GTU BE 1st and 2nd Semester MTH001 CALCULUS Summer 2018 Question Paper

Seat No.: _____________________ Enrolment No.:_________________
GUJARAT TECHNOLOGICAL UNIVERSITY
SPFU-SEMESTER-1
st
/ 2
nd
EXAMINATION-Summer 2018
Subject Code: MTH001 Date: 17-05-2018
Subject Name: CALCULUS
Time: 02:30 PM to 05:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Objective Section (MCQ)Q.1
The sum of the series is
1
(A)0 (B) 1 (C) -1 (D)
Q.2

1 (A) Convergent (B) Divergent (C) Oscillatory (D) None of these
Q.3

1 (A) ( (B) ( (C) 1 (D) 0
Q.4

1 (A) 1 (B) (C) (D)
Q.5
is homogeneous function with degree
1 (A) -1 (B) 0 (C) 1 (D) None of these
Q.6 If is homogeneous function of degree then

1 (A) (B) 0 (C) (D)
Q.7
The series where is???.
1 (A) Divergent (B) Convergent (C) Alternative (D) None of above
Q.8 The homogeneous function f(x, y) of degree can written as 1
(B) (C) (D) None of these
Q.9
The series is
1 (A) Divergent (B) Convergent (C) Alternative (D) None of above
Q.10

1 (A) (B) (C) 1 (D)
Q.11
If , then
1 (A) (B) (C) -1 (D)
Q.12 If for some series then the series is 1 (A)Convergent (B) Divergent (C) Oscillatory (D) None of these
Q.13
=
1 (A) 0 (B) 1 (C) -1 (D) None of these
Q.14 If ) is continuous then 1 (A) (B) (C) (D)

Seat No.: _____________________ Enrolment No.:_________________
GUJARAT TECHNOLOGICAL UNIVERSITY
SPFU-SEMESTER-1
st
/ 2
nd
EXAMINATION-Summer 2018
Subject Code: MTH001 Date: 17-05-2018
Subject Name: CALCULUS
Time: 02:30 PM to 05:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Objective Section (MCQ)Q.1
The sum of the series is
1
(A)0 (B) 1 (C) -1 (D)
Q.2

1 (A) Convergent (B) Divergent (C) Oscillatory (D) None of these
Q.3

1 (A) ( (B) ( (C) 1 (D) 0
Q.4

1 (A) 1 (B) (C) (D)
Q.5
is homogeneous function with degree
1 (A) -1 (B) 0 (C) 1 (D) None of these
Q.6 If is homogeneous function of degree then

1 (A) (B) 0 (C) (D)
Q.7
The series where is???.
1 (A) Divergent (B) Convergent (C) Alternative (D) None of above
Q.8 The homogeneous function f(x, y) of degree can written as 1
(B) (C) (D) None of these
Q.9
The series is
1 (A) Divergent (B) Convergent (C) Alternative (D) None of above
Q.10

1 (A) (B) (C) 1 (D)
Q.11
If , then
1 (A) (B) (C) -1 (D)
Q.12 If for some series then the series is 1 (A)Convergent (B) Divergent (C) Oscillatory (D) None of these
Q.13
=
1 (A) 0 (B) 1 (C) -1 (D) None of these
Q.14 If ) is continuous then 1 (A) (B) (C) (D)
Q.15
Area enclosed by the ellipse is
1 (A) (B) (C) (D)
Q.16 The series 1-1+1-1+1-1+1-1+?.

1 (A) Convergent (B) Divergent (C) Oscillatory (D) None of these
Q.17
If as ,then the series
1 (A) Convergent (B) Divergent (C) Oscillatory (D) None of these
Q.18
The series is
1 (A) Convergent (B) Divergent (C) Oscillatory (D) None of these
Q.19
For , the value of is
1 (A)1 (B) 0 (C) (D)
Q.20
The sum of the series is
1 (A) 9 (B)
(C) 1 (D)
Q.21
If implicit function then
1 (A) (B) (C) (D) None of these
Q.22
If change the order of integration of then

1 (A) (B) (C) (D)
Q.23 Equation of tangent plane of at (2,0,2) is 1 (A) (B) (C) (D)
Q.24
The series converges if
1 (A) (B) (C) (D) None of these
Q.25
If , then is
1 (A) (B) (C) (D)
Q.26 The series is convergent if 2 (A) (B) (C) (D)
Q.27 Express 5.232323? as a ratio of two integers is 2 (A) (B) (C) (D)
Q.28

2
(A) 2 (B) (C) 0 (D)
Q.29

2 (A) 4 (B) (C) 0 (D)
Q.30
=
2 (A) 0 (B) 1 (C) -1 (D) None of these

Seat No.: _____________________ Enrolment No.:_________________
GUJARAT TECHNOLOGICAL UNIVERSITY
SPFU-SEMESTER-1
st
/ 2
nd
EXAMINATION-Summer 2018
Subject Code: MTH001 Date: 17-05-2018
Subject Name: CALCULUS
Time: 02:30 PM to 05:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Objective Section (MCQ)Q.1
The sum of the series is
1
(A)0 (B) 1 (C) -1 (D)
Q.2

1 (A) Convergent (B) Divergent (C) Oscillatory (D) None of these
Q.3

1 (A) ( (B) ( (C) 1 (D) 0
Q.4

1 (A) 1 (B) (C) (D)
Q.5
is homogeneous function with degree
1 (A) -1 (B) 0 (C) 1 (D) None of these
Q.6 If is homogeneous function of degree then

1 (A) (B) 0 (C) (D)
Q.7
The series where is???.
1 (A) Divergent (B) Convergent (C) Alternative (D) None of above
Q.8 The homogeneous function f(x, y) of degree can written as 1
(B) (C) (D) None of these
Q.9
The series is
1 (A) Divergent (B) Convergent (C) Alternative (D) None of above
Q.10

1 (A) (B) (C) 1 (D)
Q.11
If , then
1 (A) (B) (C) -1 (D)
Q.12 If for some series then the series is 1 (A)Convergent (B) Divergent (C) Oscillatory (D) None of these
Q.13
=
1 (A) 0 (B) 1 (C) -1 (D) None of these
Q.14 If ) is continuous then 1 (A) (B) (C) (D)
Q.15
Area enclosed by the ellipse is
1 (A) (B) (C) (D)
Q.16 The series 1-1+1-1+1-1+1-1+?.

1 (A) Convergent (B) Divergent (C) Oscillatory (D) None of these
Q.17
If as ,then the series
1 (A) Convergent (B) Divergent (C) Oscillatory (D) None of these
Q.18
The series is
1 (A) Convergent (B) Divergent (C) Oscillatory (D) None of these
Q.19
For , the value of is
1 (A)1 (B) 0 (C) (D)
Q.20
The sum of the series is
1 (A) 9 (B)
(C) 1 (D)
Q.21
If implicit function then
1 (A) (B) (C) (D) None of these
Q.22
If change the order of integration of then

1 (A) (B) (C) (D)
Q.23 Equation of tangent plane of at (2,0,2) is 1 (A) (B) (C) (D)
Q.24
The series converges if
1 (A) (B) (C) (D) None of these
Q.25
If , then is
1 (A) (B) (C) (D)
Q.26 The series is convergent if 2 (A) (B) (C) (D)
Q.27 Express 5.232323? as a ratio of two integers is 2 (A) (B) (C) (D)
Q.28

2
(A) 2 (B) (C) 0 (D)
Q.29

2 (A) 4 (B) (C) 0 (D)
Q.30
=
2 (A) 0 (B) 1 (C) -1 (D) None of these

Subjective Section
Attempt any five:
Q.1
If show that
.
7
Q.2 Find the extreme values of . 7
Q.3
Test the convergence of .
7
Q.4
For what values of does the series converge? and find radius of
convergence.
7
Q.5
Sketch the region of integration and evaluate the by reversing its
order.
7
Q.6
Evaluate , where R is the region bounded by the lines y=x, y=2x and
x+y=2.
7
Q.7
Evaluate by changing to polar coordinates.
7

.