Symmetry

Q1: Assertion (A): The order of rotational symmetry in the given figure is 2.
Reason (R): Each figure has a rotational symmetry of order 1.

Step 1: Analyzing Assertion (A):
The given figure consists of a central geometric pattern between two bars. If we rotate the figure by 180°, it coincides with its original position exactly. Since it maps onto itself at 180° and 360°, the order of rotational symmetry is 2. Thus, Assertion (A) is True.
Step 2: Analyzing Reason (R):
By definition, every figure matches itself after a full rotation of 360°. Therefore, every figure has a rotational symmetry of order at least 1. Thus, Reason (R) is a True statement in general geometry.
Answer: a. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Q2: Assertion (A): The minimum angle by which a regular hexagon has to be rotated so as to coincide with its original position for first time is 60°.
Reason (R): A figure that possesses a point symmetry attains its original form upon being rotated through 120°.

Assertion (A)

Step 1: A regular hexagon has 6 equal sides and 6 equal angles.
Step 2: The angle of rotation for a regular polygon is given by:
Minimum angle of rotation = 360° ÷ number of sides
Step 3: For a regular hexagon,
Minimum angle of rotation = 360° ÷ 6 = 60°
Step 4: Hence, the Assertion (A) is TRUE.

Reason (R)

Step 1: A figure possessing point symmetry coincides with itself after a rotation of 180°.
Step 2: Rotation through 120° is not a general condition for point symmetry.
Step 3: Therefore, the given Reason (R) is FALSE.
Answer: c. Assertion (A) is true but Reason (R) is false.