36. What is the angle in radian through which a pendulum swings and its length is 75 cm and the tip describes an arc of length 21 cm.

1. 1. 	3		R
      	25

   
   
   

   2. 	7		R
      	25

   
   
   

   3. 	4		R
      	21

      
      

   
   
   

   4. 	2		R
      	15

   
   
   

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1. View Hint View Answer Discuss in Forum

   We know that,
   

   Angle =	arc
   	radius

   
   

   ⇒ θ =	21
   	75

   
   

   θ =		7		R
   		25

   
   

   Correct Option: B

   We know that,
   

   Angle =	arc
   	radius

   
   

   ⇒ θ =	21
   	75

   
   

   θ =		7		R
   		25

   
   

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37. What will be the radius of circle in which a central angle of 60° intercepts an arc of length 37.4 cm.
    

1. 1. 35 cm
      

   
   
   

   2. 34.7 cm
      

   
   
   

   3. 35.7 cm
      

   
   
   

   4. 40 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here,
   
   θ = 60°
   l = 37.4 cm
   r = ?
   We know that,
   

   1° =		π		R
   		180°

   
   

   ⇒ 60° =		π	× 60		R
   		180°

   
   

   ⇒ 60° =		π		R
   		3

   
   We know that,
   

   θ =	l
   	r

   
   

   ⇒	π	=	37.4
   	3		4

   
   

   ⇒ r =	37.4 × 3
   	π

   
   

   r =	37.4 × 3 × 7
   	22

   
   = 1.7 × 21 = 35.7 cm

   Correct Option: C

   Here,
   
   θ = 60°
   l = 37.4 cm
   r = ?
   We know that,
   

   1° =		π		R
   		180°

   
   

   ⇒ 60° =		π	× 60		R
   		180°

   
   

   ⇒ 60° =		π		R
   		3

   
   We know that,
   

   θ =	l
   	r

   
   

   ⇒	π	=	37.4
   	3		4

   
   

   ⇒ r =	37.4 × 3
   	π

   
   

   r =	37.4 × 3 × 7
   	22

   
   = 1.7 × 21 = 35.7 cm

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38. What is the value of cosec (–1410°) ?
    

1. 1. 2
      √3

   
   
   

   2. 2

   
   
   

   3. √3
      2

   
   
   

   4. 2
      √3

   
   
   

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1. View Hint View Answer Discuss in Forum

   cosec (–1410°) = – cosec (1410°)
   ∵cosec (– θ)
   = – cosecθ = –cosec (360° × 3 + 330°)
   = –cosec (330°) = –cosec (360° – 30°)
   = cosec 30°
   = 2

   Correct Option: B

   cosec (–1410°) = – cosec (1410°)
   ∵cosec (– θ)
   = – cosecθ = –cosec (360° × 3 + 330°)
   = –cosec (330°) = –cosec (360° – 30°)
   = cosec 30°
   = 2

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39. The value of cos		π	+ x		+ cos			π	- x		will be
    		4						4

1. 1. √2sinx
      

   
   
   

   2. √2cosx

   
   
   

   3. √2cosecx
      

   
   
   

   4. √2tanx

   
   
   

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1. View Hint View Answer Discuss in Forum

   cos		π	+ x		+ cos			π	- x
   		4						4

   
   

   = 2cos

   π

   + x -

   π

   - x

   cos

   π

   + x -

   π

   + x

   4

   4

   4

   4

   2

   2

   
   ∵ cosC + cosD
   

   = 2cos		C + D		cos			C - D
   		2					2

   
   

   = 2cos		π		cosx
   		4

   
   

   =	2	.cosx
   	√2

   
   = √2cosx

   Correct Option: B

   cos		π	+ x		+ cos			π	- x
   		4						4

   
   

   = 2cos

   π

   + x -

   π

   - x

   cos

   π

   + x -

   π

   + x

   4

   4

   4

   4

   2

   2

   
   ∵ cosC + cosD
   

   = 2cos		C + D		cos			C - D
   		2					2

   
   

   = 2cos		π		cosx
   		4

   
   

   =	2	.cosx
   	√2

   
   = √2cosx

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40. If cosq = – 1/2 and θ lies in third quadrant, then what will be the value of sinθ + tanθ
    

1. 1. 1
      2

      
      

   
   
   

   2. 2
      √3

   
   
   

   3. √3
      2

   
   
   

   4. 1
      √3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here, cosθ = – 1/2 and θ, lies in third quadrant
   
   Consider ∆ABC,
   Using Pythagoras theorem,
   AC² = AB² + BC²
   2² = (–1)² + BC²
   ⇒ BC² = 4 – 1
   BC² = 3
   BC = √3
   

   tanθ + sinθ = –		√3		+ -			√3
   		- 1					2

   
   ∵ In third quadrant sinθ is negative and tanθ is positive.
   =

   =	√3
   	2

   Correct Option: C

   Here, cosθ = – 1/2 and θ, lies in third quadrant
   
   Consider ∆ABC,
   Using Pythagoras theorem,
   AC² = AB² + BC²
   2² = (–1)² + BC²
   ⇒ BC² = 4 – 1
   BC² = 3
   BC = √3
   

   tanθ + sinθ = –		√3		+ -			√3
   		- 1					2

   
   ∵ In third quadrant sinθ is negative and tanθ is positive.
   =

   =	√3
   	2

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