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

Questions 61–70 of 174. Imported answers require independent review unless marked reviewed.

For the matrix

which of the following statements is/are TRUE?

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

[A] = has a unique solution

[A] = does not have a unique solution

[A] has three linearly independent eigenvectors

[A] is a positive definite matrix

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The probabilities of occurrences of two independent events A and B are 0.5 and 0.8, respectively. What is the probability of occurrence of at least A or B (rounded off to one decimal place)?

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In the differential equation

is a positive constant. If

, and

, the value of

is _____________ (rounded off to three decimal places).

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The steady-state temperature distribution in a square plate ABCD is governed by the 2-dimensional Laplace equation. The side AB is kept at a temperature of 100 °C and the other three sides are kept at a temperature of 0 °C. Ignoring the effect of discontinuities in the boundary conditions at the corners, the steady-state temperature at the center of the plate is obtained as T₀ °C. Due to symmetry, the steady-state temperature at the center will be same (T₀ °C), when any one side of the square is kept at a temperature of 100 °C and the remaining three sides are kept at a temperature of 0 °C. Using the principle of superposition, the value of T₀ is __________ (round off to two decimal places).

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A function

, that is smooth and convex-shaped between interval

is shown in the figure. This function is observed at odd number of regularly spaced points. If the area under the function is computed numerically, then ________.

Diagram for Civil Engineering question 36

Your answerChoose one option.

the numerical value of the area obtained using the trapezoidal rule will be less than the actual

the numerical value of the area obtained using the trapezoidal rule will be more than the actual

the numerical value of the area obtained using the trapezoidal rule will be exactly equal to the actual

with the given details, the numerical value of area cannot be obtained using trapezoidal rule

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The solution of the differential equation

is expressed as

, where

, and

are constants, with

and

being distinct and not equal to 2.5. Which of the following options is correct for the values of

and

Your answerChoose one option.

1 and 2

−1 and −2

2 and 3

−2 and −3

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Two vectors

and

belong to the null space of a 4 × 4 matrix of rank 2. Which one of the following vectors also belongs to the null space?

Your answerChoose one option.

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Cholesky decomposition is carried out on the following square matrix

Let

and

be the (i,j)

elements of matrices

and

, respectively. If the element

of the decomposed lower triangular matrix

is 1.968, what is the value (rounded off to the nearest integer) of the element

Your answerChoose one option.

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For the matrix

which of the following statements is/are TRUE?

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

The eigenvalues of

are same as the eigenvalues of

The eigenvalues of

are the reciprocals of the eigenvalues of

The eigenvectors of

are same as the eigenvectors of

The eigenvectors of

are same as the eigenvectors of

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For the function

, which of the following statements is/are TRUE?

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

The function is continuous at all

The function is differentiable at all

The function is periodic

The function is bounded

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GATE CE area:engineering-mathematics PYQs

Question 25

Question 29

Question 30

Question 31

Question 36

Question 36

Question 37

Question 38

Question 47

Question 48