Class 11

Exercise 15.1 Find the mean deviation about the mean for the data in Exercises 1 and 2. 1. 4, 7, 8, 9, 10, 12, 13, 17 Ans. Mean of the given data Mean deviation about mean = = = 3 2. 38, 70, 48, 40, 42, 55, 63, 46, 54, 44 Ans. Mean of the … Read more

The s block elements  1. What are the common physical and chemical features of alkali metals? 2. Discuss the general characteristics and gradation in properties of alkaline earth metals. 3. Why are alkali metals not found in nature? 4. Find the oxidation state of sodium in 5. Explain why is sodium less reactive than potassium? … Read more

Exercise 15.2 Find the mean and variance for each of the data in Exercises 1 to 5. 1. 6, 7, 10, 12, 13, 4, 8, 12 Ans. Given: = 6, 7, 10, 12, 13, 4, 8, 12 = 6 + 7 + 10 + 12 + 13 + 4 + 8 + 12 = 72 … Read more

16. Starting with sodium chloride how would you proceed to prepare (i) sodium metal (ii) sodium hydroxide (iii) sodium peroxide (iv) sodium carbonate? 17. What happens when (i) magnesium is burnt in air (ii) quick lime is heated with silica (iii) chlorine reacts with slaked lime (iv) calcium nitrate is heated ? 18. Describe two … Read more

Exercise 15.3 1. From the data given below state which group is more variable, A or B: Ans. Group A Mean = = 45 – 0.4 = 44.6 Standard deviation = = = = 15.09 Group B Mean = = 45 – 0.4 = 44.6 Standard deviation = = = = 15.61 2. From the … Read more

20. What happens when (a) Borax is heated strongly, (b) Boric acid is added to water, (c) Aluminium is treated with dilute NaOH, (d) is reacted with ammonia? 21. Explain the following reactions (a) Silicon is heated with methyl chloride at high temperature in the presence of copper; (b) Silicon dioxide is treated with hydrogen … Read more

Exercise 2.2 1. Let A = {1, 2, 3, ……., 14}. Define a relation R from A to A by R = where Write down its domain co-domain and range. Ans. Given: A = {1, 2, 3, ……….., 14} The ordered pairs which satisfy are (1, 3), (2, 6), (3, 9) and (4, 12). R … Read more

Exercise 5.1 Express each of the complex numbers given in the exercises 1 to 10 in the form : 1. Ans. Here = = =3 2. Ans. Here = 3. Ans. = = 4. Ans. Here = 5. Ans. Here = 6. Ans. Here = = 7. Ans. Here = = = = 8. Ans. … Read more

Exercise 9.1 Write the first five terms of each of the sequences in Exercises 1 to 6 whose terms are: 1. Ans. Given: Putting and 5, we get, Therefore, the first five terms are 3, 8, 15, 24 and 35. 2. Ans. Given: Putting and 5, we get, Therefore, the first five terms are and … Read more

Miscellaneous Exercise 1. The relation is defined by . The relation is defined by . Show that is a function and is not a function. Ans. Given: and At and It is observed that takes unique value at each point in its domain [0, 10]. Therefore, is a function. Now, and At and Therefore, does … Read more

Exercise 5.2 Find the modulus and the argument of each of the complex numbers in exercises 1 to 2. 1. Ans. Given: and Squaring both sides and adding both the equations, we get and and [ lies in third quadrant] Therefore, and arg 2. Ans. Given: and Squaring both sides and adding both the equations, … Read more

Exercise 9.2 1. Find the sum of odd integers from 1 to 2001. Ans. Odd integers from 1 to 2001 are 1, 3, 5, 7, …….., 2001. Here, and Now, = 1002001 2. Find the sum of all natural numbers lying between 100 and 1000 which are multiples of 5. Ans. According to question, series … Read more

Exercise 2.3 1. Which of the following are functions? Give reasons. If it is a function determine its domain and range. (i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} (ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} (iii) {(1, 3), (1, 5), (2, … Read more

Exercise 5.3 Solve each of the following equations: 1. Ans. Given: 2. Ans. Given: Comparing with , and = = = Therefore, and 3. Ans. Given: Comparing with , and = = = Therefore, and 4. Ans. Given: Comparing with , and = = = Therefore, and 5. Ans. Given: Comparing with , and = … Read more

Exercise 9.3 1. Find the 20th and terms of the G.P. Ans. Here and = And = = 2. Find the 12th term of a G.P. whose 8th term is 192 and the common ratio if 2. Ans. Let be the first term of given G.P. Here and = == 3072 3. The 5th, 8th … Read more

Exercise 1.1 1. Which of the following are sets? Justify your answer. (i) The collection of all the 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 batmen of the world. (iv) The collection of all boys in your … Read more

Miscellaneous Exercise 1. Evaluate: Ans. Given: = = = = = = = = 2. For any two complex numbers and prove that Ans. Let and Then and Now, = = = 3. Reduce to the standard form. Ans. Here: = = = = = = = = = 4. If prove that Ans. Given: … Read more

16. Find a G.P. for which sum of the first two terms is and the fifth term is 4 times the third term. Ans. Let be the first term and be the common ratio of given G.P. Given: ……..(i) And Putting in eq. (i), we get Therefore, required G.P. is Putting in eq. (i), we … Read more