NCERT Solutions

Exercise 1.5 1. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find: (i) A’ (ii) B’ (iii) (A C)’ (iv) (A B)’ (v) (A’)’ (vi) (B – C)’ Ans. Given: U = … Read more

Exercise 7.2 1. Evaluate: (i) 8! (ii) (ii) 4! – 3! Ans. (i) 8! = = 40320 (ii) 4! – 3! = = 24 – 6 = 18 2. Is 3! + 4! = 7!? Ans. L.H.S. = 3! + 4! = = 6 + 24 = 30 R.H.S. = 7! = = 5040 L.H.S. … Read more

Exercise 10.3 1. Reduce the following equations into slope-intercept form and find their slopes and the intercepts. (i) (ii) (iii) Ans. (i) Given: ……….(i) Comparing with we have and (ii) Given: ……….(i) Comparing with we have and (iii) Given: ……….(i) Comparing with we have and 2. Reduce the following equations into intercept form and find … Read more

Exercise 3.1 1. Find the radian measures corresponding to the following degree measures: (i) (ii) (iii) (iv) Ans. (i) (ii) (iii) (iv) 2. Find the degree measures corresponding to the following radian measures . (i) (ii) (iii) (iv) Ans. (i) = (ii) = (iii) (iv) 3. A wheel makes 360 revolutions in one minute. Through … Read more

Exercise 7.3 1. How many 3-digit numbers can be formed by using the digits 1 to 9 if no digits is repeated? Ans. Total number of digits = 9 and Number of digits used without repetition = 3 Number of permutations = = = 504 2. How many 4-digit numbers are there with no digit … Read more

Miscellaneous Exercise 1. Find the values of K for which the line is: (a) parallel to the axis (b) parallel to the axis (c) passing through the origin. Ans. Given: Equation of line (a) If the line parallel to axis, then (b) If the line parallel to axis, then (c) If the line passes through … Read more

Exercise 3.2 Find the values of other trigonometric functions in exercises 1 to 5. 1. lies in third quadrant. Ans. Given: [ lies in third quadrant] Now, 2. lies in second quadrant. Ans. Given: [ lies in second quadrant] Now, 3. lies in third quadrant. Ans. Given: [ lies in third quadrant] Now, 4. lies … Read more

Exercise 7.4 1. If find Ans. Given: 2. Determine if: (i) (ii) Ans. (i) Given: (ii) Given: 3. How many chords can be drawn through 21 points on a circle? Ans. There are 21 points on the circumference of a circle. Since one and only one chord can be drawn by joining 2 distinct points, … Read more

Exercise 11.1 In each of the following Exercises 1 to 5, find the equation of the circle with: 1. Centre (0, 2) and radius 2. Ans. Given: and Equation of the circle = 2. Centre and radius 4. Ans. Given: and Equation of the circle = 3. Centre and radius Ans. Given: and Equation of … 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