# Engineering Mathematics [GATE (Graduate Aptitude Test in Engineering) Electronics]: Questions 7 - 11 of 71

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## Question 7

Appeared in Year: *2019*

### Question

MCQ▾Consider the line integral

The integral being taken in a counterclockwise direction over the closed curve C that forms the boundary of the region shown in the figure below. The region R is the area enclosed by the union of a rectangle and a semi-circle of radius . The line integral evaluates to

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 8

Appeared in Year: *2010*

### Question

MCQ▾Given f (t) = L^{-1} . If , then the value of k is

### Choices

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

a. | 3 | |

b. | 4 | |

c. | 1 | |

d. | 2 |

## Question 9

Appeared in Year: *2019*

### Question

MCQ▾The families of curves represented by the solution of the equation

For n = – 1 and n =+ 1, respectively, are

(Carry One Mark Each)

### Choices

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

a. | Hyperbolas and Parabolas | |

b. | Parabolas and Circles | |

c. | Circles and Hyperbolas | |

d. | Hyperbolas and Circles |

## Question 10

Appeared in Year: *2010*

### Question

MCQ▾The Eigen values of a skew-symmetric matrix are (One Mark)

### Choices

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

a. | Always pure imaginary | |

b. | Either zero or pure imaginary | |

c. | Always zero | |

d. | Always real |