# Basic Mathematics-Arithmetic (KVPY Stream-SA (Class 11) Math): Questions 75 - 77 of 77

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## Question number: 75

» Basic Mathematics » Arithmetic » Number Games

### Question

Let be natural numbers in an arithmetic progression such that in the cube of an integer and is square of integer. The least possible value of the number of digits of is. (Model Paper)

### Choices

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

a. | 16 | |

b. | 4 | |

c. | 25 | |

d. | 9 |

## Question number: 76

» Basic Mathematics » Arithmetic » Simplifying Expressions

### Question

The least positive integer for which

is – (Model paper)

### Choices

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

a. | 7 | |

b. | 2 | |

c. | 4 | |

d. | 3 |

## Question number: 77

» Basic Mathematics » Arithmetic » Simplifying Expressions

### Question

Let be non – zero real number such that and , then is equal to, (Model paper)

### Choices

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

a. | - 75 | |

b. | 55 | |

c. | - 55 | |

d. | 150 |