Question : PM and PN are two tangents of a circle from an external point P. M and N are points on the circle. If PM = y2 – 9 and PN = 55, then what is the value of y?
Option 1: 64
Option 2: 17
Option 3: 8
Option 4: 12
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Correct Answer: 8
Solution : PM and PN are two tangents of a circle from an external point P. Given: PM = $\text{y}^2$ – 9 and PN = 55 Tangents are equal in length if drawn from an outside point on the circle. According to the concept, PM = PN ⇒ $\text{y}^2$ – 9 = 55 ⇒ $\text{y}^2$ = 64 $\therefore$ y = 8 Hence, the correct answer is 8.
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Question : What is the expansion of (a - 4)3?
Option 1: a3 – 12a2 + 48a + 64
Option 2: a3 + 12a2 + 48a + 64
Option 3: a3 –12a2 + 48a – 64
Option 4: a3 +12a2 + 48a – 64
Question : A is a point outside of a circle with centre O. AP and AQ are two tangents of the circle. If AP = a2 + 14 and AQ = 239, then what is the value of a?
Option 1: 22
Option 2: 13
Option 3: 15
Option 4: 14
Question : If (x – 8)2 – (x + 8)2 = 0. What is the value of x?
Option 1: 1
Option 2: 32
Option 3: 0
Option 4: –32
Question : If a + b + c = 0, then the value of (a + b – c)2 + ( b + c – a)2 + ( c + a – b)2 is:
Option 1: 0
Option 2: 8abc
Option 3: 4(a2 + b2 + c2)
Option 4: 4(ab + bc + ca)
Question : What is the value of (a + b)3 – a3 – b3?
Option 1: – 3ab(a – b)
Option 2: 3ab(a + b)
Option 3: – 3ab(a + b)
Option 4: 3ab(a – b)
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