Class 11

Exercise 16.2 1. A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive? Ans. When a die is rolled, then S = {1, 2, 3, 4, 5, 6} E: die shows 4 = {4} and F: die shows … Read more

ORGANIC CHEMISTRY – SOME BASIC PRINCIPLES AND TECHNIQUES  1. What are hybridisation states of each carbon atom in the following compounds? 2. Indicate the bonds in the following molecules: 3. Write bond line formulas for: Isopropyl alcohol, 2,3-Dimethyl butanal, Heptan-4-one. 4. Give the IUPAC names of the following compounds: (a) (b) (c) (d) (e) (f) … Read more

Miscellaneous Exercise 1. Three vertices of a parallelogram ABCD are A B and C Find the coordinates of the fourth vertex. Ans. Let D be the fourth vertex of parallelogram ABCD. Since, the diagonals of a parallelogram bisect each other. Therefore, the mid-point of AAAC and BD coincide. Coordinates of mid-point of AC = = … Read more

Exercise 16.3 1. Which of the following cannot be valid assignment of probabilities for outcomes of sample space S = Assignment (a) 0.1 0.01 0.05 0.03 0.01 0.2 0.6 (b) (c) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (d) –0.1 0.2 0.3 0.4 –0.2 0.1 0.3 (e) Ans. (a) Here probability of each outcome is … Read more

HYDROCARBONS1.How do you account for the formation of ethane during chlorination of methane? 2. Write IUPAC names of the following compounds: a. b. c. d. e. f. g. 3.For the following compounds, write structural formulas and IUPAC names for all possible isomers having the number of double or triple bond as indicated: (a) (one double … Read more

Exercise 1.2 1. Which of the following are examples of the null set: (i) Set of odd natural numbers divisible by 2. (ii) Set of even prime numbers. (iii) { is a natural number, and } (iv) { is a point common to any two parallel lines} Ans. (i) Set of odd natural numbers divisible … Read more

Exercise 6.1 1. Solve when: (i) is a natural number (ii) is an integer Ans. Given: Dividing both sides by 24, (i) When is a natural number then values of that make statement true are 1, 2, 3, 4. The solution set of inequality is {1, 2, 3, 4}. (ii) When is an integer then … Read more

Exercise 9.4 Find the sum to terms in each of the series in Exercises 1 to 7. 1. Ans. Given:to terms = [ term of 1, 2, 3, ………..][ term of 2, 3, 4, 5, ………] = = = = = = = = = 2. Ans. Given: to terms = [ term of 1, … Read more

Exercise 1.4 1. Find the union of each of the following pairs of sets: (i) X = {1, 3, 5} and Y = {1, 2, 3} (ii) A = and B = (iii) A = { is a natural number and multiple of 3} and B = { is a natural number less than 6} … Read more

Exercise 6.2 Solve the following inequalities graphically in two dimensional planes: 1. Ans. Given: Table of values satisfying the equation 1 2 4 3 Putting (0, 0) in the given in equation, 0 < 5 which is true. Therefore, Half plane of towards origin. 2. Ans. Given: Table of values satisfying the equation 1 2 … Read more

Miscellaneous Exercise 1. Show that the sum of  and  terms of an A.P. is equal to twice the  terms. Ans. Here,  …..(i) and   …..(ii) To prove: Adding eq. (i) and (ii), we get                  2. If the sum of three numbers in A.P., is 24 and their product is 440. … Read more

Exercise 1.6 1. If X and Y are two sets such that and find Ans. Given: and 2. If X and Y are two sets such that has 18, X has 8 elements and Y has 15 elements; how many elements has ? Ans. Given: and 3. In a group of 400 people, 250 can … Read more

Exercise 6.3 Solve the following systems of inequalities graphically: 1. Ans. Given: Putting (0, 0) in which is false. Half plane of is away from origin. Again Putting (0, 0) in which is false. Half plane of is away from origin. 2. Ans. Given: Table of values satisfying the equation 2 4 3 0 Putting … Read more

17. If  are in G.P., prove that  are in G.P. Ans. Given:  are in G.P. To prove:  are in G.P.    Let       And    Also    Now,         Therefore,  are in G.P. 18. If  and  are the roots  and  are roots of  where  form a G.P. Prove that   Ans. … Read more

Miscellaneous Exercise 1. Decide among the following sets, which sets are subsets of each another: A = { R and satisfies }, B = {2, 4, 6}, C = {2, 4, ,6 , 8…….}, D = {6} Ans. Given: A = { R and satisfies } = { R and satisfies } = {2, 6} … Read more

Miscellaneous Exercise Solve the inequalities: 1. Ans. Given: 2. Ans. Given: 3. Ans. Given: 4. Ans. Given: 5. Ans. Given: 6. Ans. Given: Solve the inequalities in Exercises 7 to 10 and represent the solution graphically on number line: 7. Ans. Given: and and and 8. Ans. Given: and and and and 9. Ans. Given: … Read more