NCERT Solutions

Exercise 12.1 1. A point is on the axis. What are its coordinates and coordinates? Ans. We know that coordinates of any point on the axis will be Therefore, coordinate and coordinate of the point are zero. 2. A point is on XZ-plane. What can you say about its coordinate? Ans. We know that coordinates … Read more

Miscellaneous Exercise 1. The mean and variance of eight observations are 9 and 9.25 respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations. Ans. Let two required observations be and Then, According to question, ……….(i) Also ……….(ii) When then on solving and we get and … 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 12.2 1. Find the distance between the following pairs of points: (i) (2, 3, 5) and (4, 3, 1) (ii) and (iii) and (iv) and Ans. (i) Let A (2, 3, 5) and B (4, 3, 1) be two points, then AB = = = units (ii) Let A (–3, 7, 2) and B … Read more

Exercise 16.1 In each of the following exercises 1 to 7, describe the sample space for the indicated experiment. 1. A coin is tossed three times. Ans. S = {HHH, HHT, HTH, THH, TTH, HTT, TTT} 2. A die is thrown two times. Ans. S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, … Read more

States of matter1. What will be the minimum pressure required to compress of air at 1 bar to 200 at 30°C? 2. A vessel of 120 mL capacity contains a certain amount of gas at 35 °C and 1.2 bar pressure. The gas is transferred to another vessel of volume 180 mL at 35 °C. … Read more

Exercise 12.3 1. Find the coordinates of the point which divides the line segment joining the points and in the ratio: (i) 2: 3 internally, (ii) 2: 3 externally. Ans. (i) Let P be any point which divides the line segment joining points A and B in the ratio 2: 3 internally. Then Therefore, Coordinates … Read more

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

Class –VIII Mathematics (Ex. 3.4) NCERT SOLUTION 1. State whether true or false: (a) All rectangles are squares. (b) All rhombuses are parallelograms. (c) All squares are rhombuses and also rectangles. (d) All squares are not parallelograms. (e) All kites are rhombuses. (f) All rhombuses are kites. (g) All parallelograms are trapeziums. (h) All squares … 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