171. What is the measure of central angle of the arc whose length is 11 cm and radius of the circle is 14 cm?

1. 1. 45°

   
   
   

   2. 60°

   
   
   

   3. 75°

   
   
   

   4. 90°
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   θ=	l	radian
   	r

   
   

   =	11	radian
   	14

   
   ∵ π radian = 180°
   

   ∴ 1 radian =	180°
   	π

   
   
   

   =	180 × 11 × 7	= 45°
   	22 × 14

   
   

   Correct Option: A

   θ=	l	radian
   	r

   
   

   =	11	radian
   	14

   
   ∵ π radian = 180°
   

   ∴ 1 radian =	180°
   	π

   
   
   

   =	180 × 11 × 7	= 45°
   	22 × 14

   
   

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172. If θ is an acute angle and sin (θ + 18°) = (1 / 2) , then the value of θ in circular measure is :

1. 1. 	π	radians
      	12

   
   
   

   2. 	π	radians
      	15

   
   
   

   3. 	2π	radians
      	5

   
   
   

   4. 	3π	radians
      	13

   
   
   

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1. View Hint View Answer Discuss in Forum

   sin (θ + 18°) =	1	= sin 30°
   	2

   
   ⇒ θ + 18° = 30°
   ⇒ θ = 30° – 18° = 12°
   ∵ 180° = π radian
   

   ∴ 12° =	π	× 12
   	180

   
   

   =	π	radian
   	15

   
   

   Correct Option: B

   sin (θ + 18°) =	1	= sin 30°
   	2

   
   ⇒ θ + 18° = 30°
   ⇒ θ = 30° – 18° = 12°
   ∵ 180° = π radian
   

   ∴ 12° =	π	× 12
   	180

   
   

   =	π	radian
   	15

   
   

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173. Which of the following relations is correct for 0 < θ < 90° ?

1. 1. sinθ = sin²θ

   
   
   

   2. sinθ < sin²θ

   
   
   

   3. sinθ > sin²θ

   
   
   

   4. sinθ = cosecθ

   
   
   

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1. View Hint View Answer Discuss in Forum

   For 0 < θ < 90°,
   0 < sinθ < 1
   sinθ > sin² θ
   If θ = 30°,
   

   sin θ = sin30° =	1
   	2

   
   

   sin² θ = sin² 30° =	1
   	4

   
   

   clearly,		1	>	1
   		2		4

   
   

   Correct Option: C

   For 0 < θ < 90°,
   0 < sinθ < 1
   sinθ > sin² θ
   If θ = 30°,
   

   sin θ = sin30° =	1
   	2

   
   

   sin² θ = sin² 30° =	1
   	4

   
   

   clearly,		1	>	1
   		2		4

   
   

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174. The circular measure of the included angle formed by the hour hand and minute hand of a clock at 3 p.m. will be

1. 1. 	π
      	4

   
   
   

   2. 	π
      	3

   
   
   

   3. 	5π
      	12

   
   
   

   4. 	π
      	2

   
   
   

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1. View Hint View Answer Discuss in Forum

   The hour hand of a watch traces an angle of 30° in an hour.
   ∴ Angle traced at 3 O’clock
   = 3 × 30° = 90°
   ∵ 180° = π radian
   

   ∴ 90° =	π	× 90°
   	180

   
   

   =	π	radian
   	2

   
   

   Correct Option: D

   The hour hand of a watch traces an angle of 30° in an hour.
   ∴ Angle traced at 3 O’clock
   = 3 × 30° = 90°
   ∵ 180° = π radian
   

   ∴ 90° =	π	× 90°
   	180

   
   

   =	π	radian
   	2

   
   

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175. If the sum and difference of two angles are (22 / 9) radian and 36° respectively, then the value of smaller angle in degree taking the value of π as (22 / 7) is :

1. 1. 52°

   
   
   

   2. 60°

   
   
   

   3. 56°

   
   
   

   4. 48°

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   ∵ π radian = 180°
   

   ∴		22	radian =	180	×	22
   		9		π		9

   
   

   ∴		180	×	22 × 7	= 140° ....(i)
   		22		9

   
   According to the question,
   A + B =140°
   and, A – B = 36° ....(ii)
   On adding,
   

   2A = 176° ⇒ A =	176	= 88°
   	2

   
   From equation (i),
   ∴ 88° + B = 140°
   ⇒ B = 140° – 88° = 52°

   Correct Option: A

   Using Rule 1,
   ∵ π radian = 180°
   

   ∴		22	radian =	180	×	22
   		9		π		9

   
   

   ∴		180	×	22 × 7	= 140° ....(i)
   		22		9

   
   According to the question,
   A + B =140°
   and, A – B = 36° ....(ii)
   On adding,
   

   2A = 176° ⇒ A =	176	= 88°
   	2

   
   From equation (i),
   ∴ 88° + B = 140°
   ⇒ B = 140° – 88° = 52°

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