Find the principal and general solutions of the equation tanx = √3 Solution: tanx = √3 We know that, tan π/3 = √3 and tan4π/3 = tan(π + π/3) = tan π/3 = √3 therefore, the principal solutions are x = π/3 and 4π/3 Now, tanx = tan π/3 x =n π+ π/3, where n… Continue reading Trigonometry Functions – Class XI – Exercise 3.4

# Tag: NCERT class 11 Mathematics

## Trigonometry Functions – Class XI – Exercise 3.3

sin2 π/6 + cos2 π/3 – tan2 π/4 = -1/2 Solution: L.H.S = sin2 π/6 + cos2 π/3 – tan2 π/4 = (1/2)2 + (1/2)2 – (1)2 = 1/4 + 1/4 – 1 = -1/2 = R.H.S Prove that 2sin2 π/6 + coses2 7π/6 cos2 π/3 = 3/2 Solution: L.H.S = 2sin2 π/6 + coses2… Continue reading Trigonometry Functions – Class XI – Exercise 3.3

## Trigonometry Functions – Class XI – Exercise 3.2

Find the values of other five trigonometric functions if cos x = -1/2, x lies in third quadrant. Solution: cos x = ‑1/2 sec x = 1/cosx = 1/(-1/2) = -2 We know, sin2x + cos2x = 1 ⇒sin2x = 1 - cos2x ⇒sin2x = 1 – (‑1/2)2 ⇒sin2x = 1 – 1/4 = 3/4… Continue reading Trigonometry Functions – Class XI – Exercise 3.2

## Trigonometry Functions – Class XI -Exercise 3.1

Find the radian measures corresponding to the following degree (i) 25˚ (ii) -47˚30’ (iii) 240˚ (iv) 520˚ Solution: (i) 25˚ We know that 180˚ = π radian 25˚ = π/180 x 25radian = 5π/36 radians (ii) -47˚30’ -47˚30’ = -471/2 = -95/2 degree -95/2 degree = π/180 x -95/2 radians = (-19/36x2) π radian =… Continue reading Trigonometry Functions – Class XI -Exercise 3.1

## Relations and Functions – Class XI – Exercise 2.3

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), (17, 1)} (ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} (iii) {(1, 3), (1, 5), (2, 5)} Solution:… Continue reading Relations and Functions – Class XI – Exercise 2.3

## Relations and Functions – Class XI – Exercise 2.2

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 down its domain, co-domain and range. Solution: The relation R from A to A is given as R = {(x, y): 3x – y… Continue reading Relations and Functions – Class XI – Exercise 2.2

## Relations and Functions – Class XI – Exercise 2.1

If (x/3 +1, y – 2/3) = (5/3, 1/3) find the values of x and y Solution: It is given that (x/3 +1, y – 2/3) = (5/3, 1/3) since the ordered pairs are equal the corresponding elements will also be equal. Therefore (x/3 +1 = 5/3) and (y – 2/3 = 1/3) x/3 +1… Continue reading Relations and Functions – Class XI – Exercise 2.1

## Sets – Class XI – Exercise 1.6

If X and Y are two sets such that n(X) = 17, n(Y) = 23 and n(X ∪ Y) = 38, find n(X ∩Y). Solution: It is given that: n(X) = 17, n(Y) = 23, n(X ∪ Y) = 38 n(X ∩ Y) = ? We know that, n(X ∩Y) = n(X) + n(Y) –… Continue reading Sets – Class XI – Exercise 1.6

## Sets – Class XI – Exercise 1.5

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) (AUC)’ (iv) (AUB)’ (v)(A’)’ (vi)(B-C)’ Solution: U ={1, 2, 3, 4, 5, 6, 7, 8, 9} A = {1,… Continue reading Sets – Class XI – Exercise 1.5

## Sets – Class XI – Exercise 1.4

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}; B = {a, b, c} (iii) A = {x: x is a natural number and multiple of 3} B = {x: x is a… Continue reading Sets – Class XI – Exercise 1.4