21.Discuss the chemistry of Lassaigne’s test. 22. Differentiate between the principle of estimation of nitrogen in an organic compound by (i) Dumas method and (ii) Kjeldahl’s method. 23. Discuss the principle of estimation of halogens, sulphur and phosphorus present in an organic compound. 24. Explain the principle of paper chromatography. 25. Why is nitric acid … Read more
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
NCERT Solutions for Class 8 Maths Exercise 3.1 Class 8 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 8 … Read more
NCERT Solutions for Class 10 Hindi Course A Ehi Thaiyan Jhulani Herani ho Rama Class 10 Hindi Course A Class book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE … 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
NCERT Solutions For Class 11 Physics Waves Class 11 Physics Class book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 11 … Read more
Miscellaneous Exercise Prove that: 1. Ans. L.H.S. = = = = = = 0 = R.H.S. 2. Ans. L.H.S. = = = = = 0 = R.H.S. 3. Ans. L.H.S. = = = = = = R.H.S. 4. Ans. L.H.S. = = = = = = R.H.S. 5. Ans. L.H.S. = = = = = … Read more
Exercise 8.2 Find the coefficient of: 1. in Ans. General form of the expansion is ………(i) Putting in eq. (i), Therefore, coefficient of on the expansion is = 1512. 2. in Ans. General form of the expansion is ………(i) Putting in eq. (i), Therefore, coefficient of on the expansion is = Write the general term … Read more
Exercise 11.4 In each of the Exercises 1 to 6, find the coordinates of the foci, and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas. 1. Ans. Given: Equation of hyperbola in the form Since, the foci and vertices of the hyperbola lies on axis. and Coordinates of foci … Read more
Exercise 2.1 1. If find the values of and Ans. Here and and and and 2. If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A B). Ans. Number of elements in set A = 3 and Number of elements in set … Read more
Exercise 4.1 Prove the following by using the principle of mathematical induction for all N: 1. Ans. Let For 1 = 1 is true. Now, let be true for ……….(i) For [Using eq. (i)] is true. Therefore, is true. is true. Hence by Principle of Mathematical Induction, is true for all N. 2. Ans. Let … Read more
Miscellaneous Exercise 1. Find and in the expansion of if the first three terms of the expansion are 729, 7290 and 30375 respectively. Ans. Given: …..(i) …..(ii) And …..(iii) Multiplying eq. (i) and eq. (iii), …..(iv) Squaring both sides in eq. (ii), …..(v) Dividing eq. (iv) by eq. (v), From eq. (i), And From eq. … Read more
Miscellaneous Exercise 1. In a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus. Ans. A parabolic reflector with diameter PR = 20 cm and OQ = 5 cm Vertex of parabola is (0, 0) Let focus of the parabola be Now, PR = 20 cm PQ = 10 cm … 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