# Mathematical Physics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 38 - 44 of 76

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## Question 38

Appeared in Year: *2010*

### Question

MCQ▾Consider an anti – symmetric tensor with the indices and running from to . The number of independent components of the tensor is –

### Choices

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

a. | 9 | |

b. | 3 | |

c. | 6 | |

d. | 10 |

## Question 39

Appeared in Year: *2010*

### Question

MCQ▾If , then the Laplace transform of is –

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 40

Appeared in Year: *2010*

### Question

MCQ▾For the complex function, , which of the following statements is correct?

### Choices

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

a. | is an essential singularity | |

b. | is a branch point | |

c. | is a removable singularity | |

d. | is a pole of order one |

## Question 41

Appeared in Year: *2010*

### Question

MCQ▾The solution of the differential equation for , subject to the initial conditions and , is –

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 42

Appeared in Year: *2010*

### Question

MCQ▾Given the recurrence relation for the Legendre polynomials , which of the following integrals has a non – zero value?

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 43

Appeared in Year: *2009*

### Question

MCQ▾The value of the integral , where the contour is the circle is –

### Choices

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

a. | ||

b. | ||

c. | ||

d. |