How many sets of two letters in the word GENERAL have as many letters between them as they have in the English alphabet ?\nGENERAL शब्द में दो अक्षरों के ऐसे कितने समूह हैं जिनके बीच उतने ही अक्षर हैं जितने कि उनके बीच अंग्रेज़ी वर्णमाला में हैं?
Explanation:
To solve this, we need to list the letters of the word 'GENERAL' and their corresponding positions in the English alphabet (A=1, B=2, ..., Z=26).\nWord: G E N E R A L\nAlphabetical values: G=7, E=5, N=14, E=5, R=18, A=1, L=12 \nWe will check every possible pair of letters in the word and compare the count of letters between them in the word with the count of letters between them in the alphabet. The count of letters between two letters $X$ and $Y$ in the alphabet is $| \text{alphabetical value of } Y - \text{alphabetical value of } X | - 1$. \nLet's examine pairs: 1. **G (pos 1) and E (pos 2):** Letters in word: $0$. (No letters between G and E) Letters in alphabet: $|5 - 7| - 1 = 2 - 1 = 1$ (F between G and E). No match. 2. **E (pos 2) and A (pos 6):** Letters in word: $3$ (N, E, R are between E and A). Letters in alphabet: $|1 - 5| - 1 = 4 - 1 = 3$ (D, C, B are between E and A). **Match found! (E-A)** \nLet's continue checking other pairs for completeness: - G (pos 1) and N (pos 3): Word count = 1 (E). Alphabet count = $|14-7|-1 = 6$. No. - G (pos 1) and E (pos 4): Word count = 2 (N, E). Alphabet count = $|5-7|-1 = 1$. No. - G (pos 1) and R (pos 5): Word count = 3 (E, N, E). Alphabet count = $|18-7|-1 = 10$. No. - G (pos 1) and A (pos 6): Word count = 4 (E, N, E, R). Alphabet count = $|1-7|-1 = 5$. No. - G (pos 1) and L (pos 7): Word count = 5 (E, N, E, R, A). Alphabet count = $|12-7|-1 = 4$. No. - E (pos 2) and N (pos 3): Word count = 0. Alphabet count = $|14-5|-1 = 8$. No. - E (pos 2) and E (pos 4): Word count = 1 (N). Alphabet count = $|5-5|-1 = -1$ (meaning 0 letters between identical letters). No. - E (pos 2) and R (pos 5): Word count = 2 (N, E). Alphabet count = $|18-5|-1 = 12$. No. - E (pos 2) and L (pos 7): Word count = 4 (N, E, R, A). Alphabet count = $|12-5|-1 = 6$. No. - N (pos 3) and E (pos 4): Word count = 0. Alphabet count = $|5-14|-1 = 8$. No. - N (pos 3) and R (pos 5): Word count = 1 (E). Alphabet count = $|18-14|-1 = 3$. No. - N (pos 3) and A (pos 6): Word count = 2 (E, R). Alphabet count = $|1-14|-1 = 12$. No. - N (pos 3) and L (pos 7): Word count = 3 (E, R, A). Alphabet count = $|12-14|-1 = 1$. No. - E (pos 4) and R (pos 5): Word count = 0. Alphabet count = $|18-5|-1 = 12$. No. - E (pos 4) and A (pos 6): Word count = 1 (R). Alphabet count = $|1-5|-1 = 3$. No. - E (pos 4) and L (pos 7): Word count = 2 (R, A). Alphabet count = $|12-5|-1 = 6$. No. - R (pos 5) and A (pos 6): Word count = 0. Alphabet count = $|1-18|-1 = 16$. No. - R (pos 5) and L (pos 7): Word count = 1 (A). Alphabet count = $|12-18|-1 = 5$. No. - A (pos 6) and L (pos 7): Word count = 0. Alphabet count = $|12-1|-1 = 10$. No. \nOnly one such pair, E-A, satisfies the condition. The correct option is (2) 1.