FINALTERM EXAMINATION
Spring 2009
MTH101- Calculus And Analytical Geometry (Session - 1)
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
► 
► 
► 
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
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 a decreasing function ► is an increasing function
is an increasing function ► is a constant function
is a constant functionQuestion 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 up on (a, b). ► is concave down on (a, b)
is concave down on (a, b) ► is linear 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
and Question No: 15 ( Marks: 1 ) - Please choose one
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 :
► 
► 
► 
► 
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? ► 
► 
► 
► 
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
is divided into two sub-intervals of equal length and 
and 
are left endpoint of each sub-interval.
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
is divided into two sub-intervals of equal length and and are right endpoint of each sub-interval.
and are right endpoint of each sub-interval. ► 8
► 10
► 12
Question No: 22 ( Marks: 1 ) - Please choose one
► 1
► 
► 
► 
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?
► 
► 
► 
► 
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? ► 
► 
► 
► 
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
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? ► 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
Let 
be a series with nonzero terms and suppose that 
if
, then which of the following is true? ► Then the series diverges
diverges ► The series converges absolutely and therefore converges
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
► 
► 
► 
► 
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? ► 
► 
► 
► 
Question No: 40 ( Marks: 1 ) - Please choose one
Which of the following are first two terms for the 
at x = 0? ► 
► 
► 
► 
Question No: 41 ( Marks: 2 )
Evaluate the integral 
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 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
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 revolved about the x – axis.
No comments:
Post a Comment