MTH101- Calculus And Analytical Geometry

FINALTERM  EXAMINATION

Spring 2009

MTH101- Calculus And Analytical Geometry (Session - 1)

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Question No: 1    ( Marks: 1 )    - Please choose one

 If f is a twice differentiable function at a stationary point  and    then f has relative …………. At

       ► Minima

       ► Maxima

       ► None of these

   

Question No: 2    ( Marks: 1 )    - Please choose one

 If f is a twice differentiable function at a stationary point  and    then f has relative …………. At

       ► Minima    

       ► Maxima

       ► None of these

   

Question No: 3    ( Marks: 1 )    - Please choose one

 

       ► 2

       ► 4

       ► 1

       ►

   

Question No: 4    ( Marks: 1 )    - Please choose one

       ► 1

       ► 0

       ► e

       ► None of these

   

Question No: 5    ( Marks: 1 )    - Please choose one

 

       ►

       ►

       ►

       ►

   

Question No: 6    ( Marks: 1 )    - Please choose one

 If  then

       ► 0

       ►

       ►

       ►

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Question No: 7    ( Marks: 1 )    - Please choose one

 Consider a function and a constant  then

       ► 0

       ►

       ►

       ►

   

Question No: 8    ( Marks: 1 )    - Please choose one

 Suppose that and  are differentiable  functions of   then

 

       ►

       ►

       ►

       ►

   

Question No: 9    ( Marks: 1 )    - Please choose one

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 The power rule,     holds if n is __________

       ► An integer

       ► A rational number

       ► An irrational number

       ► All of the above

   

Question No: 10    ( Marks: 1 )    - Please choose one

 Let a function  be defined on an interval, and let   and    denotes two distinct points in that interval. If   for all points  and   then which of the following statement is correct?

       ►  is a decreasing function

       ►  is an increasing function

       ► is a constant function

   

Question No: 11    ( Marks: 1 )    - Please choose one

 If  on an open interval (a,b) then which of the following statement is correct?

       ►  is concave up on (a, b).

       ►  is concave down on (a, b)

       ► is linear on (a, b).

   

Question No: 12    ( Marks: 1 )    - Please choose one

 What does 'n' represent in Riemann Sum ?

       ► No. of Circles

       ► No. of Rectangles

       ► No. of Loops

       ► No. of Squares

   

Question No: 13    ( Marks: 1 )    - Please choose one

 If   is continuous function such that   then  has  _________  on 

       ► maximum value but no minimum

       ► minimum value but no maximum

       ► both maximum and minimum value

   

Question No: 14    ( Marks: 1 )    - Please choose one

 The expression  , represents a function of :

       ►                      

       ►

       ►

       ►  Both  and

   

Question No: 15    ( Marks: 1 )    - Please choose one

    

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if c is a constant

       ► 0

       ►

       ►

       ►

   

Question No: 16    ( Marks: 1 )    - Please choose one

 Sigma notation is represented by which of the following Greek letter?

       ►

       ►

       ►

       ►

   

Question No: 17    ( Marks: 1 )    - Please choose one

 In the following figure, the area enclosed is bounded below by :

                                  

       ►

       ►

       ►

       ►

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Question No: 18    ( Marks: 1 )    - Please choose one

 In the following figure, the area bounded on the sides by the lines are :

                                  

       ►

       ►

       ►

       ►

   

Question No: 19    ( Marks: 1 )    - Please choose one

 What is the area of the region in the following figure?

                                   

       ►

       ►

       ►

       ►

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Question No: 20    ( Marks: 1 )    - Please choose one

 Which of the following is approximate area under the curve  over the interval , evaluated by using the formula

If the interval  is divided into two sub-intervals of equal

 length and  and  are left endpoint of each sub-interval.

       ► 17

       ► 20

       ► 23

   

Question No: 21    ( Marks: 1 )    - Please choose one

 Which of the following is approximate area under the curve  over the interval , evaluated by using the formula

If the interval  is divided into two sub-intervals of equal

length and  and  are right endpoint of each sub-interval.

       ► 8

       ► 10

       ► 12

   

Question No: 22    ( Marks: 1 )    - Please choose one

 

       ► 1

       ►

       ►

       ►

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Question No: 23    ( Marks: 1 )    - Please choose one

 Suppose  and  are integrable functions on [a,b] and c is a constant, then  

       ►

       ►

       ►

       ► 0

   

Question No: 24    ( Marks: 1 )    - Please choose one

 If the function  is continuous on [a,b] and if  for all  in [a,b], then which of the following gives area under the curve  over the interval [a,b]?

       ►

       ►

       ►

       ► (Width) (Height)

   

Question No: 25    ( Marks: 1 )    - Please choose one

 Let region R in the first quadrant enclosed between    is revolved about the

x-axis .Which of the following equation gives the volume of a solid by cylindrical shells?

     http://www.allvupastpapers.blogspot.com/  

  ►

       ►

       ►

       ►

   

Question No: 26    ( Marks: 1 )    - Please choose one

 Let f is a smooth function on [a, b]. What will be the arc length L of the curve y = f(x) from x = a to x = b?

       ►

       ►

       ►

       ►

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Question No: 27    ( Marks: 1 )    - Please choose one

 If f is continuous on (a, b] but does not have a limit from the right then the integral defined by   is called :

       ► Improper

       ► Proper

       ► Line

   

Question No: 28    ( Marks: 1 )    - Please choose one

 For a sequence  if the ratio of  successive terms then the sequence is known as:

       ► Increasing

       ► Decreasing

       ► Nondecreasing

       ► Nonincreasing

   

Question No: 29    ( Marks: 1 )    - Please choose one

 For a sequence  if the ratio of successive terms then the sequence is known as:

       ► Increasing

       ► Decreasing

       ► Nondecreasing

       ► Nonincreasing

   

Question No: 30    ( Marks: 1 )    - Please choose one

 Consider the indefinite integral

http://www.allvupastpapers.blogspot.com/  

Let

Is the following substitution correct?

       ► Yes

       ► No

   

Question No: 31    ( Marks: 1 )    - Please choose one

 The series  be a series with positive terms and suppose that   if   , then which of the following is true?

       ► Converges

       ► Diverges

       ► May converges or diverges

       ► Gives no information

   

Question No: 32    ( Marks: 1 )    - Please choose one

 The series  be a series with positive terms and suppose that   if  , then which of the following is true?

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       ► Converges

       ► Diverges

       ► May converges or diverges

       ► Gives no information

   

Question No: 33    ( Marks: 1 )    - Please choose one

 If the series  converges  , then which of the following is true for ?

       ► Converges

       ► Diverges

       ► Gives no information

   

Question No: 34    ( Marks: 1 )    - Please choose one

 Lehttp://www.allvupastpapers.blogspot.com/  

t  be a series with nonzero terms and suppose that    if , then which of the following is true?

       ► Then the series  diverges

       ► The series  converges absolutely and therefore converges

       ►  May converges or diverges

       ► Gives no information

   

Question No: 35    ( Marks: 1 )    - Please choose one

 

       ► -2

       ► 0

       ► 2

       ► 4

   

Question No: 36    ( Marks: 1 )    - Please choose one

 How many critical points exist for a function  if

       ► Zero

       ► One

       ► Two

       ► Four

   

Question No: 37    ( Marks: 1 )    - Please choose one

 http://www.allvupastpapers.blogspot.com/  

   

       ►

       ►

       ►

       ►

   

Question No: 38    ( Marks: 1 )    - Please choose one

     

       ►

       ►

       ►

       ►

   

Question No: 39    ( Marks: 1 )    - Please choose one

 Let  then which of the following is the length of the curve?

       vhttp://www.allvupastpapers.blogspot.com/  

►

       ►

       ►

       ►

   

Question No: 40    ( Marks: 1 )    - Please choose one

 Which of the following are first two terms for the Taylor series of  at x = 0?

       ►

       ►

       ►

       ►

   

Question No: 41    ( Marks: 2 )

 Evaluate the integral

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Question No: 42    ( Marks: 2 )

 Evaluate the improper integral

   

Question No: 43    ( Marks: 2 )

 A function  has critical point 2 in an interval [0, 5]. Find the maximum value of the function and  point having this value.

   

Question No: 44    ( Marks: 3 )

 Evaluate:

   

Question No: 45    ( Marks: 3 )

 Find the area of the region bounded by the curve , and bounded on the sides by the lines and

So http://www.allvupastpapers.blogspot.com/  

we have

   

Question No: 46    ( Marks: 3 )

 Determine whether the following sequence converges or diverges. If it converges, find the limit.

   

Question No: 47    ( Marks: 5 )

 Use the Alternating series Test to determine whether the given series converges

 

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Question No: 48    ( Marks: 5 )

 Evaluate the integral

Solution

   

Question No: 49    ( Marks: 5 )

 Evaluate the sums

   

Question No: 50    ( Marks: 10 )

 Find the volume of the solid that results when the region enclosed by the given curves is revhttp://www.allvupastpapers.blogspot.com/  

olved about the x – axis.

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