Sum of probabilities Thus, the assignment is valid. (b) ω1 ω2 ω3 ω4 ω5 ω6 ω7 Here, each of the numbers p(ωi) is positive and less than 1. Sum of probabilities Thus, the assignment is valid. (c) ω1 ω2 ω3 ω4 ω5 ω6 ω7 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Here, each of the […] xi fi fi xi 10 4 40 40 160 30 24 720 20 480 50 28 1400 0 0 70 16 1120 20 320 90 8 720 40 320 80 4000 1280 Question 7: Find the mean deviation about the median for the data. xi 5 7 9 10 12 15 fi 8 6 2 […] Page No 324: Question 1: Which of the following sentences are statements? Give reasons for your answer. (i) There are 35 days in a month. (ii) Mathematics is difficult. (iii) The sum of 5 and 7 is greater than 10. (iv) The square of a number is an even number. (v) The sides of a […] Page No 301: Question 1: Evaluate the Given limit: Answer: Question 2: Evaluate the Given limit: Answer: Question 3: Evaluate the Given limit: Answer: Question 4: Evaluate the Given limit: Answer: Question 5: Evaluate the Given limit: Answer: Question 6: Evaluate the Given limit: Answer: Put x + 1 = y so that y → […] Page No 271: Question 1: A point is on the x-axis. What are its y-coordinates and z-coordinates? Answer: If a point is on the x-axis, then its y-coordinates and z-coordinates are zero. Question 2: A point is in the XZ-plane. What can you say about its y-coordinate? Answer: If a point is in the XZ plane, then its y-coordinate is zero. Question 3: […] Page No 241: Question 1: Find the equation of the circle with centre (0, 2) and radius 2 Answer: The equation of a circle with centre (h, k) and radius r is given as (x – h)2 + (y – k)2 = r2 It is given that centre (h, k) = (0, 2) and radius (r) = 2. Therefore, the equation of the circle is (x – […] Page No 211: Question 1: Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area. Answer: Let ABCD be the given quadrilateral with vertices A (–4, 5), B (0, 7), C (5, –5), and D (–4, –2). Then, by plotting A, B, […] Page No 180: Question 1: Write the first five terms of the sequences whose nth term is Answer: Substituting n = 1, 2, 3, 4, and 5, we obtain Therefore, the required terms are 3, 8, 15, 24, and 35. Question 2: Write the first five terms of the sequences whose nth term is Answer: Substituting n = 1, 2, 3, […] Page No 166: Question 1: Expand the expression (1– 2x)5 Answer: By using Binomial Theorem, the expression (1– 2x)5 can be expanded as Question 2: Expand the expression Answer: By using Binomial Theorem, the expression can be expanded as Question 3: Expand the expression (2x – 3)6 Answer: By using Binomial Theorem, the expression (2x – 3)6 can be expanded […] Page No 138: Question 1: How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) repetition of the digits is allowed? (ii) repetition of the digits is not allowed? Answer: (i) There will be as many ways as there are ways of filling 3 vacant places […]