Categories: 1st and 2nd Semester

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

.

746268 PAPER V - REHABILITATION MEDICINE INCLUDING GERIATRIC MEDICINETHE TAMIL NADU DR. M.G.R. MEDICAL UNIVERSITY…

4 years ago

746268 PAPER V - REHABILITATION MEDICINE INCLUDING GERIATRIC MEDICINETHE TAMIL NADU DR. M.G.R. MEDICAL UNIVERSITY…

4 years ago

746267 PAPER IV - P.T. IN ORTHOPAEDICSTHE TAMIL NADU DR. M.G.R. MEDICAL UNIVERSITY [LN 6267]…

4 years ago

746267 PAPER IV - P.T. IN ORTHOPAEDICSTHE TAMIL NADU DR. M.G.R. MEDICAL UNIVERSITY [LN 6267]…

4 years ago

746266 PAPER III – CLINICAL ORTHOPAEDICSTHE TAMIL NADU DR. M.G.R. MEDICAL UNIVERSITY [LN 6266] AUGUST…

4 years ago

746265 PAPER II – P.T. IN NEUROLOGYTHE TAMIL NADU DR. M.G.R. MEDICAL UNIVERSITY [LN 6265]…

4 years ago