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Exercise 4.1 Prove the following by using the principle of mathematical induction for all N: 1. Ans. Let For 1 = 1 is true. Now, let be true for ……….(i) For [Using eq. (i)] is true. Therefore, is true. is true. Hence by Principle of Mathematical Induction, is true for all N. 2. Ans. Let … Read more
Miscellaneous Exercise 1. Find and in the expansion of if the first three terms of the expansion are 729, 7290 and 30375 respectively. Ans. Given: …..(i) …..(ii) And …..(iii) Multiplying eq. (i) and eq. (iii), …..(iv) Squaring both sides in eq. (ii), …..(v) Dividing eq. (iv) by eq. (v), From eq. (i), And From eq. … Read more
Miscellaneous Exercise 1. In a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus. Ans. A parabolic reflector with diameter PR = 20 cm and OQ = 5 cm Vertex of parabola is (0, 0) Let focus of the parabola be Now, PR = 20 cm PQ = 10 cm … Read more
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