Exam Details
| Subject | advanced mathematics (group-1) | |
| Paper | ||
| Exam / Course | diploma engineering | |
| Department | ||
| Organization | Gujarat Technological University | |
| Position | ||
| Exam Date | January, 2019 | |
| City, State | gujarat, ahmedabad |
Question Paper
1/11
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
DIPLOMA ENGINEERING- C to D Bridge Course Examination WINTER 2018
Subject Code: C320002 Date: 03-01-2019
Subject Name: ADVANCED MATHEMATICS (GROUP-1)
Time: 10:30 AM TO 12:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Each question is of 1 mark.
4. Use of only simple calculator is permitted. (Scientific/Higher Version not allowed).
5. English version is authentic.
No.
Question Text and Option.
1.
If z i 2 then
A.
i 2
B.
i 2
C.
i 2
D.
i
z i 2
A.
i 2
B.
i 2
C.
i 2
D.
i
2.
8 i 6
A.
10
B.
100
C.
√10
D.
√90
8 i 6
A.
10
B.
100
C.
√10
D.
√90
3.
arg 1 i
A.
B.
−
C.
D.
arg 1 i
A.
B.
−
C.
D.
4.
1 i
A.
12 12
B.
12 − 12
C.
−12 12
D.
−12 − 12
1 i
A.
12 12
B.
12 − 12
C.
−12 12
D.
−12 − 12
5.
z
A.
2
B.
Re
C.
2
D.
2 i
z
A.
2
B.
Re
C.
2
D.
2 i
6.
3 2i 2
2/11
A.
13 12 i
B.
9 12 i
C.
5 12 i
D.
5 6 i
3 2i 2
A.
13 12 i
B.
9 12 i
C.
5 12 i
D.
5 6 i
7.
cos sin sin
A.
cos i sin
B.
cos i sin
C.
cos i sin
D.
cos i sin
cos sin sin
A.
cos i sin
B.
cos i sin
C.
cos i sin
D.
cos i sin
8.
cos i sin cos i sin
A.
cos i sin
B.
cos i sin
C.
cos i sin
D.
-cos i sin
cos i sin cos i sin
A.
cos i sin
B.
cos i sin
C.
cos i sin
D.
-cos i sin
9.
If
A.
0
B.
14
C.
1
D.
−14
A.
0
B.
14
C.
1
D.
−14
10.
√−4 .
A.
2
B.
±2
C.
−2
D.
√−4 .
A.
2
B.
±2
C.
−2
D.
2i
11.
If then .
A.
B.
C.
D.
−1
.
A.
B.
C.
D.
−1
12.
i 9
A.
1
B.
C.
i
D.
i
i 9
A.
1
B.
C.
i
D.
i
13.
If f x x then f 2
A.
2
B.
C.
1
D.
f x x f 2
A.
2
B.
C.
1
D.
3/11
14.
If f x log x then f
A.
B.
C.
D.
f x log x f
A.
B.
C.
D.
15.
If .
A.
1
B.
e
C.
0
D.
.
A.
1
B.
e
C.
0
D.
16.
If .
A.
cos x
B.
cos x
C.
sin x
D.
sin x
.
A.
cos x
B.
cos x
C.
sin x
D.
sin x
17.
0
A.
1
B.
C.
D.
0
0
A.
1
B.
C.
D.
0
18.
0
A.
loge(23)
B.
1
C.
0
D.
loge(32)
0
A.
loge(23)
B.
1
C.
0
D.
loge(32)
19.
A.
32
B.
32
C.
1
D.
0
A.
32
B.
32
C.
1
D.
0
20.
.
A.
1
B.
3
C.
0
D.
13
.
4/11
A.
1
B.
3
C.
0
D.
13
21.
2
A.
1
B.
16
C.
D.
80
2
A.
1
B.
16
C.
5
D.
80
22.
∞
A.
∞
B.
0
C.
1
D.
3
∞
A.
∞
B.
0
C.
1
D.
3
23.
2
A.
2
B.
1
C.
3
D.
0
2
A.
2
B.
1
C.
3
D.
0
24.
.
A.
1
B.
C.
2
D.
2
.
A.
1
B.
C.
2
D.
2
25.
− − .
A.
0
B.
3
C.
2
D.
1
− − .
A.
0
B.
3
C.
2
D.
1
26.
.
A.
0
B.
5
C.
3
D.
8
.
A.
0
B.
5
C.
3
D.
8
27.
.
A.
5
B.
C.
0
D.
1
.
5/11
A.
5
B.
C.
0
D.
1
28.
(cosec
A.
sec x tan x
B.
cosec x cot x
C.
cosec x cot x
D.
cot2x
(cosec
A.
sec x tan x
B.
cosec x cot x
C.
cosec x cot x
D.
cot2x
29.
A.
1√1+
B.
1√1−
C.
1√
D.
11−
A.
1√1+
B.
1√1−
C.
1√
D.
11−
30.
A.
1
B.
0
C.
D.
2√1−
A.
1
B.
0
C.
D.
2√1−
31.
A.
B.
x
C.
x
D.
1
A.
B.
x
C.
x
D.
1
32.
A.
1 log x
B.
C.
D.
A.
1 log x
B.
C.
D.
33.
cos 2 x
A.
2 sin x cos x
B.
sin 2x
C.
sin 2x
D.
sin2 x
cos 2 x
A.
2 sin x cos x
B.
sin 2x
C.
sin 2x
D.
sin2 x
34.
If y
A.
1
B.
24
6/11
C.
4
D.
0
y
A.
1
B.
24
C.
4
D.
0
35.
If y r
A.
B.
C.
D.
y r
A.
B.
C.
D.
36.
If f x then f
A.
0
B.
1
C.
2
D.
Non of above
f x f
A.
0
B.
1
C.
2
D.
Non of above
37.
If equation of motion of a particle velocity at t 4 sec is
A.
12m/sec
B.
8m/sec
C.
12m/sec2
D.
8m/sec2
t 4
A.
12m/sec
B.
8m/sec
C.
12m/sec2
D.
8m/sec2
38.
If y
A.
B.
C.
D.
y
A.
B.
C.
D.
39.
Function if has minima at 2 .
A.
B.
C.
D.
2
A.
B.
C.
D.
40.
A.
log
B.
1
C.
D.
None of this
7/11
A.
log
B.
1
C.
D.
None of this
41.
If then
A.
0
B.
100
C.
99
D.
1
A.
0
B.
100
C.
99
D.
1
42.
A.
B.
C.
D.
A.
B.
C.
D.
43.
A.
B.
C.
D.
A.
B.
C.
D.
44.
C.
A.
B.
C.
D.
3
C.
A.
B.
C.
D.
3
45.
.
A.
cosec x c
B.
cosec x c
C.
cot x x c
D.
cot x x c
.
A.
cosec x c
B.
cosec x c
C.
cot x x c
D.
cot x x c
46.
A.
log x3 c
B.
3 log x3 c
C.
log 3x2 1 c
D.
log 3x2 c
A.
log x3 c
B.
3 log x3 c
C.
log 3x2 1 c
D.
log 3x2 c
47.
41 X 210
8/11
A.
B.
C.
D.
41 X 210
A.
B.
C.
D.
48.
0
A.
0
B.
C.
D.
0
A.
0
B.
C.
D.
49.
C.
A.
B.
C.
D.
C.
A.
B.
C.
D.
50.
C
A.
B.
C.
D.
C
A.
B.
C.
D.
51.
.
A.
0
B.
C.
D.
.
A.
0
B.
C.
D.
52.
.
A.
B.
C.
D.
.
A.
B.
9/11
C.
D.
53.
.
A.
0
B.
1
C.
2
D.
3
.
A.
0
B.
1
C.
2
D.
3
54.
.
A.
B.
C.
D.
.
A.
B.
C.
D.
55.
Area covered by the curve is .
A.
B.
C.
D.
9
JS| äFZF YFIPf
A.
B.
C.
D.
9
56.
c
A.
B.
C.
D.
c
A.
B.
C.
D.
57.
A.
B.
C.
D.
A.
B.
C.
D.
58.
Volume of solid generation by revolving region bounded by and
around X-asis is .
A.
B.
C.
D.
None of this
VG[ J0[ V1F VF;5F; 5lZE|D6YL AGTF WGG] WGO/
10/11
K[P
A.
B.
C.
D.
None of this
59.
.
A.
e-1
B.
1-e
C.
e
D.
.
A.
e-1
B.
1-e
C.
e
D.
60.
A.
log sin x c
B.
log cos x c
C.
log sec x c
D.
log |cosec x
A.
log sin x c
B.
log cos x c
C.
log sec x c
D.
log |cosec x
61.
Solution of the differential equation y .
A.
B.
C.
D.
None of these
lJS,Ÿ ;DLSZ6 y
A.
B.
C.
D.
None of these
62.
The order of the differential equation
A.
3
B.
2
C.
1
D.
0
lJS,Ÿ ;DLSZ6 GL S1FF K[P
A.
3
B.
2
C.
1
D.
0
63.
The degree of the differential equation is
A.
3
B.
2
C.
1
D.
Not defined
lJS,Ÿ ;DLSZ6 5ZLDF6 K[P
A.
3
B.
2
C.
1
D.
Not defined
64.
The degree of differential equation is
A.
4
B.
3
C.
2
D.
1
lJS,Ÿ ;DLSZ6 5ZLDF6 K[P
A.
4
B.
3
C.
2
D.
1
65.
Differential equation of y a is .
A.
B.
C.
D.
None of these
y a lJS,Ÿ K[P
A.
B.
11/11
C.
0
D. None of these
66. Which of the following is standard from of linear differential equation?
A.
B.
C.
D. None of these
GLR[ 5{SL lJS,Ÿ ;DLSZ6 5|DFl6T SI] K[m
A.
B.
C.
D. None of these
67. Which of the following is not the differential equation?
A. xydy+xydx=1 B. y=secx
C.
0
D.
GLR[ 5{SL SI] lJS,Ÿ ;DLSZ6 GYLm
A. xydy+xydx=1 B. y=secx
C.
0
D.
68.
Orders of differential equation 2
2
dx
y d
4y 0.
A. 1 B. 2
C. 0 D. None of the above
lJS,Ÿ ;DLSZ6 2
2
dx
d y
4y 0 GL S1FF K[P
A. 1 B. 2
C. 0 D. None of the above
69. For differential equation
I.F
A. B.
C. D. None of the above
lJS,Ÿ ;DLSZ6
DF8[ K[P
A. B.
C. D. None of the above
70. Integrating factor of the equation
A. sec B. cosec
C. cos D.
GM ;S<ISFZS VJIJ K[P
A. sec B. cosec
C. cos D.
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
DIPLOMA ENGINEERING- C to D Bridge Course Examination WINTER 2018
Subject Code: C320002 Date: 03-01-2019
Subject Name: ADVANCED MATHEMATICS (GROUP-1)
Time: 10:30 AM TO 12:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Each question is of 1 mark.
4. Use of only simple calculator is permitted. (Scientific/Higher Version not allowed).
5. English version is authentic.
No.
Question Text and Option.
1.
If z i 2 then
A.
i 2
B.
i 2
C.
i 2
D.
i
z i 2
A.
i 2
B.
i 2
C.
i 2
D.
i
2.
8 i 6
A.
10
B.
100
C.
√10
D.
√90
8 i 6
A.
10
B.
100
C.
√10
D.
√90
3.
arg 1 i
A.
B.
−
C.
D.
arg 1 i
A.
B.
−
C.
D.
4.
1 i
A.
12 12
B.
12 − 12
C.
−12 12
D.
−12 − 12
1 i
A.
12 12
B.
12 − 12
C.
−12 12
D.
−12 − 12
5.
z
A.
2
B.
Re
C.
2
D.
2 i
z
A.
2
B.
Re
C.
2
D.
2 i
6.
3 2i 2
2/11
A.
13 12 i
B.
9 12 i
C.
5 12 i
D.
5 6 i
3 2i 2
A.
13 12 i
B.
9 12 i
C.
5 12 i
D.
5 6 i
7.
cos sin sin
A.
cos i sin
B.
cos i sin
C.
cos i sin
D.
cos i sin
cos sin sin
A.
cos i sin
B.
cos i sin
C.
cos i sin
D.
cos i sin
8.
cos i sin cos i sin
A.
cos i sin
B.
cos i sin
C.
cos i sin
D.
-cos i sin
cos i sin cos i sin
A.
cos i sin
B.
cos i sin
C.
cos i sin
D.
-cos i sin
9.
If
A.
0
B.
14
C.
1
D.
−14
A.
0
B.
14
C.
1
D.
−14
10.
√−4 .
A.
2
B.
±2
C.
−2
D.
√−4 .
A.
2
B.
±2
C.
−2
D.
2i
11.
If then .
A.
B.
C.
D.
−1
.
A.
B.
C.
D.
−1
12.
i 9
A.
1
B.
C.
i
D.
i
i 9
A.
1
B.
C.
i
D.
i
13.
If f x x then f 2
A.
2
B.
C.
1
D.
f x x f 2
A.
2
B.
C.
1
D.
3/11
14.
If f x log x then f
A.
B.
C.
D.
f x log x f
A.
B.
C.
D.
15.
If .
A.
1
B.
e
C.
0
D.
.
A.
1
B.
e
C.
0
D.
16.
If .
A.
cos x
B.
cos x
C.
sin x
D.
sin x
.
A.
cos x
B.
cos x
C.
sin x
D.
sin x
17.
0
A.
1
B.
C.
D.
0
0
A.
1
B.
C.
D.
0
18.
0
A.
loge(23)
B.
1
C.
0
D.
loge(32)
0
A.
loge(23)
B.
1
C.
0
D.
loge(32)
19.
A.
32
B.
32
C.
1
D.
0
A.
32
B.
32
C.
1
D.
0
20.
.
A.
1
B.
3
C.
0
D.
13
.
4/11
A.
1
B.
3
C.
0
D.
13
21.
2
A.
1
B.
16
C.
D.
80
2
A.
1
B.
16
C.
5
D.
80
22.
∞
A.
∞
B.
0
C.
1
D.
3
∞
A.
∞
B.
0
C.
1
D.
3
23.
2
A.
2
B.
1
C.
3
D.
0
2
A.
2
B.
1
C.
3
D.
0
24.
.
A.
1
B.
C.
2
D.
2
.
A.
1
B.
C.
2
D.
2
25.
− − .
A.
0
B.
3
C.
2
D.
1
− − .
A.
0
B.
3
C.
2
D.
1
26.
.
A.
0
B.
5
C.
3
D.
8
.
A.
0
B.
5
C.
3
D.
8
27.
.
A.
5
B.
C.
0
D.
1
.
5/11
A.
5
B.
C.
0
D.
1
28.
(cosec
A.
sec x tan x
B.
cosec x cot x
C.
cosec x cot x
D.
cot2x
(cosec
A.
sec x tan x
B.
cosec x cot x
C.
cosec x cot x
D.
cot2x
29.
A.
1√1+
B.
1√1−
C.
1√
D.
11−
A.
1√1+
B.
1√1−
C.
1√
D.
11−
30.
A.
1
B.
0
C.
D.
2√1−
A.
1
B.
0
C.
D.
2√1−
31.
A.
B.
x
C.
x
D.
1
A.
B.
x
C.
x
D.
1
32.
A.
1 log x
B.
C.
D.
A.
1 log x
B.
C.
D.
33.
cos 2 x
A.
2 sin x cos x
B.
sin 2x
C.
sin 2x
D.
sin2 x
cos 2 x
A.
2 sin x cos x
B.
sin 2x
C.
sin 2x
D.
sin2 x
34.
If y
A.
1
B.
24
6/11
C.
4
D.
0
y
A.
1
B.
24
C.
4
D.
0
35.
If y r
A.
B.
C.
D.
y r
A.
B.
C.
D.
36.
If f x then f
A.
0
B.
1
C.
2
D.
Non of above
f x f
A.
0
B.
1
C.
2
D.
Non of above
37.
If equation of motion of a particle velocity at t 4 sec is
A.
12m/sec
B.
8m/sec
C.
12m/sec2
D.
8m/sec2
t 4
A.
12m/sec
B.
8m/sec
C.
12m/sec2
D.
8m/sec2
38.
If y
A.
B.
C.
D.
y
A.
B.
C.
D.
39.
Function if has minima at 2 .
A.
B.
C.
D.
2
A.
B.
C.
D.
40.
A.
log
B.
1
C.
D.
None of this
7/11
A.
log
B.
1
C.
D.
None of this
41.
If then
A.
0
B.
100
C.
99
D.
1
A.
0
B.
100
C.
99
D.
1
42.
A.
B.
C.
D.
A.
B.
C.
D.
43.
A.
B.
C.
D.
A.
B.
C.
D.
44.
C.
A.
B.
C.
D.
3
C.
A.
B.
C.
D.
3
45.
.
A.
cosec x c
B.
cosec x c
C.
cot x x c
D.
cot x x c
.
A.
cosec x c
B.
cosec x c
C.
cot x x c
D.
cot x x c
46.
A.
log x3 c
B.
3 log x3 c
C.
log 3x2 1 c
D.
log 3x2 c
A.
log x3 c
B.
3 log x3 c
C.
log 3x2 1 c
D.
log 3x2 c
47.
41 X 210
8/11
A.
B.
C.
D.
41 X 210
A.
B.
C.
D.
48.
0
A.
0
B.
C.
D.
0
A.
0
B.
C.
D.
49.
C.
A.
B.
C.
D.
C.
A.
B.
C.
D.
50.
C
A.
B.
C.
D.
C
A.
B.
C.
D.
51.
.
A.
0
B.
C.
D.
.
A.
0
B.
C.
D.
52.
.
A.
B.
C.
D.
.
A.
B.
9/11
C.
D.
53.
.
A.
0
B.
1
C.
2
D.
3
.
A.
0
B.
1
C.
2
D.
3
54.
.
A.
B.
C.
D.
.
A.
B.
C.
D.
55.
Area covered by the curve is .
A.
B.
C.
D.
9
JS| äFZF YFIPf
A.
B.
C.
D.
9
56.
c
A.
B.
C.
D.
c
A.
B.
C.
D.
57.
A.
B.
C.
D.
A.
B.
C.
D.
58.
Volume of solid generation by revolving region bounded by and
around X-asis is .
A.
B.
C.
D.
None of this
VG[ J0[ V1F VF;5F; 5lZE|D6YL AGTF WGG] WGO/
10/11
K[P
A.
B.
C.
D.
None of this
59.
.
A.
e-1
B.
1-e
C.
e
D.
.
A.
e-1
B.
1-e
C.
e
D.
60.
A.
log sin x c
B.
log cos x c
C.
log sec x c
D.
log |cosec x
A.
log sin x c
B.
log cos x c
C.
log sec x c
D.
log |cosec x
61.
Solution of the differential equation y .
A.
B.
C.
D.
None of these
lJS,Ÿ ;DLSZ6 y
A.
B.
C.
D.
None of these
62.
The order of the differential equation
A.
3
B.
2
C.
1
D.
0
lJS,Ÿ ;DLSZ6 GL S1FF K[P
A.
3
B.
2
C.
1
D.
0
63.
The degree of the differential equation is
A.
3
B.
2
C.
1
D.
Not defined
lJS,Ÿ ;DLSZ6 5ZLDF6 K[P
A.
3
B.
2
C.
1
D.
Not defined
64.
The degree of differential equation is
A.
4
B.
3
C.
2
D.
1
lJS,Ÿ ;DLSZ6 5ZLDF6 K[P
A.
4
B.
3
C.
2
D.
1
65.
Differential equation of y a is .
A.
B.
C.
D.
None of these
y a lJS,Ÿ K[P
A.
B.
11/11
C.
0
D. None of these
66. Which of the following is standard from of linear differential equation?
A.
B.
C.
D. None of these
GLR[ 5{SL lJS,Ÿ ;DLSZ6 5|DFl6T SI] K[m
A.
B.
C.
D. None of these
67. Which of the following is not the differential equation?
A. xydy+xydx=1 B. y=secx
C.
0
D.
GLR[ 5{SL SI] lJS,Ÿ ;DLSZ6 GYLm
A. xydy+xydx=1 B. y=secx
C.
0
D.
68.
Orders of differential equation 2
2
dx
y d
4y 0.
A. 1 B. 2
C. 0 D. None of the above
lJS,Ÿ ;DLSZ6 2
2
dx
d y
4y 0 GL S1FF K[P
A. 1 B. 2
C. 0 D. None of the above
69. For differential equation
I.F
A. B.
C. D. None of the above
lJS,Ÿ ;DLSZ6
DF8[ K[P
A. B.
C. D. None of the above
70. Integrating factor of the equation
A. sec B. cosec
C. cos D.
GM ;S<ISFZS VJIJ K[P
A. sec B. cosec
C. cos D.
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