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EXERCISE 9.1
MULTIPLE CHOICE QUESTIONS
1. The common end point of two rays is called:
(A) Radian (B) Degree (C) Vertex (D) None of these
2. The vertex of an angle in standard form is at:
(A) (1,0) (B) (0,1) (C) (1,1) (D) (0,0)
°
3. 𝜃 is measured in :
(A) Circular System (B) Sexagesimal System
(C) Radian measure (D) Rotation Measure
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4. rotation anti-clockwise equals:
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(A) 45° (B) 90° (C) 180° (D) 360°
5. One degree is equal to:
180 𝜋
(A) (B) radian (C) 𝜋 radian (D) 180°
𝜋 180
6. 1° is equal to:
(A) 0.1745 Radians (B) 1.1745 Radians
(C) 0.01745 Radians (D) 0.010745 Radians
7. 1° Equals:
𝜋 180 𝜋 𝜋
(A) 180 (B) 𝜋
(C) 90 (D) 360
8. Angle of 30 degrees is equal to:
𝜋 𝜋
(A) radian (B) radian
3 30
𝜋 𝜋
(C) 6
radian (D) 4 radian
9. If a length of arc is equal to the radius of the circle, then angle subtended at the center of the circle
is equal to:
(A) One degree (B) One radian
°
(C) 180 (D) 𝜋 radians
10. One radian is equal to:
(A) 45° (B) 50° (C) 60° (D) 57.296°
11. One radian is equal to:
(A) 57.296° (B) 57° (C) 56° (D) 0175°
12. 𝜋 radians =:
(A) 180° (B) 180′ (C) 360° (D) 360′
13. Which one is true:
(A) 1 radian < 1° (B) 1 radian > 1°
(C) 1 radian = 1° (D) 5 radian = 2°
14. 3 radians is equal to in degrees:
(A) 169.78 (B) 171.888 (C) 170.889 (D) 171.5
5𝜋
15. 4
rad =:
(A) 360° (B) 335° (C) 270° (D) 225°
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2𝜋
16. 3
radian equals =:
(A) 120° (B) 150° (C) 270° (D) 190°
17. In one hour , the hour hand clock of a clock turns through
𝜋 𝜋
(A) 2 radians (B) 3 radians
𝜋 𝜋
(C) radians (D) radians
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18. Arc length of a circle of radius r, central angle 𝜃 rad is:
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(A) 2 𝑟 2 𝜃 (B) 𝜋𝑟 2 (C) 2𝜋𝑟 (D) 𝑟𝜃
19. An arc length of 8 cms, subtends an angle of 1 radian at the centre of a circle. Its radius is:
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(A) 4cm (B) 8cm (C) cm (D) None of these
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20. If 𝑙 = 35 𝑐𝑚 and 𝜃 = 1 𝑟𝑎𝑑, then 𝑟 =:
(A) 35° (B) 35 𝑐𝑚 (C) 35 𝑟𝑎𝑑 (D) 35 𝑚

SHORT QUESTIONS
(i) Define angle in the standard position with figure.
(ii) Define angle and angle in standard position.
(iii) What is the sexagesimal system of angles?
(iv) Convert the angle 21.256° to the 𝐷 ° 𝑀′ 𝑆 ′′ (𝑑𝑒𝑔𝑟𝑒𝑒, 𝑚𝑖𝑛𝑢𝑡𝑒, 𝑠𝑒𝑐𝑜𝑛𝑑) form.
(v) Convert 21.56° to the 𝐷 ° 𝑀′ 𝑆 ′′
(vi) Define radian.
(vii) Prove that 1 radian=57.3°
1 °
(viii) Convert (22 2) to radians using 𝜋 = 3.1416.
(ix) Convert 54° 45′ into radians.
(x) Convert 150° into radians.
(xi) Convert 75° 6′ 30′′ to radians.
(xii) Convert 154° 20′′ to radian measure.
2𝜋
(xiii) Convert the angle 3
radians into degrees.
2𝜋
(xiv) Convert the 3
radians into degrees.
25𝜋
(xv) Convert into the measure of sexagesimal system.
36
19𝜋
(xvi) Express 32 into the measure of sexagesimal system.
°
(xvii) An arc subtends an angle of 70 at the center of circle and its length is 132 m. Find the radius of the
circle.
(xviii) Find 𝑙 when 𝜃 = 𝜋 radian, r = 6cm.
(xix) Find the length ‘𝑙’ if𝜃 = 65° 20′ , r=18 mm.
(xx) Find the ‘𝑙’ if 𝜃 = 65° 20′ , r=18 mm.
(xxi) Find 𝜃, if 𝑙 = 1.5 cm and r=2.5 cm.
(xxii) Find 𝜃 when 𝑙 = 1.5 cm and r=2.5 cm.
(xxiii) Find r when 𝑙 =56cm, 𝜃 = 45° .
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(xxiv) Find r when 𝜃 = 45° , 𝑙 =56cm.

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(xxv) Using usual notations find “r” when 𝜆 = 5 𝑐𝑚, 𝜃 = radians
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(xxvi) What is the length of arc intercepted on a circle of radius 14cm by the arms of a central angle of
45° ?
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(xxvii) Show that the area of sector of a circular region radius ‘r’ is 2 𝑟 2 𝜃 where 𝜃 is central angle of the
sector.

LONG QUESTIONS
a) What is the length of arc intercepted on a circle of radius 14cm by the arms of a central angle of
45° ?
b) A railway train is running on a circular track of radius 500 meters at the rate of 30 km per hour.
Through what angle will it turn in 10 sec?
c) If 𝑙 is the arc length of a circle , central angle of an arc is 𝜃 radian and 𝑟 is radius of a circle, then
prove that 𝑙 = 𝑟𝜃.