Question

How many of the following letters have rotational symmetry of order more than one?
R, B, F, H, O, P, S, W, X, Z, N
(a) 4
(b) 9
(c) 5
(d) 8

Answer 1

Hint: In this question, we will use the concept of order of rotation to find the order of rotation of each letter.That order of rotation will be considered where the letters have a symmetry.

Complete step-by-step answer:
When an object is rotated, clockwise or anti clockwise, and for the same angle of rotation such that, after rotation it looks exactly same as in its original position, then we say that objects have rotational symmetry, also order of rotation is the number of times, object will look exactly the same for angles less than${{360}^{\circ }}$ or equal to ${{360}^{\circ }}$. Now any object, when rotated ${{360}^{\circ }}$will look the same as in its original position. Hence the order of rotation of rotation of all objects is either 1 or more than 1.
Here, for given letters, we have,
R has order of rotation 1, as for no angel it will be exactly the same but for only ${{360}^{\circ }}$.
B has order of rotation 1, as for no angel other than ${{360}^{\circ }}$ it will be exactly the same.
F has order of rotation 1, as for no angle other than ${{360}^{\circ }}$, it will be exactly the same.
H will have a rotation of 2, as for ${{180}^{\circ }}$ and ${{360}^{\circ }}$, it will look exactly the same.
P will have order of rotation 1, as for no angle other than ${{360}^{\circ }}$, it will look exactly the same.
S will have a rotation of 2, as for angel ${{180}^{\circ }}$ and ${{360}^{\circ }}$, it will look exactly the same.
We will have rotation of 1, as for an angel other than ${{360}^{\circ }}$, it will look exactly the same.
X will have a rotation of 4. As for angels ${{90}^{\circ }}$, ${{180}^{\circ }}$, ${{270}^{\circ }}$and ${{360}^{\circ }}$, it will look exactly same.
Z will have order of symmetry 1, as for no angle other than ${{360}^{\circ }}$, it will look exactly same
N will have order of symmetry 2, as for ${{180}^{\circ }}$ and ${{360}^{\circ }}$, it will look exactly the same.
Hence for 5 letters, the order of rotation is more than 1.
Therefore, the correct option is (c).

Note: In this type of question, when we are to find order of rotation for letters, we just need to check 4 angles, which are ${{90}^{\circ }}$, ${{180}^{\circ }}$, ${{270}^{\circ }}$ and ${{360}^{\circ }}$.