# Mathematical Physics-Linear Differential Equations [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 1 - 5 of 12

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## Question 1

Appeared in Year: *2014*

### Question MCQ▾

The solution of the differential equation

Subject to the boundary condition and , is –

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 2

Appeared in Year: *2015*

### Question MCQ▾

A function satisfies the ordinary differential equation , where Consider the four statements P, Q, R, S as given below.

P: and are linearly independent solution for all values of

Q: and are linearly independent solution for all values of

R: and 1 are linearly independent solution for

S: and are linearly independent solution for all values of

The correct option for the combination of valid statements is –

### Choices

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

a. | Q and R | |

b. | P and R | |

c. | R and S | |

d. | P, R and S |

## Question 3

Appeared in Year: *2015*

### Question MCQ▾

If and , then –

### Choices

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

a. | is discontinuous at | |

b. | and are differentiable everywhere | |

c. | is differentiable everywhere but is not | |

d. | is differentiable everywhere but is not |

## Question 4

Appeared in Year: *2016*

### Question MCQ▾

Consider the linear differential equation . If at then the value of at is given by,

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 5

Appeared in Year: *2013*

### Question MCQ▾

For a scalar function satisfying the Laplace equation, has –

### Choices

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

a. | Zero curl and zero divergence | |

b. | Zero curl and non – zero divergence | |

c. | Non – zero curl and non – zero divergence | |

d. | Non – zero curl and zero divergence |