CBSE Test Paper 02
CH-01 Sets
Section A
1. Let A and B be two sets such that ,
find
a. 25
b. 19
c. 18
d. 17
2. If A = { 2,3,4,8,10 } , B = { 3,4,5,10,12 } and C = { 4,5,6,12,14 } , then
is equal to
a. { 4,5,8,10,12 }
b. { 2,4,5,10,12 }
c. { 3,8,10,12 }
d. { 2,3,4,5,8,10,12 }
3. If A , B and C are non – empty sets , then ( A – B ) ( B – A ) equals :
a.
b. ( A B) (A B)
c. ( A B)-B
d. ( A B)–(A B)
4. If A and B are two sets then =....
a.
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b. A
c.
d. B
5. Sets A and B have 3 and 6 elements respectively. What can be the maximum number
of elements in A B.
a. 3
b. 9
c. 18
d. 6
6. Fill in the blanks:
If A = {e, f, g} and B = , then A B is ________.
7. Fill in the blanks:
The total number of subsets and a proper subset of a finite set containing 'n' element
is ________ and ________, respectively.
8. If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find:
9. Describe {x R: x > x) set in Roster form.
10. Is set C = { x : x - 5 = 0} and E = {x : x is an integral positive root of the equation x 2 - 2x
- 15 = 0} are equal?
11. Show that need not imply B = C?
12. Write the set of all natural numbers x such that 4x + 9 < 50 in roster form.
13. In the following, state whether A = B or not: A = {a, b, c, d} B = {d, c, b, a}
14. If X = {a, b, c, d} and Y = {f, b, d, g}, then find
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i. X - Y
ii. Y - X
iii. X Y
iv. X Y
15. In a group of 100 people, 65 like to play Cricket, 40 like to play Tennis and 55 like to
play Volleyball. All of them like to play at least one of the three games. If 25 like to
play both Cricket and Tennis, 24 like to play both Tennis and Volleyball and 22 like to
play both Cricket and Volleyball, then
i. how many like to play all the three games?
ii. how many like to play Cricket only?
iii. how many like to play Tennis only?
Represent the above information in a Venn diagram.
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CBSE Test Paper 02
CH-01 Sets
Solution
Section A
1. (c) 18
Explanation:
Given that
We have
Therefore
2. (d) { 2,3,4,5,8,10,12 }
Explanation:
Given A= 2,3,4,8,10, B= 3,4,5,10,12 and C= 4,5,6,12,14
Here
Now,
3. (d) ( A B)–(A B)
Explanation:
4. (b) A
Explanation:
5. (b) 9
Explanation:
n(A B)= n(A) +n(B)-n(A B)
if n(A B) =0 then n(A B) is max.
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so max. number of element in A B=9
6.
7. 2n, 2n - 1
8. Here A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}
= {11}
9. We know that given any x R, x is always less than or equal to itself, i.e.,x x. Hence,
the above set is empty i.e, .
10. C = {5}
x2-2x-15=0
x2-5x+3x-15=0
x(x-5)+3(x-5)=0
(x-5)(x+3)=0
x=5
x=-3 [x= -3 reject]
x= 5
E= {5}
Hence C = E.
11. Let A = {1, 2, 3, 4} , B = {2, 3, 4, 5, 6}, C = {2, 3, 4, 9, 10}
= {1, 2, 3, 4} {2, 3, 4, 5, 6}
= {2,3, 4}
= {1, 2, 3, 4}, B = {2, 3, 4, 5, 6}, C = {2, 3, 4, 9, 10}
= {2, 3, 4}
= {1, 2, 3, 4} {2, 3, 4, 9, 10}
= {2, 3, 4}
Now we have
But
12. According to the question,
4x + 9 < 50
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4x + 9 - 9 < 50 - 9 [subtracting 9 from both sides]
4x < 41
Since, x is a natural number, so x can take values 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Required set = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
13. A = {a, b, c, d} and B = {d, c, b, a} are equal sets because order of elements does not
change a set. A = B = {a, b, c, d}
14. Given, X = {a, b, c, d} and Y = {f, b, d, g}
i. X - Y
X - Y will contain elements of X which are not present in Y.
So, X - Y = {a, b, c, d } - { f , b, d, g} = {a, c}
This is also shown with the help of Venn diagram. The shaded portion is X - Y
ii. Y - X
Y - X will contain elements of Y which are not present in X.
So, Y - X = {f, b, d, g} - {a, b, c, d} = {f, g}
This is also shown with the help of Venn diagram. The shaded portion is Y - X
iii. X Y = {a, b, c, d) { f, b, d, g} = {b, d}
This is also shown with the help of Venn diagram. The shaded portion is X Y
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iv. X Y = (a, b, c, d} {f, b, d, g } = {a ,b ,c ,d ,f ,g}
This is also shown with the help of Venn diagram. The shaded portion is X Y
15. Let n(C) represent the number of people playing Cricket, n(T) represents the number
of people playing Tennis and n(V) represents the number of people playing Volleyball.
Let in Venn diagram a, b, c, d, e, f and g denote the number of elements in respective
regions.
Now, from the Venn diagram, we have
n( ) = a + b + c + d + e + f + g = 100 ...(i)
..........(ii)
..........(iii)
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......... (iv)
...............(v)
...........(vi)
...........(vii)
and n(C T V) = d
Using the identity,
-[n(C) + n(T) + n(V)] +
Thus, n( ) = d = 11
From Eq. (v), we get
From Eq. (vi), we get,
From Eq. (vii), we get,
From Eq. (iv), we get,
From Eq. (iii), we get,
From Eq. (ii), we get,
Hence,
i. the number of people who like to play all three games,
ii. the number of people who like to play Cricket only,
iii. the number of people who like to play Tennis only,
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