# NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 97 - 101 of 101

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## Question number: 97

» Convergence of Positive Series Test

Appeared in Year: 2007

### Question

Which of the following series are convergent?

### Choices

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

a. |
| |

b. |
| |

c. |
| |

d. | Both b. and c. are correct |

## Question number: 98

Appeared in Year: 2007

### Describe in Detail

Find the interval of convergence of the series

### Explanation

The given series is

Put

So the given series is

(By Cauchy’s second theorem on limits)

… (243 more words) …

## Question number: 99

Appeared in Year: 2011

### Describe in Detail

Evaluate

### Explanation

Let …………. eq. (1)

………. eq. (2)

Subtracting eq. (2) from (1)

If

… (230 more words) …

## Question number: 100

Appeared in Year: 2012

### Statements

If …………. eq. (1)

Where , then the polynomial has a root in the interval .

If is continuous and differentiable in , where and if

Then there exists such that

The polynomial has only one real root.

### Choices

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

a. | None of the statements is correct. | |

b. | Both statement Ⅰ & statement Ⅱ are true. | |

c. | All the statements are correct. | |

d. | Only statement Ⅱ is true. |

## Question number: 101

Appeared in Year: 2005

### Question

Let

Pick out the true statements:

### Choices

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

a. |
| |

b. | is a decreasing function on the entire real line | |

c. | None of the above | |

d. | Question does not provide sufficient data or is vague |