Question 15 - CBSE Class 10 Sample Paper for 2026 Boards - Maths Standard [Term I] - Solutions of Sample Papers for Class 10 Boards

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Question 15 If the probability of the letter chosen at random from the letters of the word "Mathematics" to be a vowel is 2/(2𝑥+1), then 𝑥 is equal to (A) 4/11 (B) 9/4 (C) 11/4 (D) 4/9Word ‘MATHEMATICS has total 11 letters M, M, A, A, T, T, H, E, I, C, S Number of letters in word ‘MATHEMATICS’ = 11 Vowels are a, e, i, o, u Vowels in in word ‘MATHEMATICS’ is A, A, E, I Number of vowels in word ‘MATHEMATICS’ = 4 Now, Required Probability = (𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒗𝒐𝒘𝒆𝒍𝒔 𝑖𝑛 𝑤𝑜𝑟𝑑 𝑀𝐴𝑇𝐻𝐸𝑀𝐴𝑇𝐼𝐶𝑆)/(𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒍𝒆𝒕𝒕𝒆𝒓𝒔 𝑖𝑛 𝑤𝑜𝑟𝑑 𝑀𝐴𝑇𝐻𝐸𝑀𝐴𝑇𝐼𝐶𝑆) = 𝟒/𝟏𝟏 Now, given that Required Probability = 2/(2𝑥+1) Putting values 𝟒/𝟏𝟏 = 𝟐/(𝟐𝒙+𝟏) 4(2x + 1) = 2 × 11 8x + 4 = 22 8x = 22 – 4 8x = 18 x = 18/8 x = 𝟗/𝟒 So, the correct answer is (b)