Buds Public School, Dubai
Grade 11 Mathematics Holiday Assignment
1. List all the element of the set A = { x : x is an integer x2 ≤ 4} .
2. From the sets given below pair the equivalent sets. A = { 1, 2, 3}, B = {x, y, z, t}, C = {a, b, c} D = {0, a} .
3. Write the following as interval (i) {x : x ϵ R, - 4 < x ≤ 6} (ii) {x : x ϵ R, 3 ≤ x ≤ 4} .
4. If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} Find (A ∩ B) ∩ ( B ∪ C) .
5. Write the set {1/3, 3/5, 5/7, 7/9, 9/11, 11/13} in set builder form.
6. In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?
7. Let A, B and C be three sets A ∪ B = A ∪ C and A ∩ B = A ∩ C show that B = C
8. If ∪ = {a, e, i. o. u} A = {a, e, i} And B = {e, o, u} C = {a, i, u} Then verity that A ∩ (B – C) = (A ∩ B) – (A ∩ C)
9. In a town of 10,000 families, it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C. 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three papers. Find the no. of families which buy (i) A only (ii) B only (iii) none of A, B, and C.
10. Two finite sets have m and n elements. The total no. of subsets of the first set is 56 more than the total no. of subsets of second set. Find the value of m and n.
11. Write the set in roster form A = The set of all letters in the word T R I G N O M E T R Y .
12. Are the following pair of sets equal? Give reasons A, the set of letters in “ALLOY” and B, the set of letters in “LOYAL”.
13. Write down the power set of A, A = {1, 2, 3}
14. A = {1, 2, {3, 4}, 5} which is incorrect and why. (i) {3, 4} ⊂ A (ii) {3, 4} ∈A
15. Fill in the blanks. (i) A ∪ A’= ------(ii) ( ) (A ′) ′ = ------(iii) A∩A’= ------
16. 8. If A, B, and C, are three sets and U is the universe set such that n(U) = 1000, n(A) = 300, n (B) =300 and n(A∩ B) = 200 ,find n (A’∩B’ ) .
17. A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medal in all the three sports, how many received medals in exactly two of the three sports?
18. In a survey of 60 people, it was found that 25 people read news paper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspaper. Find (i) The no. of people who read at least one of the newspapers. (ii) The no. of people who read exactly one news paper.
19. Convert into radian measures. -370 30’.
20. Prove Sin (n+1) x Sin (n+2) x + Cos (n+1) x. Cos (n+2) x = Sin (x + y) .
21. Find the value of Sin 31π3.
22. Find the principal solution of the equation, tan x = -13.
23. Prove that sin(x+y)sin(x-y) = tanx+tanytanx-tany .
24. If in two circles, arcs of the same length subtend angles 600 and 750 at the centre find the ratio of their radii.
25. Prove that Cos 6x= 32 Cos6x – 48 Cos4 x + 18 Cos2 x-1 .
26. Solve Sin2x-Sin4x+Sin6x=0.
27. Prove that Sin3x +Sin2x-Sinx = 4Sinx.Cos x2. Cos 3x2 .
28. Prove that 2Cos π13 .Cos 9π13 + Cos 3π13 + Cos 5π13 =0 .
29. . If Cot x =-512x lies in second quadrant find the values of other five trigonometric functions.
30. Prove that Sin 5x - 2Sin 3x + Sin x Cos 5x - Cos x = tan x .
31. Prove that Sin x + Sin 3x + Sin 5x + Sin 7x = 4 Cos x. Cos 2x. Sin 4x .
32. Prove that cos2x +cos2(x + π3)+ cos2(x - π3) =3/2.
33. Prove that Cos 2x. Cos x2 - Cos 3x Cos 9x2 = sin 5x sin 5x2.
34. Express in the form of a + ib. (1+3i)-1 .
35. Explain the fallacy in -1 = i. i. =√-1 x √-1 = -1(-1) = 1 .
36. Find the conjugate of 12-3i.
37. Find the conjugate of – 3i – 5.
38. Let z1 = 2 – i, z2 = -2+I, Find Rez1z2z2
39. If x – iy = a-ibc-id , Prove that x2+y22 = a2+b2c2+d2 .
40. If a +ib = c+ic-i ,where a, b, c are real prove that a2+b2 = 1 and ba = 2cc2- 1
41. If z1 = 2-i and Z2 = 1+i , Find z1+z2+1z1- z2+i.
42. If (p + iq)2 = x + iy Prove that (p2 + q2) 2 = x2 + y2 .
43. Convert into polar form -161+ 3 i .
44. Solve 5x - 3 ≤ 3x + 1, when x is an integer.
45. Solve 30 x < 200 when x is a natural no.
46. Solve the inequality x2≥5x-23 - 7x-35.
47. Solve graphically x –y ≤ 0 .
48. A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second.
49. 6. The water acidity in a pool is considered normal when the average Ph reading of three daily measurements is between 7.2 and 7.8 If the first Ph reading are 7.48 and7.85, find the range of Ph value for the third reading that will result in the acidity level being normal.
50. How many litres of water will have to be added to 1125 litres of the 45% sol. Of acid so that the resulting mixture will contain more than 25%but less than 30% acid content.
51. Solve graphically 3x+2y ≤ 150 , x + y ≤ 80 ,x ≤ 1 ,x ≥0 , y≥0.
52. . Solve : 52x-7-32x+3≤0 and 2x+19≤6x+47 and represent the solution on
the number line .
53. Solve : a) -5 ≤2-3x4≤9 b) 3x-2≤12 c) y-1≥4
54. Solve and draw the graph of the following inequalities
a) 5-2x3≤x6- 5 b) 4x-55 < 2x-54 c) -2-x4 ≤1+x3 , 3-x<4(x-3)
55. Solve the system of following inequations graphically :
a) 2x+y ≥4 , x+y ≤3 , 2x-3y≤6
b) 3x+4y ≤12, 4x+3y ≤12, x≥0 and y≥0
c) x+2y ≤10 , x+2y≥1 , x-y ≤0, x≥0 and y≥0
d) 3x+4y ≤60 , x+3y≤30 , x≥0,y≥0
e) x+y≤6 , x+y ≥4
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