Question : A polygon has 54 diagonals. The number of sides in the polygon is:
Option 1: 7
Option 2: 9
Option 3: 12
Option 4: 15
Correct Answer: 12
Solution : Let the number of sides be $n$. Then, number of diagonals of the polygon = $\frac{n(n-3)}{2}$ So, $\frac{n(n-3)}{2}=54$ ⇒ $n^2-3n=108$ ⇒ $n^2-3n-108=0$ ⇒ $(n-12)(n+9)=0$ ⇒ $n$ =12, the negative value is rejected. Hence, the correct answer is 12.
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Question : Each interior angle of a regular polygon is $18^{\circ}$ more than eight times an exterior angle. The number of sides of the polygon is:
Option 1: 10
Option 2: 15
Option 3: 20
Option 4: 25
Question : The diagonals of two squares are in the ratio of 3 : 7. What is the ratio of their areas?
Option 1: 3 : 7
Option 2: 9 : 49
Option 3: 4 : 7
Option 4: 7 : 3
Question : The value of $9\times [(9 - 4) \div{\{(8 \div 8\ \text{of}\ 4) +(4 \div 4 \ \text{of}\ 2)}\}]$ is:
Option 1: $20$
Option 2: $60$
Option 3: $\frac{15}{4}$
Option 4: $\frac{15}{2}$
Question : Directions: A series of figures are given which can be grouped into classes. Select from the alternatives one set of groups into which the figures can be classified.
Option 1: 1, 3, 6; 2, 4, 6; 5, 7, 9
Option 2: 1, 4, 9; 3, 6, 8; 2, 5, 7
Option 3: 3, 4, 7; 9, 8, 7; 4, 3, 1
Option 4: 2, 3, 6; 9, 3, 4; 6, 3, 2
Question : Directions: If 72 A 7 B 9 = 16, and 52 A 5 B 7 = 12, then 92 A 3 B 8 = ?
Option 1: 17
Option 2: 92
Option 3: 86
Option 4: 35
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