# GATE (Graduate Aptitude Test in Engineering) Mathematics: Questions 26 - 32 of 34

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## Question 26

Appeared in Year: *2008*

### Question

MCQ▾Consider a function where *x* is a real number. Then the function has

### Choices

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

a. | Three maxima | |

b. | Only one minimum | |

c. | Only two minima | |

d. | Three minima |

## Question 27

### Question

MCQ▾The local maxima or local minima and corresponding maximum or minimum value of the function

### Choices

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

a. | Local minima at | |

b. | Local maxima at | |

c. | Local maxima at | |

d. | Local minima at |

## Question 28

### Write in Short

Short Answer▾The function satisfy the equation The value of ‘t’ is ________.

## Question 29

Appeared in Year: *2009*

### Question

MCQ▾The distance between the origin and the point nearest to it on the surface is?

### Choices

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

a. | 0 | |

b. | 2 | |

c. | 1 | |

d. | 4 |

## Question 30

Appeared in Year: *2004*

### Question

MCQ▾The function has a

### Choices

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

a. | Maximum at | |

b. | Minimum at | |

c. | Maximum at | |

d. | Minimum at |

## Question 31

### Question

MCQ▾The numbers, whose sum is 16 and the sum of whose cubes is minimum, are

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 32

Appeared in Year: *2009*

### Question

MCQ▾A cubic polynomial with real coefficients?

### Choices

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

a. | May have up to three extrema and up to 2 zero crossings | |

b. | Cannot have more than two extrema and more than three zero crossings | |

c. | Can possibly no extrema and no zero crossings? | |

d. | Will always have an equal number of extrema and zero crossings |