Maths Unit Test
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NAME__________________________________
PEARL ACADEMY Anjali Apartment Near Sapna Hall Makarpura road Vadodara-390 009 Cell:-9825283326 9426765811
MATHS TEST – l Total marks: 50 Time allotted: 1.5 hour ___________________________________________________________________________________
Q-1.Let A = { x ∈ Z / x3 =x}, B = { x ∈ Z / x2 = x} and C = { x ∈ N / x2 = x}, [5] verify the results by taking A as the universal set. (1) B ∪ B’ = A (2) B ∩ B’ = { } (3) ( C’ )’ = C (4) ( B ∪ C )’ = B’ ∩ C’ (5) ( B ∩ C )’ = B’ ∪ C’ Q-2.For the set X = { 8, 9 ,10}, Y = { 2, 3, 4} and Z = { 2, 3, 8 ,9} and taking [6] the universal set {x∈ N / 1 ≤ x ≤ 10}, verify (1) Union is distributive over intersection. (2) Intersection is distributive over union (3) Both the laws of De’ morgan Q-3.
Q-4.
[4] The price of an item is fixed in such a way that a profit of 25 % is gained. However 1 the profit becomes 12 % when a discount is given on this price. Find the percentage 2 of discount. [4] The printed price of a book is Rs. 500. 25% discount is given on this price. In a book fair an additional discount of 20% is given. What will be the final price of the book customer pays. What is the percentage of actual discount customer gets.
Q-5.
If two ordered pairs (2x + 3, 18) and (11, 3y) are equal then find x and y. [2]
Q-6.
The number of elements in A × A is 4 for a set A. If (1,3) ∈ A × A, then [2] find the remaining elements of A × A
Q-7.
There are 9 elements in B × B for a set B. If (1,-1) and (-1, 2) are two elements of B × B, then obtain B × B
Q-8. Taking U= {x∈ N / 1 ≤ x ≤ 10} and A = {x∈ N / 1 ≤ x ≤ 5}, verify (1) A ∪ A’ = U (2) A ∩ A’ = ∅ (3) (A’)’ = A
[2]
[3]
Q-9.
Plot the points X (2, 5) and Y (2, -5) and obtain the co ordinates of the point of the intersection of the line XY with the Y axis.
[3]
Q-10. If the two ordered pairs (3x-4, x-1) and (2x +5, 2) are equal then find x and y.
[2]
Q-11. Banking 2nd sum from text book
[6]
Q-12. Find the index of cost of living
[6]
ITEM A
Price ( Rs / kg) Base year Current year 250 300
Consumption (kg) 50
B
120
150
40
C
80
15
50
D
70
35
45
E
35
60
25
F
45
50
10
Q-13. If A = { a, b, c}, B = { 1, 2, 3}, C = { a, b, c, d} and D = { 1, 2, 3, 4}, then show that (A ∪ B) ⊂ ( C ∪ D)
[5]
PEARL ACADEMY Anjali Apartment Near Sapna Hall Makarpura road Vadodara-390 009 Cell:-9825283326 9426765811
MATHS TEST – l Total marks: 50 Time allotted: 1.5 hour ___________________________________________________________________________________
Q-1.Let A = { x ∈ Z / x3 =x}, B = { x ∈ Z / x2 = x} and C = { x ∈ N / x2 = x}, [5] verify the results by taking A as the universal set. (1) B ∪ B’ = A (2) B ∩ B’ = { } (3) ( C’ )’ = C (4) ( B ∪ C )’ = B’ ∩ C’ (5) ( B ∩ C )’ = B’ ∪ C’ Q-2.For the set X = { 8, 9 ,10}, Y = { 2, 3, 4} and Z = { 2, 3, 8 ,9} and taking [6] the universal set {x∈ N / 1 ≤ x ≤ 10}, verify (1) Union is distributive over intersection. (2) Intersection is distributive over union (3) Both the laws of De’ morgan Q-3.
Q-4.
[4] The price of an item is fixed in such a way that a profit of 25 % is gained. However 1 the profit becomes 12 % when a discount is given on this price. Find the percentage 2 of discount. [4] The printed price of a book is Rs. 500. 25% discount is given on this price. In a book fair an additional discount of 20% is given. What will be the final price of the book customer pays. What is the percentage of actual discount customer gets.
Q-5.
If two ordered pairs (2x + 3, 18) and (11, 3y) are equal then find x and y. [2]
Q-6.
The number of elements in A × A is 4 for a set A. If (1,3) ∈ A × A, then [2] find the remaining elements of A × A
Q-7.
There are 9 elements in B × B for a set B. If (1,-1) and (-1, 2) are two elements of B × B, then obtain B × B
Q-8. Taking U= {x∈ N / 1 ≤ x ≤ 10} and A = {x∈ N / 1 ≤ x ≤ 5}, verify (1) A ∪ A’ = U (2) A ∩ A’ = ∅ (3) (A’)’ = A
[2]
[3]
Q-9.
Plot the points X (2, 5) and Y (2, -5) and obtain the co ordinates of the point of the intersection of the line XY with the Y axis.
[3]
Q-10. If the two ordered pairs (3x-4, x-1) and (2x +5, 2) are equal then find x and y.
[2]
Q-11. Banking 2nd sum from text book
[6]
Q-12. Find the index of cost of living
[6]
ITEM A
Price ( Rs / kg) Base year Current year 250 300
Consumption (kg) 50
B
120
150
40
C
80
15
50
D
70
35
45
E
35
60
25
F
45
50
10
Q-13. If A = { a, b, c}, B = { 1, 2, 3}, C = { a, b, c, d} and D = { 1, 2, 3, 4}, then show that (A ∪ B) ⊂ ( C ∪ D)
[5]
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