider a probability distribution given by the density function

The probability that

lies between 2 and 3, i.e.,

is __________. (rounded off to three decimal places)

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The unit interval (0,1) is divided at a point chosen uniformly distributed over (0,1) in ℝ into two disjoint subintervals.

The expected length of the subinterval that contains 0.4 is __________. (rounded off to two decimal places)

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Let

be a function such that

, where

is the set of all real numbers. The set of all points where

is NOT differentiable is

Your answerChoose one option.

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The product of all eigenvalues of the matrix

Your answerChoose one option.

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GATE CSE area:engineering-mathematics PYQs

Question 23

Question 31

Question 32

Question 41

Question 44

Question 56

Question 58

Question 65

Question 11

Question 12