Download GTU BE/B.Tech 2019 Summer 1st And 2nd Sem (New And SPFU) 2110014 Calculus Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 1st And 2nd Sem (New And SPFU) 2110014 Calculus Previous Question Paper

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ?I &II (NEW) EXAMINATION ? SUMMER-2019
Subject Code: 2110014 Date: 06/06/2019

Subject Name: Calculus

Time: 10:30 AM TO 01:30 PM Total Marks: 70

Instructions:

1. Question No.1 is compulsory. Attempt any four out of remaining six questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

Q.1 Objective Question (MCQ)
Marks

(a) 07
1. For the Jacobian , value of the is
(a) (b) (3) (4)

2.
Value of for
(a) (b) (c) (d)

3.
is a homogeneous function of degree
(a) 1/2 (b) (c) (d)

4. The curve is
(a) straight line (b) point at distance ?2? on initial line
(c) circle with centre origin and radius 2 (d) cardioid

5. If ,then which is correct?
(a) (b)
(c) (d)

6. Infinite Sequence is
(a) convergent (b) divergent (c) oscillatory (d) None of these

7. Infinite Series
(a) convergent (b) divergent (c) oscillatory (d) None of these

(b) 07
1.
Infinite series is
(a) convergent (b) divergent (c) oscillatory (d) None of these

2. Curve is symmetric to
(a) X-axis (b) line (c) line (d) Y- axis

3.

(a) (b) 0 (c) (d)

4.
The sum of the series is
(a) (b) (c) 2 (d) 1

5. The Maclaurin series for the function is
(a) (b) (c) (d)

6. The straight line is revolved about x- axis between
. The generated solid is
(a)cone (b) sphere (c) cuboid (d) cylinder

7. For a series , if , then
(a) series is convergent (b) series is divergent
(c) sum of series is finite number
(d) series is conditionally convergent




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Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ?I &II (NEW) EXAMINATION ? SUMMER-2019
Subject Code: 2110014 Date: 06/06/2019

Subject Name: Calculus

Time: 10:30 AM TO 01:30 PM Total Marks: 70

Instructions:

1. Question No.1 is compulsory. Attempt any four out of remaining six questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

Q.1 Objective Question (MCQ)
Marks

(a) 07
1. For the Jacobian , value of the is
(a) (b) (3) (4)

2.
Value of for
(a) (b) (c) (d)

3.
is a homogeneous function of degree
(a) 1/2 (b) (c) (d)

4. The curve is
(a) straight line (b) point at distance ?2? on initial line
(c) circle with centre origin and radius 2 (d) cardioid

5. If ,then which is correct?
(a) (b)
(c) (d)

6. Infinite Sequence is
(a) convergent (b) divergent (c) oscillatory (d) None of these

7. Infinite Series
(a) convergent (b) divergent (c) oscillatory (d) None of these

(b) 07
1.
Infinite series is
(a) convergent (b) divergent (c) oscillatory (d) None of these

2. Curve is symmetric to
(a) X-axis (b) line (c) line (d) Y- axis

3.

(a) (b) 0 (c) (d)

4.
The sum of the series is
(a) (b) (c) 2 (d) 1

5. The Maclaurin series for the function is
(a) (b) (c) (d)

6. The straight line is revolved about x- axis between
. The generated solid is
(a)cone (b) sphere (c) cuboid (d) cylinder

7. For a series , if , then
(a) series is convergent (b) series is divergent
(c) sum of series is finite number
(d) series is conditionally convergent





Q.2 (a)
Find the Taylor series for at .
03
(b)


(c)
Is the series absolutely convergent or conditionally convergent?

(i) Discuss the convergence of the series

(ii) Find the Radius of convergence for the series .
04


04



03

Q.3 (a) Evaluate 03
(b)
(c)
Trace the curve
Prove that the series is convergent if and divergent
if
04
07

Q.4 (a)
Evaluate .
03
(b)


(c)
Find the equation of the tangent plane and normal line to the surface
at .

(i)Evaluate .
(ii) Evaluate
04


04

03

Q.5 (a) If , prove that . 03
(b)


(c)
Find maximum and minimum values.


If , prove that
(i)
(ii)
04



07

Q.6 (a) The region between the curve and the -axis is
revolved about the -axis to generate a solid. Find its volume.
03
(b)

(c)
Using volume by slicing method, find the volume of a cylinder with
radius ? ? and height ? ? .
Evaluate ; is triangle using
transformations .
04

07


Q.7 (a) Evaluate over the area bounded between the circles
and .
03
(b)




(c)
Evaluate

Change the order of integration and evaluate.

04




07
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