Mth101 Collection of Old Papers

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http:// vujannat.ning.comLargest Online Community of VU StudentsFinal term EXAMINATION

SEMESTER Fall 2005

Subject code – MTH101 (Fall 2005)

Total Marks: 60

Duration:2 Hour

Maximum Time Allowed: ( 2 Hour)

Please read the following instructions carefully before attempting any of the questions:

1. Attempt all questions. Marks are written adjacent to each question.2. Do not ask any questions about the contents of this examination from anyone.

a. If you think that there is something wrong with any of the questions, attempt itto the best of your understanding.b. If you believe that some essential piece of information is missing, make an

appropriate assumption and use it to solve the problem.c. Write all steps, missing steps may lead to deduction of marks.

3. You should copy the data directly from MATHTYPE into the exam software copyingMATHTYPE images from MICROSOFT WORD to the exam application may cause someproblem of visibility.4. The duration of this examination is 120 minutes.5. This examination is closed book, closed notes, closed neighbors.6. Calculator is allowed

**WARNING: Please note that Virtual University takes serious note of unfair means.Anyone found involved in cheating will get an `F` grade in this course.

For Teacher’s use only

Question Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Total

Marks

Question No: 1 Marks=2

5∑2m +1 = --------------m =3

a- 100b- 112c- 120d- 140


1 5

If ∫ f (x)dx = −2 and ∫ f (x)dx =10 0

5

Then ∫ f (x)dx = ?1

a- -1b- -3c- 3d- -2


x dtLet F(x) = ∫ t

, the point where the graph of F(x)1

crosses the x-axis is

a- 0b- 1c- -1d- None of the above.


The series

5+5 + 5 + ...+ 5 + ...4 42 4k −1

a- Convergent Seriesb- Divergent Series.c- Cannot be determined.d- None of the above.


Find a non zero value for the costant k so that⎧ tan kx, x < 0

f(x) =⎪

x⎨⎪3x + 2k 2 , x ≥ 0⎩will be continuous at x=0.

Note: In order to get maximum marks do all necessary steps.


Finddy

ifdx

2y3t + t3 y =1 anddt = 1

dx Cost



Prove (by subsitution); If m and n are positive inegers, then1 1∫ xm (1− x)n dx = ∫ xn (1− x)m dx0 0



Find the volume of the solid that results when the region enclosed

by the curves x = Csc y, y = π /4, y = 3π /4, x = 0

is revolved about the y-axis.



Find the arc length in the second quadrant of the curve

x2/3 + y2 /3 = a2 /3 from the point x= -a to x = -1

a (a>0).8



Find limit

lim x ln⎛ x +1⎞

x →+∞ ⎜ x −1 ⎟⎝ ⎠Note: In order to get maximum marks do all necessary steps.


Determine whether the series converges or diverges

+∞ 2+ (−1)k∑ 5kk =1


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MTH101 Calculus and Analytical GeometryFinal Term Examination – Spring 2005

Time Allowed: 150 Minutes

Maximum Time Allowed: ( 150 mins)

Please read the following instructions carefully beforeattempting any of the questions:

1. Pasting the equations of math type from word file intosoftware may cause some visibility problem, so pleasenote that do not copy equations of math type intosoftware from word file. Paste the equations from mathtype directly into software.

2. Do not ask any questions about the contents of thisexamination from anyone.

a. If you think that there is something wrong with any ofthe questions, attempt it to the best of your understanding.b. If you believe that some essential piece of information ismissing, make an appropriate assumption and use it tosolve the problem.c. Write all steps, missing steps may lead to deduction ofmarks.

**WARNING: Please note that Virtual University takes seriousnote of unfair means. Anyone found involved in cheating willget an `F` grade in this course.

Total Marks: 65 Total Questions: 12

Question No. 1 Marks : 05

∞

Using the concept of infinite series expresses 4.212121…………………. as a ratio ofintegers.

Note: In order to get the maximum marks you have to show all the necessary steps


Ify =

then

f (x)

f ′( x0 )is the function whose value at x0 is the average rate of change of y with respect to x at thepoint x0.


Determine whether the series converges or diverges. If it converges, find the sum⎛ −=3 ⎞k−1∑ ⎜ ⎟k=1 ⎝ 4 ⎠

Note: In order to get the maximum marks you have to show all the necessary steps


Find the area of the region enclosed by :

y = x3 + 5x2 +3, y = x2 + 7x + 3,

x = 0, x = 3.Note: In order to get the maximum marks you have to show all the necessary steps


y = (2x2 + 7x − 2)2

Find the slope of the curve at the point x= -2.Note: In order to get the maximum marks you have to show all the necessary steps


∞The series

∑ 1

n =1 nis

o Convergeso Absolutely convergeso Divergeso None of the above


If the lim ( f(x) / g(x) ) is not an indeterminate form then L ' Hopital's rule cannot beapplied

o Trueo False


Two non vertical lines with slopes m1 and m2 respectively are parallel if and only if

o m1 m 2

o m1 m 2

= 1= −1

m1

o m 2

m1

o m 2

= 1

= −1


Solve the following integral

zdz∫ 3 z2 +1

by substitution method.Note: In order to get the maximum marks you have to show all the necessary steps


Find the limit using L' Hopital's Rule

⎨⎩

limx→π + sin x

x −πNote: In order to get the maximum marks you have to show all the necessary steps

Question No. 11 Marks : 10⎧x2 +1 , 0 < x ≤1

f (x) = ⎪x , 1< x ≤ 4⎪2x +1 , 4 ≤ x

Is continuous at x = 1?

Write all necessary steps and justify your answer.

Note: In order to get the maximum marks you have to show all the necessary steps.


Which of the following statement is true

Let f be a function that is defined at all points in the interval [a, b].

o If f is continuous on [a, b], then f is integrable on [a, b]o If f is bounded on [a, b] and has only finitely many points of discontinuity

on [a, b], then f is integrable on [a, b]o If f is not bounded on [a, b], then f is not integrable on [a, b].o All of above are true

⎝ ⎠ .

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MTH101-Calculus and Analytical GeometryFinal Term Examination – Spring 2006


Please read the following instructions carefully before attempting anyof the questions:

1. Pasting the equations of math type from word file into softwaremay cause some visibility problem, so please note that do notcopy equations of math type into software from word file. Pastethe equations from math type directly into software.

2. Do not ask any questions about the contents of this examination fromanyone.

a. If you think that there is something wrong with any of thequestions, attempt it to the best of your understanding.b. If you believe that some essential piece of information is missing,

make an appropriate assumption and use it to solve the problem.c. Write all steps, missing steps may lead to deduction of marks.

**WARNING: Please note that Virtual University takes serious note ofunfair means. Anyone found involved in cheating will get an `F` grade inthis course.


Find the area of the surface generated by revolving the curvey = x3 , 0 ≤ x≤ 1

2 about the x-axis.



Find the limit using L’ Hopital’s Rulex

lim ⎛ x +1 ⎞x →+∞⎜ x + 2 ⎟


∞

∞


Determine whether the series converges or diverges. If it converges, find the sum⎛ −=3 ⎞k −1∑⎜ ⎟k =1 ⎝ 4 ⎠



Two non vertical lines with slopes m1 and m2 respectively are parallel if and only if

m1m2 =1m1m2 = −1

m1 / m2 =1m1 / m2 = −1


What is the difference between differentiation and integration?



The series ∑ 1

n −1 n

ConvergesAbsolutely convergesDivergesNon of the other


Acceleration of a moving particle is given as a (t ) = 9t2 −7t +3 . We can findfor the moving particle.

Velocity functionPosition functionBoth (a) & (b)None of the other

⎨⎩


100∑ k = ?k −3

504750505053None of the other


If the distance traveled by the car is y = f(x) given in the function below, then find the velocityd y

d xof the car.

Where

lny = e y sinx


Question No. 10 Marks : 10⎧x2 +1 , 0 < x ≤1

Is f (x) = ⎪x , 1< x ≤ 4 continuous at x = 1?⎪2x +1 , 4 ≤ x

Write all necessary steps and justify your answer.



Evaluatez

dz3 z2 +1


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MIDTERM EXAMINATIONFALL 2007

MTH101 - CALCULUS AND ANALYTICAL GEOMETRY(Session - 7 )

Marks: 40

Time: 120min

StudentID/LoginID:

Student Name:

Center Name/Code:

Exam Date: Thursday, December 06, 2007


1. Attempt all questions. Marks are written adjacent to each question.

2. Do not ask any questions about the contents of this examination

from anyone.

a. If you think that there is something wrong with any of the

questions, attempt it to the best of your understanding.

b. If you believe that some essential piece of information is

missing, make an appropriate assumption and use it to solve the

problem.

c. Write all steps, missing steps may lead to deduction of marks.

3. Calculator is allowed.

**WARNING: Please note that Virtual University takes serious note of unfair means.Anyone found involved in cheating will get an `F` grade in this course.

For Teacher's use onlyQuestion 1 2 3 4 5 6 7 8 9 10 Total

Marks

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

The equation (x+2)2 + ( y-3)2=0 represents a graph of

► Straight line

► Circle

► Single point

► None of these


If graph of a function f(x) is then represents the graph of

► f(x+2)

► f(x+2)2 -1

► f(x-2)2 +1

► f(x-2)2 -1


Which of the following statement is incorrect

► lim 2= 2x→+∞

► lim 2 = ∞x→+∞

► lim x = +∞x→+∞

► 1lim = 0x→+∞ x


1 1lim xsin( ) = 0 limsin( ) = 0x→0 x x→0 x

As so

► True

► False


A function not defined at a point can never be continuous at that point; it however may bedifferentiable at that point.

► True

► False

Question No: 6 ( Marks: 6 )

Prove that (0, -2), (-4, 8), and (3, 1) lie on a circle with center (-2, 3).


Find a formula for the function f graphed in figure given below


Evaluate

l i m3 x + 9

x → − 3 x 2 − 9

Question No: 9 ( Marks: 9 )⎧ x − a

f (x) = ⎪(x − a)

, when x ≠ a⎨⎪1 , when x = a⎩If , Check whether f(x) is continuous at x = a


y = 2x3 + 4x − 2 x = 3Find the slope of the curve at

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MTH101 Calculus And Analytical GeometryMid Term Examination – Spring 2006


Maximum Time Allowed: ( 1.5 Hours)


1. Attempt all questions. Marks are written adjacent to each question.2. Do not ask any questions about the contents of this examination fromanyone.

a. If you think that there is something wrong with any of thequestions, attempt it to the best of your understanding.b. If you believe that some essential piece of information is

missing, make an appropriate assumption and use it to solvethe problem.c. Write all steps, missing steps may lead to deduction ofmarks.

3. The duration of this examination is 90 minutes.4. This examination is closed book, closed notes, closed neighbors.5. Calculator is allowed

**WARNING: Please note that Virtual University takes serious note ofunfair means. Anyone found involved in cheating will get an `F` grade in

this course.


Determine whether the points A(9,2),B(7,2)

Lie on horizontal line.Lie on vertical line.Lie on origin.None of the other.


If y = 6x5 − 4x2 , then y′′(1) = ?

1020112110


f(x) = (5/x ) + (2x / x + 4) has point of discontinuity at

x = 0 and x = 1x = 0 and x = 4x= 0 and x = -4None of the other.


Evaluate lim (x→+∞

x2 + 5x − x)

steps.Note: In order to get maximum marks do all necessary

Question No. 5 Marks : 10Find the largest interval on which f is(a) Increasing, (b) Decreasing: find the largest open interval on which f is(c) Concave up, (d) Concave down: and(e) Find the x-coordinates of all inflection points.f (x) = 3x3 − 4x + 3



Let f(x) = x2 +1, then f(1/x) = ?

1 /(x2 +1)(1/ x2 ) +1x+1None of the other.


Solve | x − 3 |2 −4 | x − 3 |= 12 for x.



Find the x-coordinate of the point on the graph of y=x2 where the tangent line isparallel to the secant line that cuts the curve at x=-1 and x=2


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Mth101 Collection of Old Papers