# NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 80 - 88 of 101

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## Question number: 80

Appeared in Year: 2014

### Question

Which of the following statements are true?

### Choices

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

a. | If , then is rational when n is even | |

b. | If , then is rational when n is odd | |

c. | If , then is Irrational when n is even | |

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

## Question number: 81

Appeared in Year: 2014

### Question

Let . Which of the following statements are true?

### Choices

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

a. |
| |

b. |
| |

c. |
| |

d. | All a. , b. and c. are correct |

## Question number: 82

Appeared in Year: 2009

### Describe in Detail

Let

Examine whether admits a local maximum or minimum at ?

### Explanation

Here

Now

At

So n

… (100 more words) …

## Question number: 83

Appeared in Year: 2010

### Describe in Detail

Find the sum of the infinite series:

### Explanation

Let

Consider the series

……. . eq. (A)

Comparing eq. (A) with the standard form i. e.

… (258 more words) …

## Question number: 84

» Convergence of Positive Series Test

Appeared in Year: 2011

### Describe in Detail

Test the following series for convergence.

a)

b)

### Explanation

Option (a) The given series is

Take

which is non –zero and finite

… (328 more words) …

## Question number: 85

Appeared in Year: 2006

### Describe in Detail

Find the interval of convergence of the series

### Explanation

The given series is

Put

The given power series

Let

By Cauchy second theorem on limits, we have

… (138 more words) …

## Question number: 86

## Question number: 87

» Definite Integral as Limit of a Sum

Appeared in Year: 2008

### Describe in Detail

Evaluate

### Explanation

Replacing by the sign of

Upper limit

Lower limit

## Question number: 88

Appeared in Year: 2016

### Question

Let Which of the following statements are true?

### Choices

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

a. | is rational for all | |

b. | is Irrational for all | |

c. | is rational if | |

d. | All of the above |