Images of consonants of the capital English alphabets are observed in a mirror. What is the number of images of these which look like their original shapes ?

Correct — option (3), 7.

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

Step 2 — the test for a mirror.
A mirror swaps left and right. A letter looks like its original shape only if a vertical line through its middle splits it into two matching halves.

Step 3 — apply the test to the 21 consonants, in plain capitals.
Symmetric about a vertical line: H, M, T, V, W, X, Y
Count: 7

Step 4 — check the rest.
B, C, D, F, G, J, K, L, N, P, Q, R, S, Z: 14 consonants whose mirror images look different.
7 + 14 = 21 ✓

The count assumes plain block capitals; a decorative typeface can break a letter's symmetry.

The idea to remember: a letter looks unchanged in a mirror only if it has a vertical line of symmetry.

Why the others are wrong

• (1)
  11 — Option (1) is the count for the whole alphabet, not the consonants. Eleven capitals have a vertical line of symmetry: A, H, I, M, O, T, U, V, W, X, Y.

  Four of those, A, I, O and U, are vowels. Taking them out leaves the 7 consonants the stem asks about.

• (2)
  9 — Option (2) is the count for a different reflection over a different set: letters unchanged in a water image, which swaps top and bottom. In plain capitals, nine letters have a horizontal line of symmetry: B, C, D, E, H, I, K, O, X.

  A mirror needs a vertical line instead, and among the consonants seven letters have one.

• (4)
  5 — Option (4) leaves out two of the seven. H, M, T, V, W, X and Y are all symmetric about a vertical line in plain capitals, so all seven look the same in a mirror.

  N, S and Z look the same upside down, but that is rotation. In a mirror each of them is reversed, so none can be added to the count either.

A plane mirror forms a laterally inverted image: left and right swap, top and bottom stay where they are.

A letter therefore looks unchanged in a mirror only when it has a vertical line of symmetry. In a water image, top and bottom swap, so a letter needs a horizontal line of symmetry.

H, I, O and X have both lines and look the same in either reflection. N, S and Z have rotational symmetry but no line of symmetry, so both reflections change them.

Key facts

• Taking A, E, I, O and U as vowels, the English alphabet has 21 consonants.
• Consonants unchanged in a mirror, in plain capitals: H, M, T, V, W, X, Y (7 letters).
• Capitals unchanged in a mirror, in plain block form: A, H, I, M, O, T, U, V, W, X, Y (11 letters).
• Capitals unchanged in a water image, in plain block form: B, C, D, E, H, I, K, O, X (9 letters).
• A plane mirror forms a virtual, erect, laterally inverted image of the same size as the object.

Common traps

• Counting the whole alphabet. Over all 26 capitals, 11 look the same in a mirror; the stem limits the count to consonants, which gives 7.
• Using the water-image axis. B, C, D and K have a horizontal line of symmetry only, so they look the same in water but reversed in a mirror.
• Taking rotation for reflection. N, S and Z look the same upside down, but each is reversed in a mirror.

• practice — not a real PYQ

  Which of the following words, written in capital letters, looks exactly the same in a mirror ?

  • (a)MOM
  • (b)DAD
  • (c)NUN
  • (d)POP
  Answer(1) — A mirror reverses the order of the letters and flips each one. MOM reads the same backwards, and M and O each have a vertical line of symmetry, so its image is unchanged. Options (2), (3) and (4) also read the same backwards, but D, N and P are reversed in a mirror.
• practice — not a real PYQ

  Images of the capital vowels A, E, I, O and U are observed in water. How many of the images look like their original shapes ?

  • (a)2
  • (b)3
  • (c)4
  • (d)5
  Answer(2) — A water image swaps top and bottom, so a letter needs a horizontal line of symmetry: E, I and O, which makes 3. A and U have only a vertical line, so their images change. Option (1) leaves one of the three out; options (3) and (4) wrongly add A, U or both.