# Engineering Mathematics [GATE (Graduate Aptitude Test in Engineering) Mechanical Engineering]: Questions 29 - 34 of 40

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## Question 29

Appeared in Year: *2019*

### Question

MCQ▾The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of variables (x + y) being greater than 20 is

### Choices

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

a. | 0 | |

b. | 0.50 | |

c. | 0.33 | |

d. | 0.25 |

## Question 30

Appeared in Year: *2021*

### Question

MCQ▾If the Laplace transform of a function f (t) is given by , then f (0) is ________. (February Shift 2)

### Choices

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

a. | 0 | |

b. | 1 | |

c. | ||

d. |

## Question 31

Appeared in Year: *2021*

### Question

MCQ▾Consider an matrix A and a non-zero vector p. Their product . where where α ϵ R and . Based on the given information, the eigen value of is: (February Shift 2)

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 32

Appeared in Year: *2019*

### Question

MCQ▾For the equation , if , then the value of is

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 33

Appeared in Year: *2019*

### Question

MCQ▾A harmonic function is analytic if it satisfies the Laplace equation. If is a harmonic function, then its conjugate harmonic function is ________.

### Choices

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

a. | ||

b. | ||

c. | ||

d. |