41. In an equilateral Δ ABC, if AD ⊥ BC, then which option is true?

1. 1. 3AB² = 2AD²

   
   
   

   2. 2AB² = 3AD²

   
   
   

   3. 3AB² = 4AD²

   
   
   

   4. 4AB² = 3AD²

   
   
   

   5. none of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Lat AB = BC = AC = a
   AB² = AD² + BD² (Pythagoras Theorem)
   

   
   

   Correct Option: C

   Lat AB = BC = AC = a
   AB² = AD² + BD² (Pythagoras Theorem)
   

   a2 = AD2 +	a2
   	4

   
   

   3a2	= AD2
   4

   
   

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42. In the given figure, AB || DC, find the value of x.
    
    
    

1. 1. x = 8

   
   
   

   2. x = 9

   
   
   

   3. x = 8 or 9

   
   
   

   4. x = 10

   
   
   

   5. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   As we know the diagonals of a trapezium divide each other proportionally
   

   ∴	AO	=	BO
   	OC		OD

   
   

   Correct Option: C

   As we know the diagonals of a trapezium divide each other proportionally
   

   ∴	AO	=	BO
   	OC		OD

   
   

   3x - 19	=	x - 3
   x - 5		3

   
   ⇒ 3(3x - 19) = ( x - 3 ) ( x - 5 )
   ⇒ 9x - 57 = x² - 8x +15
   ⇒ x² - 17x + 72 = 0
   ⇒ x = 8 or x = 9

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43. In the adjoining figure ∠A + ∠B + ∠C + ∠D + ∠E + ∠F = ?
    
    
    

1. 1. 270°

   
   
   

   2. 300°

   
   
   

   3. 360°

   
   
   

   4. 330°

   
   
   

   5. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   In ΔACE
   ∠A + ∠C + ∠E = 180°
   Similarly in ΔDFB
   ∠D + ∠F + ∠B = 180°
   

   Correct Option: C

   In ΔACE
   ∠A + ∠C + ∠E = 180°
   Similarly in ΔDFB
   ∠D + ∠F + ∠B = 180°
   ∴ (∠A + ∠C + ∠E) + (∠D + ∠F + ∠B) = 360°
   ∠A + ∠B + ∠C + ∠D + ∠E + ∠F = 360°

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44. In ΔABC, the angle bisectors of ∠B and ∠C meet at O. If ∠A = 70°, then ∠BOC is equal to:
    
    
    

1. 1. 135°

   
   
   

   2. 125°

   
   
   

   3. 115°

   
   
   

   4. 110°

   
   
   

   5. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   As we know the formula,
   

   ∠BOC = 90° +	1	∠A
   	2

   
   

   Correct Option: B

   As we know the formula,
   

   ∠BOC = 90° +	1	∠A
   	2

   
   

   ∴∠BOC = 90° +	1	(70°) = 90° + 35°
   	2

   
   ∠BOC = 125°

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45. The complement of an angle exceeds the angle by 60°. Then the angle is equal to:

1. 1. 25°

   
   
   

   2. 30°

   
   
   

   3. 15°

   
   
   

   4. 35°

   
   
   

   5. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let, the angle be A
   ⇒ Its complement angle = 90° – A
   According to the question
   (90 – A) = A + 60°
   

   Correct Option: C

   Let, the angle be A
   ⇒ Its complement angle = 90° – A
   According to the question
   (90 – A) = A + 60°
   ⇒ 90 - 60 = A + A
   ⇒ 2A = 30°
   ⇒ A = 15°

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