# Numerical Ability-Numerical Estimation [GATE (Graduate Aptitude Test in Engineering) Aptitude]: Questions 1 - 4 of 15

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## Question 1

Appeared in Year: *2011*

### Question

MCQ▾The variable cost of manufacturing a product varies according to the equation , where is the quantity produced. The fixed cost of production of same product reduces with according to the equation . How many units should be produced to minimize the total cost ?

### Choices

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

a. | 5 | |

b. | 4 | |

c. | 7 | |

d. | 6 |

## Question 2

Appeared in Year: *2011*

### Question

MCQ▾A container originally contains of pure spirit. From this container of spirit is replaced with of water. Subsequently, of the mixture is again replaced with of water and this process is repeated one more time. How much spirit is now left in the container?

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 3

Appeared in Year: *2014*

### Question

MCQ▾One percent of the people of country are taller than . Two percent of the people of country are taller than . There are thrice as many people in country as in country . Taking both countries together, what is the percentage of people taller than ?

### Choices

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

a. | 2.5 | |

b. | 1.5 | |

c. | 3.0 | |

d. | 1.25 |

## Question 4

Appeared in Year: *2015*

### Question

MCQ▾A coin is tossed thrice. Let be the event that head occurs in each of the first two tosses. Let be the event that a tail occurs on the third toss. Let be the event that two tails occur in three tosses. Based on the above information, which one of the following statement is TRUE?

### Choices

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

a. | X and Y are not independent | |

b. | Y and Z are independent | |

c. | X and Z are independent | |

d. | Y and Z are dependent |