# Engineering Mathematics [GATE (Graduate Aptitude Test in Engineering) Mechanical Engineering]: Questions 1 - 6 of 12

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## Question 1

Appeared in Year: *2015*

### Question

Numeric Answer▾Consider a spatial curve in three-dimensional space given in parametric form by

The length of the curve is

## Question 2

Appeared in Year: *2015*

### Question

Numeric Answer▾Consider an ant crawling along the curve , where and are in meters. The ant starts at the point (4,0) and moves counterclockwise with a speed of 1.57 meters per second. The time taken by the ant to reach the point (2,2) is (in seconds) ________

## Question 3

Appeared in Year: *2015*

### Question

Numeric Answer▾Simpson’s rule is used to integrate the function between and using the least number of equal sub-intervals. The value of the integral is________

## Question 4

Appeared in Year: *2015*

### Question

MCQ▾Among the four normal distributions with probability density functions as shown below, which one has the lowest variance?

### Choices

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

a. | III | |

b. | II | |

c. | I | |

d. | IV |

## Question 5

## Question 6

Appeared in Year: *2015*

### Question

MCQ▾If any two columns of a determinant are interchanged, which one of the following.

Statements regarding the value of the determinant is **CORRECT**?

### Choices

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

a. | Absolute value will change but sign will not change. | |

b. | Absolute value remains unchanged, but sign will change. | |

c. | Both absolute value and sign will change. | |

d. | Both absolute value and sign will remain unchanged. |