Page No 103: Question 1: Express the given complex number in the form a + ib: Answer: Question 2: Express the given complex number in the form a + ib: i9 + i19 Answer: Question 3: Express the given complex number in the form a + ib: i–39 Answer: Page No 104: Question 4: Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7) Answer: Question […] Page No 94: Question 1: Prove the following by using the principle of mathematical induction for all n ∈ N: Answer: Let the given statement be P(n), i.e., P(n): 1 + 3 + 32 + …+ 3n–1 = For n = 1, we have P(1): 1 =, which is true. Let P(k) be true for some positive integer k, i.e., We shall […] Page No 54: Question 1: Find the radian measures corresponding to the following degree measures: (i) 25° (ii) – 47° 30′ (iii) 240° (iv) 520° Answer: (i) 25° We know that 180° = π radian (ii) –47° 30′ –47° 30′ = degree [1° = 60′] degree Since 180° = π radian (iii) 240° We know that […] Page No 33: Question 1: If, find the values of x and y. Answer: It is given that. Since the ordered pairs are equal, the corresponding elements will also be equal. Therefore, and. ∴ x = 2 and y = 1 Question 2: If the set A has 3 elements and the set B = {3, 4, 5}, then find the […] Page No 4: Question 1: Which of the following are sets? Justify our answer. (i) The collection of all months of a year beginning with the letter J. (ii) The collection of ten most talented writers of India. (iii) A team of eleven best-cricket batsmen of the world. (iv) The collection of all boys in your class. (v) The collection […] Page No 538: Question 1: Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E). Answer: It is given that P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.2 Question 2: Compute P(A|B), if P(B) = […] Page No 513: Question 1: Maximise Z = 3x + 4y Subject to the constraints: Answer: The feasible region determined by the constraints, x + y ≤ 4, x ≥ 0, y ≥ 0, is as follows. The corner points of the feasible region are O (0, 0), A (4, 0), and B (0, 4). The values of Z at these points are as […] Page No 467: Question 1: If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines. Answer: Let direction cosines of the line be l, m, and n. Therefore, the direction cosines of the line are Question 2: Find the direction cosines of a line which makes equal angles with the coordinate axes. Answer: Let […] Page No 428: Question 1: Represent graphically a displacement of 40 km, 30° east of north. Answer: Here, vector represents the displacement of 40 km, 30° East of North. Question 2: Classify the following measures as scalars and vectors. (i) 10 kg (ii) 2 metres north-west (iii) 40° (iv) 40 watt (v) 10–19 coulomb (vi) 20 m/s2 […] Page No 382: Question 1: Determine order and degree(if defined) of differential equation Answer: The highest order derivative present in the differential equation is. Therefore, its order is four. The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined. Question 2: Determine order and degree(if defined) of […]