# NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 74 - 83 of 101

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## Question 74

## Question 75

Appeared in Year: *2015*

### Describe in Detail

Essay▾Let . Evaluate the determinant

### Explanation

Let

Applying , then

Taking common from , we get

Applying

## Question 76

Appeared in Year: *2005*

### Describe in Detail

Essay▾Evaluate

### Explanation

… eq. (A)

Replace by by the sign of .

Lower limit

Upper limit

becomes

(solution)

Hence the required solution is

… (1 more words) …

## Question 77

Appeared in Year: *2015*

### Describe in Detail

Essay▾Evaluate

### Explanation

This is exponential form form

Using the result

If

Then

## Question 78

Appeared in Year: *2011*

### Describe in Detail

Essay▾Find the cube Roots of

### Explanation

Let

Put

Put

Put

cube roots of are

## Question 79

Appeared in Year: *2007*

### Question

MCQ▾Which of the following function are differentiable at ?

### Choices

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

a. | ||

b. | ||

c. | ||

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

## Question 80

Appeared in Year: *2014*

### Question

MCQ▾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 81

Appeared in Year: *2014*

### Question

MCQ▾Let . Which of the following statements are true?

### Choices

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

a. | ||

b. | ||

c. | ||

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

## Question 82

Appeared in Year: *2009*

### Describe in Detail

Essay▾Let

Examine whether admits a local maximum or minimum at ?

### Explanation

Here

Now

At

So no conclusion can be drawn

admits a local minimum at

## Question 83

Appeared in Year: *2010*

### Describe in Detail

Essay▾Find the sum of the infinite series:

### Explanation

Let

Consider the series

… eq. (A)

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

Therefore … eq. (1)

… eq. (2)

And … eq. (3)

Rewrite eq. (2)

(Using (1) )

Hence sum of the series S is given by

Now [From (A) ]

Hence sum of the required series is .

… (4 more words) …