# Engineering Mathematics [GATE (Graduate Aptitude Test in Engineering) Electronics]: Questions 18 - 27 of 71

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## Question 18

Appeared in Year: *2016*

### Question

MCQ▾Consider a square matrix

,

Where x is unknown. If the eigenvalues of the matrix A are and , then is equal to

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | ||

c. | ||

d. |

## Question 19

Appeared in Year: *2015*

### Question

MCQ▾For the determinant of is

### Choices

Choice (4) | Response | |
---|---|---|

a. | 0 | |

b. | 1 | |

c. | ||

d. |

## Question 20

## Question 21

Appeared in Year: *2017*

### Question

Numeric Answer▾The rank of the matrix

## Question 22

Appeared in Year: *2016*

### Question

Numeric Answer▾In the following integral, the contour C encloses the point and .

The value of the integral is …

## Question 23

Appeared in Year: *2019*

### Question

Numeric Answer▾The number of distinct Eigen values of the matrix A = is equal to ________. (Carry One Mark Each)

## Question 24

Appeared in Year: *2015*

### Question

Numeric Answer▾Let If , for , then d should be equal to …

## Question 25

Appeared in Year: *2017*

### Question

MCQ▾The residues of function

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | and | |

c. | and | |

d. | and |

## Question 26

Appeared in Year: *2016*

### Question

MCQ▾Let (where I denote the identity matrix) and , , . Then for any natural number k, equals:

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | ||

c. | ||

d. |

## Question 27

Appeared in Year: *2017*

### Question

MCQ▾Consider the following statements about the linear dependence of the real valued functions . Over the field of real numbers.

I. and are linearly independent on

II. and are linearly dependent on

III. and are linearly independent on

IV. and are linearly dependent on

Which one among the following is correct?

### Choices

Choice (4) | Response | |
---|---|---|

a. | Both I and II are true | |

b. | Both II and IV are true | |

c. | Both III and IV are true | |

d. | Both I and III are true |