OCTOBER REVISION CLASS 11

CLASS 11

REVISION

Sets

Relations and Functions

 Trigonometry

1. If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A × B)?

 

2. If A = {–1, 1}, find A × A × A.

3. Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by

{(a, b): a, b ∈ A, b is exactly divisible by a}.

(i) Write R in roster form

(ii) Find the domain of R

(iii) Find the range of R.

4. Let A and B be two sets such that n(A) = 3 and n (B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y and z are distinct elements.

5. A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.

6. Find the domain and range of the following real function:

(i) f(x) = –|x| (ii) f(x) = √(9 – x2) 

7. A function f is defined by f(x) = 2x – 5. Write down the values of

(i) f(0), (ii) f(7), (iii) f(–3)

 

8. If f(x) = x2, find

9. Let f, g: R → R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and f/g.

 

10. Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true?

(i) f is a relation from A to B (ii) f is a function from A to B.

Justify your answer in each case.

 

11. Find the radian measures corresponding to the following degree measures:

(i)  240° (ii) 520°

12. Find the degree measures corresponding to the following radian measures (Use π = 22/7)

(i) 5π/3

(ii) 7π/6

13. Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use π = 22/7).

14. Prove that sin2 6x – sin2 4x = sin 2x sin 10x

 

15. Given sin x = 3/5, x lies in second quadrant, find all the other trigonometric ratios.

16. Find sin x/2, cos x/2 and tan x/2 given tan x = -4/3, x lies in the second quadrant.

17. Prove that sin 2x + 2sin 4x + sin 6x = 4cos2 x sin 4x

 

18. Prove that cos 6x = 32 cos6 x – 48 cos4 x + 18 cos2 x – 1

 

19. Prove that sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x

20. If A = {x: x is a natural number}, B ={x: x is an even natural number}

C = {x: x is an odd natural number} and D = {x: x is a prime number}, find

(i) A ∩ B

(ii) A ∩ C 

(iii) A ∩ D 

(iv) B ∩ C

(v) B ∩ D 

(vi) C ∩ D

21.If U = {1, 2, 3, 4, 5,6,7,8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that

(i) (A U B)’ = A’ ∩ B’

(ii) (A ∩ B)’ = A’ U B’

 

22. If X = {a, b, c, d} and Y = {f, b, d, g}, find

(i) X – Y

(ii) Y – X

(iii) X ∩ Y

 

23. Let A, B and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C. show that B = C.

 

24. In a up of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

 

25. Decide, among the following sets, which sets are subsets of one and another:

A= {x: x ∈ R and x satisfy x2 – 8x + 12 = 0},

B = {2, 4, 6},

C = {2, 4, 6, 8…},

D = {6}.