# Engineering Mathematics-Vector Analysis [GATE (Graduate Aptitude Test in Engineering) Electronics]: Questions 1 - 4 of 8

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## Question 1

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 2

Appeared in Year: *2015*

### Question MCQ▾

A Vector . Which of the following statements is TRUE?

### Choices

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

a. | is neither solenoidal nor irrotational | |

b. | is both solenoidal and irrotational | |

c. | is solenoidal, but not irrotational | |

d. | is irrotational, but not solenoidal, |

## Question 3

Appeared in Year: *2016*

### Question MCQ▾

The current density in a medium is given by:

The total current and the average current density flowing through the portion of a spherical surface are given, respectively, by

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 4

Appeared in Year: *2016*

### Question Numeric Answer▾

Consider the time-varying vector in Cartesian coordinates, where is a constant. When the vector magnitude is at its minimum value, the angle that I make with the x axis (in degrees, such that ) is …

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