# Mathematical Physics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 45 - 48 of 76

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## Question 45

Appeared in Year: *2009*

### Question

MCQ▾Let and , where is the Levi – Civita density, defined to be zero if two of the indices coincide and and depending on whether is even or odd permutation of . Then is equal to –

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 46

Appeared in Year: *2009*

### Question

MCQ▾The value of the contour integral, , for a circle of radius with centre at the origin is –

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 47

Appeared in Year: *2009*

### Question

MCQ▾Which one of the following curves given the solution of the differential equation , where and are positive constant with initial conditions and ?

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 48

Appeared in Year: *2009*

### Question

MCQ▾Consider the set of vectors in three – dimensional real vector space , . Which one of the following statement is true?

### Choices

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

a. | is a basis for | |

b. | An orthogonal set of vectors cannot be generated from | |

c. | The vectors in are orthogonal | |

d. | is not a linearly independent set |