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Question 1 of 5
1. Question
Let x ∈ {2, 3, 4} and y ∈ {4, 6, 9, 10). If A is the set of all order pairs (x, y) such that x is a factor of y.
Then, how many elements does the set A contain?
Correct
Ans: d
Given that, x∈{2, 3, 4) and y∈{4, 6, 9, 10)
and also A=x * y, such that r is a factor of y.
∴A {(2, 4), (2, 6), (2, 10), (3, 6), (3, 9). (4, 4)}
Hence, A contains 6 elements.
Incorrect
Ans: d
Given that, x∈{2, 3, 4) and y∈{4, 6, 9, 10)
and also A=x * y, such that r is a factor of y.
∴A {(2, 4), (2, 6), (2, 10), (3, 6), (3, 9). (4, 4)}
Hence, A contains 6 elements.

Question 2 of 5
2. Question
Which one of the following is a null set?
Correct
Ans: a
From option (a).
A={x is a real number: x> 1and x < 1}.
So, there is no element which is greater or less than 1.
So, A is a null set.
From option (b), B= {x:x+3 = 3) = {0} = Singleton set
From option (c), C = {Ø} = Singleton set
From option (d), D= {x is a real number: x ≥ and x≤ 1}
= {1} = Singleton set
Incorrect
Ans: a
From option (a).
A={x is a real number: x> 1and x < 1}.
So, there is no element which is greater or less than 1.
So, A is a null set.
From option (b), B= {x:x+3 = 3) = {0} = Singleton set
From option (c), C = {Ø} = Singleton set
From option (d), D= {x is a real number: x ≥ and x≤ 1}
= {1} = Singleton set

Question 3 of 5
3. Question
In an examination, 52% candidates failed in English and 42% failed in Mathematics. If 17% candidates failed in both English and Mathematics, then percentage of candidates passed in both the subjects?
Correct
Ans: c
Failed candidates in English, n(E) = 52%
Failed candidates in Maths, n(M) = 42%
Failed candidates in both English and Maths, n (E ∩M) = 17%
Because Total failed candidates,
n (E ∪ M) = n(E) + n(M) – n (E ∩ M)
= 52+ 42 – 17 = 77%
∴Total passed candidates = (100 – 77) = 23%
Incorrect
Ans: c
Failed candidates in English, n(E) = 52%
Failed candidates in Maths, n(M) = 42%
Failed candidates in both English and Maths, n (E ∩M) = 17%
Because Total failed candidates,
n (E ∪ M) = n(E) + n(M) – n (E ∩ M)
= 52+ 42 – 17 = 77%
∴Total passed candidates = (100 – 77) = 23%

Question 4 of 5
4. Question
The set S = {x ∈N:x+3 = 3} is a
Correct
Ans : a
Given, S = x ∈N: {x + 3 = 3}
∴S = {}
So, S is a null set.
Incorrect
Ans : a
Given, S = x ∈N: {x + 3 = 3}
∴S = {}
So, S is a null set.

Question 5 of 5
5. Question
Which one of the following is a correct statement
Correct
Ans: a
Here, {a) is an element of {{a}.{b},{c}}
Incorrect
Ans: a
Here, {a) is an element of {{a}.{b},{c}}
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