# Mathematical Physics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 57 - 62 of 76

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## Question 57

Appeared in Year: *2008*

### Question

MCQ▾Under a certain rotation of coordinate axes, a rank – 1 tensor transforms according to the orthogonal transformation defined by the relations . Under the same rotation a rank – 2 tensor would transform such that –

### Choices

Choice (4) | Response | |
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a. | ||

b. | ||

c. | ||

d. |

## Question 58

## Question 59

Appeared in Year: *2008*

### Question

MCQ▾If , where is the unit circle taken anticlockwise and is the principal branch of the Logarithm function, which one of the following is correct?

### Choices

Choice (4) | Response | |
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a. | ||

b. | ||

c. | is not defined since has a branch cut | |

d. | by residue theorem |

## Question 60

## Question 61

Appeared in Year: *2007*

### Question

MCQ▾The points, where the series solution of the Legendre differential equation will diverge, are located at –

### Choices

Choice (4) | Response | |
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a. | ||

b. | ||

c. | ||

d. |

## Question 62

Appeared in Year: *2008*

### Question

MCQ▾The set of all polynomials of a real variable of degree two or less and with real coefficients, constitutes a real linear vector space . For and , which one of the following constitutes an acceptable scalar product?

### Choices

Choice (4) | Response | |
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a. | ||

b. | ||

c. | ||

d. |