Class 11

Exercise 14.3 1. For each of the following compound statements first identify the connecting words and then break it into component statements: (i) All rational numbers are real and all real numbers are not complex. (ii) Square of an integer is positive or negative. (iii) The sand heats up quickly in the sun and does … Read more

51. The pH of 0.005M codeine ( ) solution is 9.95. Calculate its ionization constant and pKb. 52. What is the pH of 0.001 M aniline solution? The ionization constant of aniline can be taken from Table 7.7. Calculate the degree of ionization of aniline in the solution. Also calculate the ionization constant of the … Read more

Exercise 14.4 1. Rewrite the following statements with “if-then” in five different ways conveying the same meaning. If a natural number is off then its square is also odd. Ans. (i) A natural number is odd implies that its square is odd. (ii) A natural is odd only if its square is odd. (iii) For … Read more

16. Why does the following reaction occur? What conclusion about the compound (of which is a part) can be drawn from the reaction. 17. Consider the reactions: (a) (b) (c) (d) What inference do you draw about the behaviour of and from these reactions? 18. Balance the following redox reactions by ion-electron method: (a) (in … Read more

Exercise 14.5 1. Show that the statement “If is a real number such that then is 0” is true by (i) direct method (ii) method of contradiction (iii) method of contrapositive. Ans. The given compound statement is of the form “if then ”. R such that (i) Direct method: If we assume that is true … Read more

Hydrogen  1. Justify the position of hydrogen in the periodic table on the basis of its electronic configuration. 2. Write the names of isotopes of hydrogen. What is the mass ratio of these isotopes? 3. Why does hydrogen occur in a diatomic form rather than in a monoatomic form under normal conditions? 4. How can … Read more

Exercise 3.3 Prove that: 1. Ans. 1. L.H.S. = = = R.H.S. 2. Ans. L.H.S. = = = = = 3. Ans. L.H.S. = = = = = = R.H.S. 4. Ans. L.H.S. = = = = = = R.H.S. 5. Find the value of: (i) (ii) Ans. (i) = (ii) = = Prove the … Read more

Miscellaneous Exercise 1. How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER? Ans. There are 8 letters in the word DAUGHTER. In this word 3 vowels and 5 consonants. 2 vowels and 3 consonants are to be selected. Number of … Read more

Exercise 11.2 In each of the following Exercises 1 to 6, find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. 1. Ans. Given: Equation of parabola Comparing with we have Coordinates of focus are (3, 0). Axis of parabola is Equation of … Read more

Exercise 3.4 Find the principal and general solutions of the following equations: 1. Ans. Given: Here lies in first or third quadrant. or or or Therefore, the principal solutions are Now, where Z 2. Ans. Given: Here lies in first or fourth quadrant. or or or Therefore, the principal solutions are Now, where Z 3. … Read more

Exercise 8.1 Expand each of the expression in Exercises 1 to 5. 1. Ans. Using Binomial Theorem, = = 2. Ans. Using Binomial Theorem, = = 3. Ans. Using Binomial Theorem, = = 4. Ans. Using Binomial Theorem, = = 5. Ans. Using Binomial Theorem, = = Using binomial theorem evaluate each of the following: … Read more

Exercise 11.3 In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. 1. Ans. Given: Equation of ellipse: 36 > 16 Now = Coordinates of foci are Coordinates of … 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 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