Chapter No. 9 Fundamentals of Trigonometry 100+ mcqs with solution
Chapter No. 9 Fundamentals of
Trigonometry
1.
Direction of Qibla is found by
using __________
a) Plane
Geometry
b) Spherical
Trigonometry
c) Plane
Trigonometry
d) Analytical
Geometry
e) None
of these
2. If a circle is divided into 360 parts,
then the angle subtended by each part at the center of the circle is called
__________
a) 1
radian
b) 1
degree
c) 1
angstrom
d) 1
minute
e) None
of these
3. The union of two non-collinear rays
which have a common endpoint is called the ________
a) Angle
b) Radian
c) Degree
d) Minute
e) Second
4.
One degree is denoted by
__________
a) 1 rad
b) 1’
c) 1”
d) 1o
e) None
of these
5.
1rt. angle = __________
a) 90o
b) 180o
c) 270o
d) 190o
e) None
of these
6.
The 60th part of one
degree is called one ____________
a) centimeter
b) radian
c) degree
d) minute
e) none
of these
7. Measure of the central angle of an are
of a circle whose length is equal to the radius
of the circle is known as _________
a) 1
degree
b) 1
radian
c) 1 rt.
angle
d) All
of these
e) None
of these
8.
The circumference of a circle r is
considered as __________
a) 2
r
b) r
c) 3r
d) 4r
e) None
of these
9.
1 radian = __________
a) 
b) 47o
c) 37o
d) 38o
e) None of these
10.
1o = _________
a) 
b) 
c) 
d) 
e) None of these
11.
In the given figure if C is the
center of the circle, then angle 
is ________
a) 2a
b) a + b
c) a + b
+ c
d) 2- a
e) 2b –
2c
12.
The 60th part of one
minute is called one ________
a) centimeter
b) radian
c) degree
d) minute
e) second
13.
180o = ________
a) radian
b) 2 radian
c) 
d) 
e) None of these
14. An arc PQ is subtends and angle 60o at the
center of a circle of radius 1 cm. The length PQ is ________
a) 60 cm
b) 30 cm
c) 
cm
d) 
cm
e) 
cm
15.
One second is denoted by _______
a) 1 rad
b) 
c) 
d) 
e) None
of these
16.
= __________
a) 30o
b) 60o
c) 90o
d) 220o
e) None
of these
17.
If 
is ___________
a) 
b) 
c) 
d) 
e) 
18.
In the given figure the angle is __________
a) 
b) 
c) 
d) a + b + c
e) 2d – 2b
19.
________
a) 60o
b)
c) 
d) 3600o
e) None
of these
20. What is the length of an arc of a circle
of radius 5cm, whose central angle is of 140o ________
a) 2.443
radians
b) 1.443
radians
c) 0.443
radians
d) 2
radians
e) None
of these
21.
In the given figure the angle a + b
+ c is __________
a) <
BDC =
b) 
c) 
d) 
e) <
B
22.
Two right angles are the angle of
measure _________
a) 
b) 
c) 60o
d) 90o
e) 180o
23.
For a right angled triangle ABC as
shown in the figure we have Sin = _______
a) 
b) 
c) 
d) 
e) None of these
24.
Four right angles are the angle of measure ________
a) 90o
b) 180o
c) 270o
d) 360o
e)
25.
In the figure the area of triangle
ABC is
a) 28
b) 32
c) 96
d) 192
e) 182
26.
For a right angled triangle ABC as
shown in the figure, we have 
_______
a)
b)
c)
d) 
e) None of these
27. The system of measurement in which the
angle is measured in degrees, and its
subunits, minutes and seconds is called _________
a) Circular
system
b) Sexagesimal
system
c) MKS
system
d) CGS
system
e) None
of these
28.
a) 
b) 
c) 
d) 
e) None of these
29.
In the figure the surface area
(shaded) of right circular cylinder is
a) 
b) 
c) 
d) 
e) 
30.
The system of measurement in which
the angle is measured in radians is called _____
a) Circular
system
b) Sexagesimal
system
c) MKS
system
d) CGS
system
e) None
of these
31.
a)
b) 
c)
d)
e) None of these
32.
In the figure, the shaded area is
given by
a) 
b) 
c) 
d) 6
e) 
33.
a) 140o
b) 17o
c) 16o
d) 
e) 
34.
_______? For all values of angle.
a) 1
b) 0
c) 
d) – 1
e) None
of these
35.
In the figure the length of AB is
a) 7
b) 
c) 
d) 12
e) 13
36.
16o = ________
a) 960o
b) 
c) 
d)
e)
37.
In the figure the angle A is (AB =
AC = X)
a) 50o
b) 60o
c) 90o
d) 120o
e) 180o
38.
Two right angles are equal to
a)
b)
c) 
d) 
e) 
39.
The associated angle of 280o
is
a) 100o
b) 10o
c) 80o
d) – 80o
e) 190o
40.
Cot 180o = _________
a) 1
b) O
c) – 1
d) ∞
e) – 11
41. A radian is the measure of the central
angle of an arc of a circle whose length is equal to the
a) half
of radius of the circle
b) diameter
of the circle
c) radius
of the circle
d) one
third of radius of the circle
e) none
of these
42.
Sec 180o = _________
a) 1
b) 0
c) – 1
d) ∞
e) None
of these
43.
In the ΔABC the angle α is
a) 30o
b) 45o
c) 60o
d) 90o
e) 180o
44. The central angle of an arc of a circle
whose length is equal to the radius of the circle is called the
a) degree
b) radian
c) minute
d) second
e) none
of these
45.
In the 
ABC the angle 
is
a) 30o
b) 45o
c) 45o
d) 90o
e) 120o
46. Cosec 180o =________?
a) 1
b) 0
c) -1
d) 
e) 2
47. if r is the radius, m < AOB =
a) 1
radian
b) 1
degree
c) 1
minute
d) 1
second
e) None
of these
48. In the figure the angle 
is
a) 45o
b) 60o
c) 75o
d) 90o
e) – 90o
49. One minute is denoted by
a) 1rad
b) 
c) 
d) 1o
e) None
of these
50. Cos 270o =___?
a) 1
b) 0
c) -1
d)
e) 0 – 2
51. The area of the shaded portion in the
figure is
a) 
b) 
c) 
d) 
e) - 2
52 Tan 270o = _______?
a) 1
b) 0
c) -1
d)
e) 
53 1o =
a) 1
radian
b) 0.01745
radian
c) 0.5
radian
d) 2.5
radian
e) 1.01745
radian
54 Tan 30o = ______?
a) 
b)
c)
d) 
e) 
55 If an arc of length I of circle of radius r
subtends an
angle 0 radian at the center, then l =
a) 
b) 
c) 
d) 
e) None
of these
56 In the figure the angle is
a) 60o
b) 120o
c) 180o
d) 240o
e) 290o
57
In the first quadrant 
is _________
a) positive
b) negative
c) both
d) not
defined
e) none
of these
58
In the figure the length of LM is
a) x
b) 2x
c) 3x
d) 4x
e) 8
59.
Convert 
to radians
a) 0.94
radians
b) 1
radians
c) 3.97
radians
d) 4.57
radians
e) 3.54
radians
60.
1o = ________
a) 
radians
b) 
radians
c) 
radians
d) 
radians
e) radians
61
a) radians
b) radians
c) 
radians
d) radians
e) radians
62.
Convert radian measure 
to degree
a) 24.32o
b) 24.97o
c) 4.96o
d) 1.97o
e) 23.42o
63.
_______
a) 
b) 
c) 
d) 
e) 
64.
radians =
a) 360o
b) 335o
c) 270o
d) 225o
e) 125o
65. The radian measure of the angle at the
center of circle of radius 12cm which cuts off an arc 18cm long.
a) 9.47
radians
b) 1.19
radians
c) 1.5
radians
d) 2.5
radians
e) None
of these
66.
150o =
a) 
radians
b) 
radians
c) radians
d) radians
e) radians
67. The length of the arc cut off on a circle
of radius 6cm by a central angle of radians
a) 12.566cm
b) 10.033cm
c) 12.113cm
d) 9.156cm
e) 6.56cm
68.
80o =
a) radians
b) 
radians
c) radians
d) radians
e) radians
69.
The radius of the circle when l =
3cm, = 3.4 radians.
a) 0.214
cm
b) 9.419
cm
c) 3.146
cm
d) 4.978
cm
e) None
of these
70.
In one hour, the minutes hand of a
clock turns through
a) radians
b) radians
c) radians
d) radians
e) 2 radians
71.
In the second quadrant is ________
a) positive
b) negative
c) both
d) not
defined
e) none
of these
72.
In one hour, the hours hand of a
clock turns through
a) 
radians
b) radians
c) radians
d) radians
e) 2 radians
73.
If the measure of two angles of a
ΔABC is 30o and 70o then the 3rd angle is
a) 30o
b) 70o
c) 80o
d) 100o
e) 210o
74.
In one hour, the minutes hand of a
clock turns through
a) 360o
b) 180o
c) 90o
d) 60o
e) 30o
75.
a) base
b) hypotenuse
c) cos
d) tan
e) none of these
76.
In 15 minutes, the minutes hand of a
clock turns through
a) 360o
b) 180o
c) 90o
d) 60o
e) 30o
77.
a) sin
b) tan
c) cos
d) sec
e) none of these
78.
In the 2nd quadrant Sec is ________?
a) positive
b) negative
c) both
d) not
defined
e) – 1
79.
In the 2nd quadrant Cot is _______ ?
a) positive
b) negative
c) both
d) not
defined
e) <
1
80.
In 15 minutes the hours hand of a
clock turns through
a) 7.5o
b) 15o
c) 30o
d) 60o
e) 120o
81. The radian measure of the central angle of
an arc 50cm log on a circle of radius 25m is
a) 3
b) 2
c) 1
d) 0.5
e) None
of these
82.
In the 3rd quadrant Sin is _______ ?
a) positive
b) negative
c) both
d) not
defined
e) >
0
83.
Two cities whose longitudes are 30oE
and 40oW on the equator are apart
a) 1000
km
b) 2000
km
c) 2500
km
d) 3351
km
e) 7819.09
km
84.
a) cot
b) tan
c) sin
d) sec2
e) 1 – sin
85.
Two cities whose longitudes are 10oE
and 20oW on the equator are apart.
a) 1000
km
b) 2000
km
c) 2500
km
d) 3351
km
e) 6702
km
86.
In the 3rd quadrant Cosec is _________ ?
a) positive
b) negative
c) both
d) 0
e) None
of these
87. A railway train is running on a circular
track of radius 500 meters at the rate of 30 km per hour, it will turn in 10
seconds through an angle.
a) 
b) 
c) 
d) 30o
e) 60o
88. The pendulum of a clock is 30 cm long and
it swings through an angle of 30o each second. How far does the tip of the pendulum move in 1 second.
a) 10 cm
b) 15.71
cm
c) 20.94
cm
d) 28.65
cm
e) 40 cm
89. A railway train is running on a circular
track of radius 1000 meters at the rate of 30 km per hour, it will turn in 10
seconds through an angle
a)
b)
c)
d) 30o
e) 60o
90. The pendulum of a clock is 40cm long and
it swings through an angle of 30o each
second. How far does the tip of
the pendulum move in 1 seconds?
a) 10cm
b) 15.71cm
c) 20.94cm
d) 28.65cm
e) 40cm
91. In the fourth quadrant Cosec is _________ ?
a) positive
b) negative
c) both
d) 0
e) None
of these
92. A circular wire of radius 2cm is cut
straightened and then bent so as to lie along the circumference of a hoop of
radius 24cm. the measure of the angle subtended at the center of the hoop is
a) 15o
b) 30o
c) 25o
d) 60o
e) 90o
93.
sec2 - tan2 = _______
a) – 1
b) cosec
c) tan
d) 1
e) – 11
94. The area of a sector of a circular region
of radius r and the central angle of the sector radians is
a) 
b) 
c) 
d) 
e) 
95. The area of a sector with a central angle
of 1 radian in a circular region whose radius is 2m.
a) 2m2
b) 1m2
c) 0.5m2
d) m2
e) m2
96. The area of a sector with a central angle
of 0.5 radians in a circular region whose radius is 2m is
a) m2
b) m2
c) m2
d) 2m2
e) 1m2
97. An arc AB of length 5cm is marked on a
circle of radius 3cm. the area of the sector bounded by this arc and the radii
from A and B is
a) 7.5
cm2
b) 7.5 m2
c) 75 m2
d) 75 cm2
e) None
of these
98.
_________
a) 
b)
c) 2
d) 0
e) 1
99.
In which quadrant does the terminal
side lie if
sin > 0 and tan _______ ?
a) 1st
b) 2nd
c) 3rd
d) 4th
e) None
of these
100.
sec2 =
a) 1 –
cos2
b) 1 –
tan2
c) 1 +
tan2
d) 1 –
cot2
e) 1 +
cot2
101.
_______ ?
a) 1
b) 0
c) – 1
d) 11
e) None
of these
102.
_______ ?
a) 1
b) 0
c) – 1
d) 10
e) None
of these
103.
_______ ?
a) 1
b) 0
c) – 1
d) 10
e) None
of these
104.
Cosec2 - Cot2 = _______ ?
a) 1
b) 0
c) – 1
d) Tan2
e) Sec2
105.
Cos22 = _______ ?
a) 1 –
sin2
b) 1 +
sin2
c) 1 –
sin22
d) 1 -
sin
e) 1 +
sin
106.
1 + cot22 = _________ ?
a) sec2
b) cosec2
c) cosec22
d) sec2
e) none
of these
Chapter
No. 9
Fundamentals
of Trigonometry
1.
Answer: c
2. Answer: b
3. Answer: a
4.
Answer: d
5.
Answer: a
6.
Answer: d
7. Answer: b
8.
Answer: a
9.
Answer: a
10.
Answer: a
11.
Answer: a
12.
Answer: e
13.
Answer: a
14. Answer: d
15.
Answer: c
16.
Answer: e
17.
Answer: c
18.
Answer: c
19.
Answer: b
20. Answer: a
21.
Answer: c
22.
Answer: e
23.
Answer: a
24.
Answer: d
25.
Answer: c
26.
Answer: a
27. Answer: b
28.
Answer: b
29.
Answer: a
30.
Answer: a
31.
Answer: d
32.
Answer: a
33.
Answer: e
34. Answer: a
35.
Answer: a
36.
Answer: b
37.
Answer: b
38.
Answer: e
39.
Answer: c
40.
Answer: d
41. Answer: c
42.
Answer: c
43.
Answer: c
44. Answer: b
45.
Answer: a
46. Answer: d
47. Answer: a
48. Answer: d
49. Answer: b
50. Answer: b
51. Answer: a
52 Answer: d
53 Answer: b
54
Answer: a
55
Answer: d
56 Answer: b
57
Answer: a
58
Answer: a
59.
Answer: b
60.
Answer: a
61
Answer: c
62.
Answer: a
63.
Answer: b
64.
Answer: d
65. Answer: c
66.
Answer: a
67. Answer: a
68.
Answer: b
69.
Answer: e
70.
Answer: e
71.
Answer: a
72.
Answer: c
73.
Answer: c
74.
Answer: a
75.
Answer: b
76.
Answer: c
77.
Answer: e
78.
Answer: b
79.
Answer: b
80.
Answer: a
81. Answer: b
82.
Answer: b
83.
Answer: e
84.
Answer: c
85.
Answer: d
86.
Answer: b
87. Answer: b
88. Answer: b
89. Answer: a
90. Answer: d
91. Answer: b
92. Answer: b
93.
Answer: d
94. Answer: b
95. Answer: a
96. Answer: e
97. Answer: a
98.
Answer: e
99.
Answer: a
100.
Answer: c
101.
Answer: a
102.
Answer: b
103.
Answer: c
104.
Answer: a
105.
Answer: c
106.
Answer: c
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