Class 11 – Mathematics Principle of Mathematical Induction – Exercise 4.1 Question : 1 Answer: Question : 2 Answer: Question : 3 Answer: Question : 4 Answer: Question : 5 Answer: Question : 6 Answer: Question : 7 Answer: Question…

Class 11 – Mathematics Trigonometric Function – Exercise – Misc Question 1: Prove that: 2cos π/13 cos 9π/13 + cos 3π/13 cos 5π/13 = 0 Answer: LHS: 2cos π/13 * cos 9π/13 + cos 3π/13 * cos 5π/13 = 2cos…

Class 11 – Mathematics Trigonometric Function – Exercise 3.4 Question 1: Find the principal and general solutions of the equation tan x = √3 Answer: Given, tan x = √3 We know that tan π/3 = √3 and tan 4π/3…

Class 11 – Mathematics Trigonometric Function – Exercise 3.3 Question 1: sin2 π/6 + cos2 π/3 – tan2 π/4 = -1/2 Answer: LHS: sin2 π/6 + cos2 π/3 – tan2 π/4 = (1/2)2 + (1/2)2 – 12 = 1/4 +…

Class 11 – Mathematics Trigonometric Function – Exercise 3.2 Question 1: Find the values of other five trigonometric functions if cos x = -1/2, x lies in third quadrant. Answer: Given, cos x = -1/2 So, sec x = 1/cos…

Class 11 – Mathematics Trigonometric Function – Exercise 3.1 Question 1: Find the radian measures corresponding to the following degree measures: (i) 25°                            (ii) – 47° 30′                           (iii) 240°                      (iv) 520° Answer: (i) 25° We know that 180° = π…

Class 11 – Mathematics Relation – Exercise 2 – Misc Question 1: The relation f is defined by f(x) =      x2, 0 ≤ x ≤ 3 3x, 3 ≤ x ≤ 10 The relation g is defined by g(x) =    …

Class 11 – Mathematics Relation – Exercise 2.3 Question 1: Which of the following relations 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),…

Class 11 – Mathematics Relation – Exercise 2.2 Question 1: Let A = {1, 2, 3,…,14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write…

Class 11 – Mathematics Relation – Exercise 2.1 Question 1: If (x/3 + 1, y – 2/3) = (5/3, 1/3), find the values of x and y. Answer: It is given that (x/3 + 1, y – 2/3) = (5/3,…

Class 11 – Mathematics Sets – Exercise – Misc Question 1: Decide, among the following sets, which sets are subsets of one and another: A = {x : x ∈ R and x satisfy x2– 8x + 12 = 0},  …

Class 11 – Mathematics Sets – Exercise 1.6 Question 1: If X and Y are two sets such that n(x) = 17, n(Y) = 23 and n(X ∪ Y) = 38, find n(X ∩ Y). Answer: It is given that:…

Class 11 – Mathematics Sets – Exercise 1.5 Question 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,…

Class 11 – Mathematics Sets – Exercise 1.4 Question 1: Find the union of each of the following pairs of sets: (i) X = {1, 3, 5}          Y = {1, 2, 3} (ii) A = [a, e, i, o, u}        …

Class 11 – Mathematics Sets – Exercise 1.3 Question 1: Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces: (i) {2, 3, 4} . . . {1, 2, 3, 4,5} (ii) {a, b, c}…

Class 11 – Mathematics Sets – Exercise 1.2 Question 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) { x : x…

Class 11 – Mathematics Sets – Exercise 1.1 Question 1: Which of the following are sets? Justify your answer. (i) The collection of all months of a year beginning with the letter J. (ii) The collection of ten most talented…