Images of consonants of the English alphabet (Capitals) are observed in a mirror. What is the number of images of these which do not look like their original shapes ?
- (a) 13
- (b) 14 ✓ UPSC's answer
- (c) 15
- (d) 16
Why the answer is (b)
• The English alphabet has 21 consonants: B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z.
• A letter looks the same in a mirror if it has vertical symmetry (left-right symmetry).
• The consonants with vertical symmetry are: A (vowel, excluded), H, I (vowel, excluded), M, O (vowel, excluded), T, U (vowel, excluded), V, W, X, Y.
• From the list of 21 consonants, the ones with vertical symmetry are: H, M, T, V, W, X, Y. There are 7 such consonants.
• The number of consonants that do NOT look like their original shapes is Total Consonants - Symmetric Consonants = 21 - 7 = 14.
• Therefore, the correct answer is 14.
Why the other options are wrong
- (a) 13
- Option (a) is incorrect because it undercounts the asymmetric consonants by 1, likely misclassifying one symmetric letter as asymmetric or vice versa.
- (c) 15
- Option (c) is incorrect because it overcounts the asymmetric consonants by 1, likely misclassifying one symmetric letter as asymmetric.
- (d) 16
- Option (d) is incorrect because it overcounts the asymmetric consonants by 2, likely misclassifying two symmetric letters as asymmetric.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.