[Mission 2024] Insta–DART (Daily Aptitude and Reasoning Test) 1 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 (x+y) : (x-y)=3:5 and xy = positive imply that (a) X and y both positive (b) X and y are both negative (c) One of them is positive and one of them is negative (d) No real solutions for x and y exist Correct Ans: d Given that, (x+y) : (x-y) = 3:5 (x+y)/(x-y) = 3/5 Applying componendo and dividend rule, we get [(x+y)+(x-y)]/[(x+y)-(x-y)] = (3+5)/(3-5) 2x/2y = 8/-2 x/y = -4 ∴x= -4y But it is given, xy = Positive ∴-4yxy = Positive -4y2 = Poitive, which is not possible. Hence, no real solution for x and y exist. Incorrect Ans: d Given that, (x+y) : (x-y) = 3:5 (x+y)/(x-y) = 3/5 Applying componendo and dividend rule, we get [(x+y)+(x-y)]/[(x+y)-(x-y)] = (3+5)/(3-5) 2x/2y = 8/-2 x/y = -4 ∴x= -4y But it is given, xy = Positive ∴-4yxy = Positive -4y2 = Poitive, which is not possible. Hence, no real solution for x and y exist.
#### 1. Question
(x+y) : (x-y)=3:5 and xy = positive imply that
• (a) X and y both positive
• (b) X and y are both negative
• (c) One of them is positive and one of them is negative
• (d) No real solutions for x and y exist
Given that, (x+y) : (x-y) = 3:5
(x+y)/(x-y) = 3/5
Applying componendo and dividend rule, we get
[(x+y)+(x-y)]/[(x+y)-(x-y)] = (3+5)/(3-5)
2x/2y = 8/-2
But it is given, xy = Positive
∴-4yxy = Positive
-4y2 = Poitive, which is not possible.
Hence, no real solution for x and y exist.
Given that, (x+y) : (x-y) = 3:5
(x+y)/(x-y) = 3/5
Applying componendo and dividend rule, we get
[(x+y)+(x-y)]/[(x+y)-(x-y)] = (3+5)/(3-5)
2x/2y = 8/-2
But it is given, xy = Positive
∴-4yxy = Positive
-4y2 = Poitive, which is not possible.
Hence, no real solution for x and y exist.
• Question 2 of 5 2. Question If A:B = 2:3, B:C = 5:7 and C:D = 3: 10, then what is A 😀 equal to? (a) 1:7 (b) 2:7 (c) 1:5 (d) 5:1 Correct Ans: a Given, A:B = 2:3, B:C = 5:7 and C:D = 3:10 (A/D)= (A/B)x (B/C) ×(C/D)= (2/3) x(5/7)x (3/10) = 1/7 A:D = 1:7 Incorrect Ans: a Given, A:B = 2:3, B:C = 5:7 and C:D = 3:10 (A/D)= (A/B)x (B/C) ×(C/D)= (2/3) x(5/7)x (3/10) = 1/7 A:D = 1:7
#### 2. Question
If A:B = 2:3, B:C = 5:7 and C:D = 3: 10, then what is A 😀 equal to?
Given, A:B = 2:3, B:C = 5:7 and C:D = 3:10
(A/D)= (A/B)x (B/C) ×(C/D)= (2/3) x(5/7)x (3/10) = 1/7
Given, A:B = 2:3, B:C = 5:7 and C:D = 3:10
(A/D)= (A/B)x (B/C) ×(C/D)= (2/3) x(5/7)x (3/10) = 1/7
• Question 3 of 5 3. Question If a, b, c, d and e are in continued proportion, then a/e is equal to (a) a3/b3 (a) a3/b3 (c) b3/a3 (d) b4/a4 Correct Since, a, b, c, d and e are in continued proportion ∴a/b = b/c = c/d = d/e e/d = d/c = c/b = b/a ∴c= b2/a [because c/b = b/a] ∴d = c2/b = (b4/a2).(1/b = b3/a3 ∴e = d2/c =( b6/a4).(a/b2) = b4/a3 a/e = a/(b4/a3) = a4/b4 Incorrect Since, a, b, c, d and e are in continued proportion ∴a/b = b/c = c/d = d/e e/d = d/c = c/b = b/a ∴c= b2/a [because c/b = b/a] ∴d = c2/b = (b4/a2).(1/b = b3/a3 ∴e = d2/c =( b6/a4).(a/b2) = b4/a3 a/e = a/(b4/a3) = a4/b4
#### 3. Question
If a, b, c, d and e are in continued proportion, then a/e is equal to
Since, a, b, c, d and e are in continued proportion
∴a/b = b/c = c/d = d/e
e/d = d/c = c/b = b/a
[because c/b = b/a]
∴d = c2/b = (b4/a2).(1/b = b3/a3
∴e = d2/c =( b6/a4).(a/b2) = b4/a3
a/e = a/(b4/a3) = a4/b4
Since, a, b, c, d and e are in continued proportion
∴a/b = b/c = c/d = d/e
e/d = d/c = c/b = b/a
[because c/b = b/a]
∴d = c2/b = (b4/a2).(1/b = b3/a3
∴e = d2/c =( b6/a4).(a/b2) = b4/a3
a/e = a/(b4/a3) = a4/b4
• Question 4 of 5 4. Question In a certain school, the ratio of boys to girls is 7:5. If there are 2400 students in the school, then how many girls are there? (a) 500 (b) 700 (c) 800 (d) 1000 Correct Ans: d Let the number of boys and girls be 7x and 5x, respectively. Given, total number of students = 2400 7x + 5x = 2400 12x = 2400 x=200 Required number of girls = 5x = 5´ 200 = 1000 Incorrect Ans: d Let the number of boys and girls be 7x and 5x, respectively. Given, total number of students = 2400 7x + 5x = 2400 12x = 2400 x=200 Required number of girls = 5x = 5´ 200 = 1000
#### 4. Question
In a certain school, the ratio of boys to girls is 7:5. If there are 2400 students in the school, then how many girls are there?
Let the number of boys and girls be 7x and 5x, respectively.
Given, total number of students = 2400
7x + 5x = 2400
12x = 2400
Required number of girls = 5x = 5´ 200 = 1000
Let the number of boys and girls be 7x and 5x, respectively.
Given, total number of students = 2400
7x + 5x = 2400
12x = 2400
Required number of girls = 5x = 5´ 200 = 1000
• Question 5 of 5 5. Question Age of X is six times that of Y. After 4 yr, X is four times elder to Y. What is the present age of Y? (a) 4 yr (b) 5 yr (c) 6 yr (d) 7 yr Correct Ans: c Let the age of X and Y be x and y, respectively. X=6y Then, (x+4)=4(y+4) 6y+4=4y+16 2y=12 ∴y=6 So, the present age of Y is 6 yr. Incorrect Ans: c Let the age of X and Y be x and y, respectively. X=6y Then, (x+4)=4(y+4) 6y+4=4y+16 2y=12 ∴y=6 So, the present age of Y is 6 yr.
#### 5. Question
Age of X is six times that of Y. After 4 yr, X is four times elder to Y. What is the present age of Y?
Let the age of X and Y be x and y, respectively.
Then, (x+4)=4(y+4)
6y+4=4y+16
So, the present age of Y is 6 yr.
Let the age of X and Y be x and y, respectively.
Then, (x+4)=4(y+4)
6y+4=4y+16
So, the present age of Y is 6 yr.
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