Exam Details
| Subject | advanced mathematics(group-2) | |
| Paper | ||
| Exam / Course | diploma engineering | |
| Department | ||
| Organization | Gujarat Technological University | |
| Position | ||
| Exam Date | January, 2019 | |
| City, State | gujarat, ahmedabad |
Question Paper
1/10
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
DIPLOMA ENGINEERING- C to D Bridge Course Examination WINTER 2018
Subject Code: C320003 Date: 09-01-2019
Subject Name: ADVANCED MATHEMATICS(GROUP-2)
Time: 02:30 PM TO 04:00 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.
Distance between two points and is
A.
3
B.
6
C.
1
D.
9
A.
3
B.
6
C.
1
D.
9
2.
Two lines having slopes m1 and m2 respectively are perpendicular if .
A.
m1m2
B.
m1m2
C.
m1 m2
D.
m1 =m2
m1 m2
A.
m1m2
B.
m1m2
C.
m1 m2
D.
m1 =m2
3.
The slope of the line passing through the points and is
A.
1
B.
2
C.
D.
3
A.
1
B.
2
C.
D.
3
4.
Slope of the line 2x 2y 6 is
A.
B.
6
C.
D.
1
2x 2y 6
A.
B.
6
C.
D.
1
5.
Equation of a circle having centre and radius 3 is .
A.
3
B.
3
C.
9
D.
9
3
A.
3
B.
3
C.
9
D.
9
6.
x-intercept of the line 2x+3y 4 is
A.
B.
3
C.
2
D.
4
A.
B.
3
C.
2
D.
4
7.
If two lines 5x+2y-3=0 and kx+2y+7=0 are parallel, if
A.
2
B.
2/10
C.
5
D.
kx+2y+7 k
A.
2
B.
C.
5
D.
8.
If midpoint joining two points and is then x .
A.
2
B.
3
C.
4
D.
5
x
A.
2
B.
3
C.
4
D.
5
9.
The point is not on the line y 1.
A.
B.
C.
D.
y 1
A.
B.
C.
D.
10.
Equation of a circle having centre radius 3 is
A.
B.
C.
D.
3
A.
B.
C.
D.
11.
If A and B 3 then midpoint of line segment is .
A.
B.
C.
D.
3
A.
B.
C.
D.
12.
For circle 2x2 +2y2 +4x 0 centre is
A.
B.
C.
D.
2x2 +2y2 +4x 0
A.
B.
C.
D.
13.
If A 5 and B then slope of is .
A.
9/5
B.
C.
5/9
D.
A 5 B
A.
9/5
B.
C.
5/9
D.
14.
Centre of the circle x2 y2 4 is .
A.
B.
C.
D.
x2 y2 4
A.
B.
C.
D.
15.
If 2x 3x then
A.
5
B.
0
C.
1
D.
2
2x 3x
A.
5
B.
0
C.
1
D.
2
16.
If f x sin 2x then f
3/10
A.
½
B.
1/√2
C.
√3/2
D.
0
f x sin 2x f
A.
½
B.
1/√2
C.
√3/2
D.
0
17.
lim∅→0 (tan∅2∅)
A.
1
B.
2
C.
½
D.
2/3
lim∅→0 (tan∅2∅)
A.
1
B.
2
C.
½
D.
2/3
18.
A.
27
B.
9
C.
3
D.
0
A.
27
B.
9
C.
3
D.
0
19.
A.
0
B.
1
C.
2
D.
3
A.
0
B.
1
C.
2
D.
3
20.
A.
1
B.
e
C.
1/e
D.
None of above
A.
1
B.
e
C.
1/e
D.
21.
A.
log x
B.
1
C.
loge4
D.
0
A.
log x
B.
1
C.
loge4
D.
0
22.
A.
5
B.
C.
1/5
D.
0
A.
5
B.
C.
1/5
D.
0
23.
A.
B.
4
4/10
C.
D.
1
A.
B.
4
C.
D.
1
24.
lim∅→0
A.
1/7
B.
1
C.
0
D.
7
lim∅→0
A.
1/7
B.
1
C.
0
D.
7
25.
For y cosx+9
A.
y
B.
y
C.
cosx
D.
cosx
For y cosx+9
A.
y
B.
y
C.
cosx
D.
cosx
26.
A.
secx
B.
tanx
C.
1/secx
D.
cotx
A.
secx
B.
tanx
C.
1/secx
D.
cotx
27.
A.
1
B.
0
C.
D.
A.
1
B.
0
C.
D.
28.
A.
2x
B.
2x-1
C.
2x loge2
D.
2x log2e
A.
2x
B.
2x-1
C.
2x loge2
D.
2x log2e
29.
A.
1/x2
B.
1/x
C.
ex
D.
0
A.
1/x2
B.
1/x
C.
ex
D.
0
5/10
30.
cosx)
A.
3x2 cosx
B.
6x sinx
C.
6x cosx
D.
3 sinx
cosx)
A.
3x2 cosx
B.
6x sinx
C.
6x cosx
D.
3 sinx
31.
For y sin∅, x =cos∅
A.
cot ∅
B.
tan∅
C.
-tan∅
D.
-cot∅
For y sin∅, x =cos∅
A.
cot ∅
B.
tan∅
C.
-tan∅
D.
-cot∅
32.
A.
2sinxcosx
B.
sin2x
C.
-sin2x
D.
sin2x
A.
2sinxcosx
B.
sin2x
C.
-sin2x
D.
sin2x
33.
A.
B.
C.
D.
A.
B.
C.
D.
34.
If y
A.
cosx
B.
xcosx- sinx
C.
xcosx sinx
D.
xsinx -cosx
y
A.
cosx
B.
xcosx sinx
C.
xcosx sinx
D.
xsinx cosx
35.
A.
4ex
B.
4e2x
C.
2e2x
D.
2ex
A.
4ex
B.
4e2x
C.
2e2x
D.
2ex
36.
If xy 1 then
A.
1
B.
0
C.
x y 0
D.
y 0
xy 1
A.
1
B.
0
6/10
C.
x y 0
D.
y 0
37.
Equation of the motion of moving particle is given by s =t3 2t+ 51, then velocity at t=1 seconds is units.
A.
5
B.
1
C.
51
D.
3
s =t3 2t+ 51
A.
5
B.
1
C.
51
D.
3
38.
If y =log2 then dy/dx
A.
1
B.
0
C.
½
D.
x
y =log2 dy/dx
A.
1
B.
0
C.
½
D.
x
39.
If y x3/2 then dy/dx
A.
3√x/2
B.
-3√x/2
C.
3/2√x
D.
-3/2√x
y x3/2 dy/dx
A.
3√x/2
B.
-3√x/2
C.
3/2√x
D.
-3/2√x
40.
If x2 3xy 9 then
A.
B.
C.
D.
x2 3xy 9
A.
B.
C.
D.
41.
If y esinx then
A.
esinx
B.
esinxcosx
C.
ecosx
D.
ecosxcosx
y esinx
A.
esinx
B.
esinxcosx
C.
ecosx
D.
ecosxcosx
42.
If y=cosec2x- cot2x then dy/dx
A.
1
B.
2
C.
0
D.
None of above
y cosec2x- cot2x dy/dx
A.
1
B.
2
C.
0
D.
43.
A.
3x2 cosx
B.
6x cosx
C.
6x2 cosx
D.
6x- cosx
A.
3x2 cosx
B.
6x cosx
C.
6x2 cosx
D.
6x- cosx
44.
c
A.
secxdx
B.
secx tanx
7/10
C.
tanx
D.
tanx
c
A.
secxdx
B.
secx tanx
C.
tanx
D.
tanx
45.
A.
Log
B.
Log
C.
Log
D.
Log
A.
Log
B.
Log
C.
Log
D.
Log
46.
A.
x-1 c
B.
x-2 c
C.
c
D.
Log
A.
x-1 c
B.
x-2 c
C.
c
D.
Log
47.
A.
B.
C.
D.
A.
B.
C.
D.
48.
A.
B.
C.
D.
A.
B.
C.
D.
49.
A.
B.
C.
D.
A.
B.
C.
D.
50.
A.
log
B.
log
C.
log
D.
8/10
A.
log
B.
log
C.
log
D.
51.
A.
B.
C.
D.
A.
B.
C.
D.
52.
A.
B.
Log(7x) c
C.
7log
D.
1log
A.
B.
Log(7x) c
C.
7log
D.
1log
53.
A.
0
B.
1
C.
2
D.
3
A.
0
B.
1
C.
2
D.
3
54.
A.
6x
B.
3x3- x
C.
x3 3x
D.
3x3- 3x
A.
6x
B.
3x3- x
C.
x3 3x
D.
3x3- 3x
55.
A.
0
B.
1
C.
sin2x
D.
x
A.
0
B.
1
C.
sin2x
D.
x
56.
Area of region bounded by curve and x=2 .
A.
¾
B.
3/2
C.
3
D.
1
A.
¾
B.
3/2
C.
3
D.
1
57.
If y xex then
A.
ex
B.
x(ex
C.
ex
D.
x(ex
9/10
If y xex then
A.
ex
B.
x(ex
C.
ex
D.
x(ex
58.
A.
2
B.
C.
0
D.
1
A.
2
B.
C.
0
D.
1
59.
If mean of observations a 9 is 6 then value of a is
A.
6
B.
4
C.
5
D.
2
4 a 9 6 a
A.
6
B.
4
C.
5
D.
2
60.
If the mode of observations c is 3 then value of c is
A.
2
B.
7
C.
3
D.
8
c 3
A.
2
B.
7
C.
3
D.
8
61.
Mean of first five prime numbers is
A.
5.5
B.
5
C.
5.7
D.
5.6
A.
5.5
B.
5
C.
5.7
D.
5.6
62.
For information data 12, 14, 17, 7 median of information is
A.
9
B.
8
C.
8.5
D.
None of above
12, 14, 17, 7 .
A.
9
B.
8
C.
8.5
D.
63.
For information mean is 1.43 and median is 1.32 then mode is
A.
1.1
B.
1.5
C.
1.2
D.
0.9
1.43 1.32
A.
1.1
B.
1.5
C.
1.2
D.
0.9
64.
The mean deviation from the median for the observations
A.
2.5
B.
3.0
C.
3.5
D.
2.8
A.
2.5
B.
3.0
C.
3.5
D.
2.8
65.
For the data 12, 10, 15, 22, 30, 20, 32, 12, 20, 30 median is
A.
25
B.
30
C.
20
D.
22
12, 10, 15, 22, 30, 20, 32, 12, 20, 30
A.
25
B.
30
C.
20
D.
22
66.
Mean of first five even numbers is
A.
6
B.
10
10/10
C.
15
D.
30
A.
6
B.
10
C.
15
D.
30
67.
For information 10, 13, 12, 17 mean deviation from mean is
A.
4
B.
3.4
C.
3
D.
None of these
10, 13, 12, 17
A.
4
B.
3.4
C.
3
D.
68.
The range of the data 17, 15, 25, 34, 32 is
A.
18
B.
19
C.
34
D.
17
17, 15, 25, 34, 32
A.
18
B.
19
C.
34
D.
17
69.
If given data is 8 and 7 then Mode is .
A.
5
B.
7
C.
8
D.
9
8 7
A.
5
B.
7
C.
8
D.
9
70.
To find the standard deviation of ungrouped data first we have to find
A.
Median
B.
Mean
C.
Mode
D.
None of these
A.
B.
C.
D.
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
DIPLOMA ENGINEERING- C to D Bridge Course Examination WINTER 2018
Subject Code: C320003 Date: 09-01-2019
Subject Name: ADVANCED MATHEMATICS(GROUP-2)
Time: 02:30 PM TO 04:00 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.
Distance between two points and is
A.
3
B.
6
C.
1
D.
9
A.
3
B.
6
C.
1
D.
9
2.
Two lines having slopes m1 and m2 respectively are perpendicular if .
A.
m1m2
B.
m1m2
C.
m1 m2
D.
m1 =m2
m1 m2
A.
m1m2
B.
m1m2
C.
m1 m2
D.
m1 =m2
3.
The slope of the line passing through the points and is
A.
1
B.
2
C.
D.
3
A.
1
B.
2
C.
D.
3
4.
Slope of the line 2x 2y 6 is
A.
B.
6
C.
D.
1
2x 2y 6
A.
B.
6
C.
D.
1
5.
Equation of a circle having centre and radius 3 is .
A.
3
B.
3
C.
9
D.
9
3
A.
3
B.
3
C.
9
D.
9
6.
x-intercept of the line 2x+3y 4 is
A.
B.
3
C.
2
D.
4
A.
B.
3
C.
2
D.
4
7.
If two lines 5x+2y-3=0 and kx+2y+7=0 are parallel, if
A.
2
B.
2/10
C.
5
D.
kx+2y+7 k
A.
2
B.
C.
5
D.
8.
If midpoint joining two points and is then x .
A.
2
B.
3
C.
4
D.
5
x
A.
2
B.
3
C.
4
D.
5
9.
The point is not on the line y 1.
A.
B.
C.
D.
y 1
A.
B.
C.
D.
10.
Equation of a circle having centre radius 3 is
A.
B.
C.
D.
3
A.
B.
C.
D.
11.
If A and B 3 then midpoint of line segment is .
A.
B.
C.
D.
3
A.
B.
C.
D.
12.
For circle 2x2 +2y2 +4x 0 centre is
A.
B.
C.
D.
2x2 +2y2 +4x 0
A.
B.
C.
D.
13.
If A 5 and B then slope of is .
A.
9/5
B.
C.
5/9
D.
A 5 B
A.
9/5
B.
C.
5/9
D.
14.
Centre of the circle x2 y2 4 is .
A.
B.
C.
D.
x2 y2 4
A.
B.
C.
D.
15.
If 2x 3x then
A.
5
B.
0
C.
1
D.
2
2x 3x
A.
5
B.
0
C.
1
D.
2
16.
If f x sin 2x then f
3/10
A.
½
B.
1/√2
C.
√3/2
D.
0
f x sin 2x f
A.
½
B.
1/√2
C.
√3/2
D.
0
17.
lim∅→0 (tan∅2∅)
A.
1
B.
2
C.
½
D.
2/3
lim∅→0 (tan∅2∅)
A.
1
B.
2
C.
½
D.
2/3
18.
A.
27
B.
9
C.
3
D.
0
A.
27
B.
9
C.
3
D.
0
19.
A.
0
B.
1
C.
2
D.
3
A.
0
B.
1
C.
2
D.
3
20.
A.
1
B.
e
C.
1/e
D.
None of above
A.
1
B.
e
C.
1/e
D.
21.
A.
log x
B.
1
C.
loge4
D.
0
A.
log x
B.
1
C.
loge4
D.
0
22.
A.
5
B.
C.
1/5
D.
0
A.
5
B.
C.
1/5
D.
0
23.
A.
B.
4
4/10
C.
D.
1
A.
B.
4
C.
D.
1
24.
lim∅→0
A.
1/7
B.
1
C.
0
D.
7
lim∅→0
A.
1/7
B.
1
C.
0
D.
7
25.
For y cosx+9
A.
y
B.
y
C.
cosx
D.
cosx
For y cosx+9
A.
y
B.
y
C.
cosx
D.
cosx
26.
A.
secx
B.
tanx
C.
1/secx
D.
cotx
A.
secx
B.
tanx
C.
1/secx
D.
cotx
27.
A.
1
B.
0
C.
D.
A.
1
B.
0
C.
D.
28.
A.
2x
B.
2x-1
C.
2x loge2
D.
2x log2e
A.
2x
B.
2x-1
C.
2x loge2
D.
2x log2e
29.
A.
1/x2
B.
1/x
C.
ex
D.
0
A.
1/x2
B.
1/x
C.
ex
D.
0
5/10
30.
cosx)
A.
3x2 cosx
B.
6x sinx
C.
6x cosx
D.
3 sinx
cosx)
A.
3x2 cosx
B.
6x sinx
C.
6x cosx
D.
3 sinx
31.
For y sin∅, x =cos∅
A.
cot ∅
B.
tan∅
C.
-tan∅
D.
-cot∅
For y sin∅, x =cos∅
A.
cot ∅
B.
tan∅
C.
-tan∅
D.
-cot∅
32.
A.
2sinxcosx
B.
sin2x
C.
-sin2x
D.
sin2x
A.
2sinxcosx
B.
sin2x
C.
-sin2x
D.
sin2x
33.
A.
B.
C.
D.
A.
B.
C.
D.
34.
If y
A.
cosx
B.
xcosx- sinx
C.
xcosx sinx
D.
xsinx -cosx
y
A.
cosx
B.
xcosx sinx
C.
xcosx sinx
D.
xsinx cosx
35.
A.
4ex
B.
4e2x
C.
2e2x
D.
2ex
A.
4ex
B.
4e2x
C.
2e2x
D.
2ex
36.
If xy 1 then
A.
1
B.
0
C.
x y 0
D.
y 0
xy 1
A.
1
B.
0
6/10
C.
x y 0
D.
y 0
37.
Equation of the motion of moving particle is given by s =t3 2t+ 51, then velocity at t=1 seconds is units.
A.
5
B.
1
C.
51
D.
3
s =t3 2t+ 51
A.
5
B.
1
C.
51
D.
3
38.
If y =log2 then dy/dx
A.
1
B.
0
C.
½
D.
x
y =log2 dy/dx
A.
1
B.
0
C.
½
D.
x
39.
If y x3/2 then dy/dx
A.
3√x/2
B.
-3√x/2
C.
3/2√x
D.
-3/2√x
y x3/2 dy/dx
A.
3√x/2
B.
-3√x/2
C.
3/2√x
D.
-3/2√x
40.
If x2 3xy 9 then
A.
B.
C.
D.
x2 3xy 9
A.
B.
C.
D.
41.
If y esinx then
A.
esinx
B.
esinxcosx
C.
ecosx
D.
ecosxcosx
y esinx
A.
esinx
B.
esinxcosx
C.
ecosx
D.
ecosxcosx
42.
If y=cosec2x- cot2x then dy/dx
A.
1
B.
2
C.
0
D.
None of above
y cosec2x- cot2x dy/dx
A.
1
B.
2
C.
0
D.
43.
A.
3x2 cosx
B.
6x cosx
C.
6x2 cosx
D.
6x- cosx
A.
3x2 cosx
B.
6x cosx
C.
6x2 cosx
D.
6x- cosx
44.
c
A.
secxdx
B.
secx tanx
7/10
C.
tanx
D.
tanx
c
A.
secxdx
B.
secx tanx
C.
tanx
D.
tanx
45.
A.
Log
B.
Log
C.
Log
D.
Log
A.
Log
B.
Log
C.
Log
D.
Log
46.
A.
x-1 c
B.
x-2 c
C.
c
D.
Log
A.
x-1 c
B.
x-2 c
C.
c
D.
Log
47.
A.
B.
C.
D.
A.
B.
C.
D.
48.
A.
B.
C.
D.
A.
B.
C.
D.
49.
A.
B.
C.
D.
A.
B.
C.
D.
50.
A.
log
B.
log
C.
log
D.
8/10
A.
log
B.
log
C.
log
D.
51.
A.
B.
C.
D.
A.
B.
C.
D.
52.
A.
B.
Log(7x) c
C.
7log
D.
1log
A.
B.
Log(7x) c
C.
7log
D.
1log
53.
A.
0
B.
1
C.
2
D.
3
A.
0
B.
1
C.
2
D.
3
54.
A.
6x
B.
3x3- x
C.
x3 3x
D.
3x3- 3x
A.
6x
B.
3x3- x
C.
x3 3x
D.
3x3- 3x
55.
A.
0
B.
1
C.
sin2x
D.
x
A.
0
B.
1
C.
sin2x
D.
x
56.
Area of region bounded by curve and x=2 .
A.
¾
B.
3/2
C.
3
D.
1
A.
¾
B.
3/2
C.
3
D.
1
57.
If y xex then
A.
ex
B.
x(ex
C.
ex
D.
x(ex
9/10
If y xex then
A.
ex
B.
x(ex
C.
ex
D.
x(ex
58.
A.
2
B.
C.
0
D.
1
A.
2
B.
C.
0
D.
1
59.
If mean of observations a 9 is 6 then value of a is
A.
6
B.
4
C.
5
D.
2
4 a 9 6 a
A.
6
B.
4
C.
5
D.
2
60.
If the mode of observations c is 3 then value of c is
A.
2
B.
7
C.
3
D.
8
c 3
A.
2
B.
7
C.
3
D.
8
61.
Mean of first five prime numbers is
A.
5.5
B.
5
C.
5.7
D.
5.6
A.
5.5
B.
5
C.
5.7
D.
5.6
62.
For information data 12, 14, 17, 7 median of information is
A.
9
B.
8
C.
8.5
D.
None of above
12, 14, 17, 7 .
A.
9
B.
8
C.
8.5
D.
63.
For information mean is 1.43 and median is 1.32 then mode is
A.
1.1
B.
1.5
C.
1.2
D.
0.9
1.43 1.32
A.
1.1
B.
1.5
C.
1.2
D.
0.9
64.
The mean deviation from the median for the observations
A.
2.5
B.
3.0
C.
3.5
D.
2.8
A.
2.5
B.
3.0
C.
3.5
D.
2.8
65.
For the data 12, 10, 15, 22, 30, 20, 32, 12, 20, 30 median is
A.
25
B.
30
C.
20
D.
22
12, 10, 15, 22, 30, 20, 32, 12, 20, 30
A.
25
B.
30
C.
20
D.
22
66.
Mean of first five even numbers is
A.
6
B.
10
10/10
C.
15
D.
30
A.
6
B.
10
C.
15
D.
30
67.
For information 10, 13, 12, 17 mean deviation from mean is
A.
4
B.
3.4
C.
3
D.
None of these
10, 13, 12, 17
A.
4
B.
3.4
C.
3
D.
68.
The range of the data 17, 15, 25, 34, 32 is
A.
18
B.
19
C.
34
D.
17
17, 15, 25, 34, 32
A.
18
B.
19
C.
34
D.
17
69.
If given data is 8 and 7 then Mode is .
A.
5
B.
7
C.
8
D.
9
8 7
A.
5
B.
7
C.
8
D.
9
70.
To find the standard deviation of ungrouped data first we have to find
A.
Median
B.
Mean
C.
Mode
D.
None of these
A.
B.
C.
D.
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