[Mission 2024] Insta–DART (Daily Aptitude and Reasoning Test) 9 May 2024
Kartavya Desk Staff
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Considering the alarming importance of CSAT in UPSC CSE Prelims exam and with enormous requests we received recently, InsightsIAS has started Daily CSAT Test to ensure students practice CSAT Questions on a daily basis. Regular Practice would help one overcome the fear of CSAT too. We are naming this initiative as Insta– DART – Daily Aptitude and Reasoning Test. We hope you will be able to use DART to hit bull’s eye in CSAT paper and comfortably score 100+ even in the most difficult question paper that UPSC can give you in CSP-2021. Your peace of mind after every step of this exam is very important for us.
Looking forward to your enthusiastic participation (both in sending us questions and solving them on daily basis on this portal).
Wish you all the best ! 🙂
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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? a) 12 b) 10 c) 7 d) 6 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.
#### 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?
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.
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? (a) A= {x is a real number: x >1 and x < 1} (b) 8 {x: x +3= 3) (c) C= {Ø} (d) D={x is a real number : x ≥ 1 and x ≤ 1} 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
#### 2. Question
Which one of the following is a null set?
• (a) A= {x is a real number: x >1 and x < 1}
• (b) 8 {x: x +3= 3)
• (c) C= {Ø}
• (d) D={x is a real number : x ≥ 1 and x ≤ 1}
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
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? a) 18% b) 21% c) 23% d) 25% 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%
#### 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?
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%
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 a) null set b) singleton set c) infinite set d) None of these 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.
#### 4. Question
The set S = {x ∈N:x+3 = 3} is a
• a) null set
• b) singleton set
• c) infinite set
• d) None of these
Given, S = x ∈N: {x + 3 = 3}
So, S is a null set.
Given, S = x ∈N: {x + 3 = 3}
So, S is a null set.
• Question 5 of 5 5. Question Which one of the following is a correct statement (a) {a} ∈ {{a}, {b},c} (b) {a} ⊆ {{a}, b, c} (c) {a, b} ⊆{{a}, b, c} (d) a ⊆{ {a}, b, c} Correct Ans: a Here, {a) is an element of {{a}.{b},{c}} Incorrect Ans: a Here, {a) is an element of {{a}.{b},{c}}
#### 5. Question
Which one of the following is a correct statement
• (a) {a} ∈ {{a}, {b},c}
• (b) {a} ⊆ {{a}, b, c}
• (c) {a, b} ⊆{{a}, b, c}
• (d) a ⊆{ {a}, b, c}
Here, {a) is an element of {{a}.{b},{c}}
Here, {a) is an element of {{a}.{b},{c}}
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