Images of consonants of the English alphabet (capitals) are observed in a mirror. What is the number of images which do not look like their original shapes ?

Correct — option (2), 14.

Step 1 — Count the consonants.
Taking A, E, I, O and U as vowels: 26 − 5 = 21 consonants.

Step 2 — Find the consonants that look the same in a mirror.
A mirror reverses left and right, so a letter looks unchanged only if a vertical line through its middle splits it into two matching halves.
In plain capitals, those consonants are H, M, T, V, W, X, Y: 7 letters.

Step 3 — Subtract.
21 − 7 = 14.

The 14 consonants whose images look different: B, C, D, F, G, J, K, L, N, P, Q, R, S, Z.

The idea to remember: a mirror image leaves a letter unchanged only when the letter has a vertical line of symmetry.

Why the others are wrong

• (1)
  13 — 13 would need 8 consonants that look unchanged (21 − 8). But only seven consonants — H, M, T, V, W, X, Y — are symmetric about a vertical line in plain capitals.

  No eighth consonant qualifies: letters such as B, D, K and R face one way, and their mirror images face the other.

• (3)
  15 — 15 is the answer to two different counts. Over the whole alphabet, 11 capitals look the same in a mirror (A, H, I, M, O, T, U, V, W, X, Y), and 26 − 11 = 15.

  For a water image, the unchanged consonants in block form are B, C, D, H, K, X, and 21 − 6 = 15. The question asks about consonants in a mirror, which gives 14.

• (4)
  16 — 16 would need only 5 unchanged consonants (21 − 5), which leaves out two of the seven.

  H, M, T, V, W, X and Y are all symmetric about a vertical line, so all seven look the same in a mirror. Seven unchanged leaves 21 − 7 = 14 that look different.

A mirror image swaps left and right. A letter therefore looks unchanged in a mirror only when it has a vertical line of symmetry.

A water image swaps top and bottom, so a letter looks unchanged in water only when it has a horizontal line of symmetry. H, I, O and X have both lines and look the same in either.

N, S and Z look the same when turned upside down, because they have rotational symmetry, but they have no line of symmetry. Their mirror images and water images both look different.

Key facts

• Taking A, E, I, O and U as vowels, the English alphabet has 21 consonants.
• Capitals unchanged in a mirror: A, H, I, M, O, T, U, V, W, X, Y (11 letters, 7 of them consonants).
• Consonants unchanged in a mirror: H, M, T, V, W, X, Y; the other 14 consonants look different.
• Capitals unchanged in a water image, in plain block form: B, C, D, E, H, I, K, O, X.
• A plane mirror forms a virtual, erect, laterally inverted image of the same size as the object.

Common traps

• Keep to the set asked. Over all 26 capitals, 11 look the same in a mirror, which gives 15, not 14.
• Mirror and water images use different lines of symmetry. For consonants in water, B, C, D and K join the unchanged list, while M, T, V, W and Y drop out.
• N, S and Z look the same upside down, but that is rotation, not reflection. In a mirror all three look different.

UnlockIAS will link similar questions from RAS Pre 2023 here once that paper is published on this site.

• practice — not a real PYQ

  How many capital letters of the English alphabet, in plain block form, look the same both in a mirror and in a water image?

  • (a)3
  • (b)4
  • (c)5
  • (d)6
  Answer(2) — A letter must have both a vertical and a horizontal line of symmetry: H, I, O and X, which makes 4. Options (1), (3) and (4) either leave one of these out or add a letter with only one line of symmetry, such as A (vertical only) or B (horizontal only).
• practice — not a real PYQ

  Images of the vowels A, E, I, O and U (capitals) are observed in a mirror. How many of the images do not look like their original shapes?

  • (a)1
  • (b)2
  • (c)3
  • (d)0
  Answer(1) — A, I, O and U each have a vertical line of symmetry and look the same; only E, which has a horizontal line of symmetry but not a vertical one, looks different. Options (2) and (3) wrongly count symmetric vowels as changed; option (4) misses E.