(i) The polynomial 3x³ + 8x² - 15x + k has (x - 1) as a factor. Find the value of k, Hence factorize the resulting polynomial completely,

(ii) The following letters A, D, M, N, O, S, U, Y of the English alphabet are written on separate cards and put in a box. The cards are well shuffled and one card is drawn at random. What is the probability that the card drawn is a letter of the word,
(a) MONDAY?
(b) which does not appear in MONDAY?
(c) which appears both in SUNDAY and MONDAY?


(iii) Oil is stored in a spherical vessel occupying 3/4 of its full capacity. Radius of this spherical vessel is 28 cm. This oil is then poured into a cylindrical vessel with a radius of 21 cm. Find the height of the oil in the cylindrical vessel (correct to the nearest cm). [Take π = 22/7]

Solution

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