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Q1) External angle of a regular polygon is 72°. Find the sum of all the interior angles of it.

1) 360°
2) 720°
3) 540°
4) 648°

Sides = 360°/72° = 5
Sum of all the interior angles = 5×(180 - 72) = 540°
Hence, option 3.

Q2) The ratio of the numbers of sides of two regular polygons is 1:2. If each interior angle of the first polygon is 120° then the measure of each interior angle of the second polygon is

1) 160°
2) 150°
3) 140°
4) 135°

Number of sides of first polygon =
Number of sides of first polygon = 12
Exterior angle of second polygon = 360°/12 = 30°
Interior angle of second polygon = 180° - 30° = 150°
Hence, option 2.

Q3) If the diagonals of a quadrilateral are equal and bisect each other at right angles, then the quadrilateral is a

1) Rectangle
2) Square
3) Rhombus
4)Trapezium

As diagonals are equal and bisect each other at right angles so the quadrilateral is a square.
Hence, option 2.

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Q4) A quadrilateral ABCD is inscribed in a circle. If AB is parallel to CD and AC=BD, then the quadrilateral must be a

1) Trapezium
2) Parallelogram
3) Rhombus
4) None of these

Quadrilateral must be a trapezium because a quadrilateral where only one pair of opposite sides are parallel is a trapezium.
Hence, option 1.

Q5) Let X be any point within a square ABCD. On AX, a square AXYZ is described such that D is within it. Which one of the following is correct?

1) AX = DZ
2) ∠ADZ = ∠BAX
3) AD = DZ
4) BX = DZ

In ∆ ABX and ∆ ACZ
AB = AD (Side of square ABCD)
AX = AZ (Side of a square AXYZ)
∠BAX = θ; ∠XAD = 90° - θ
As AXYZ is a square.
∠ZAX = 90°
∠ZAD + ∠XAD = 90°
ZAD = 90° - (90° - θ) = θ
∠BAX = ∠ZAD
∆ ABX≅∆ ADZ
BX = DZ
Hence, option 4.

Q6) Consider the following statements:
A) The perpendicular bisector of a chord of a circle does not pass through the center of the circle.
B) The angle in a semi-circle is a right angle.
Which of the statements given above is/are correct.

1) Only A
2) Only B
3) Both A and B
4) Neither A nor B

The perpendicular bisector of a chord of a circle always pass through the center. So, statement A is wrong.
Statement B is correct.
Hence, option 2.

Q7) Each of the two circles of same radius a pass through the center of the other. If the circles cut each other at the points A, B and O, O’ be their centers, then the area of the quadrilateral AOBO’ is

1) a2/4
2) a2/2
3) 0.866a2
4) a2

Area of quadrilateral AOBO’ = Area of ∆ AOO' + Area of ∆ BOO'
AO = OO' = AO' = a
So, AOO’ is an equilateral triangle. Similarly, BOO’ is an equilateral triangle.
Area of quadrilateral AOBO’ is

Hence, option 3.

Q8) A quadrilateral ABCD is inscribed in a circle. If AB is parallel to CD and AC=BD, then the quadrilateral must be a

1) Trapezium
2) Parallelogram
3) Rhombus
4) None of these

Quadrilateral must be a trapezium because a quadrilateral where only one pair of opposite sides are parallel is a trapezium.
Hence, option 1.