UPSC Insta–DART (Daily Aptitude and Reasoning Test) 3 Feb 2025
Kartavya Desk Staff
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).
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• Question 1 of 5 1. Question How many 5-digit passwords can be formed without repetition where they start with 3 symmetric alphabets (mirror image) and the rest are numbers? (a) 89100 (b) 81900 (c) 71280 (d) 99000 Correct Answer: Option (a) Explanation: The 11 Letters A, H, I, M, O, T, U, V, W, X and Y are symmetrical. 3 letters can be arranged in 11P3 ways. i.e., 11 x 10 × 9 = 990 2 numbers can be arranged in 10P2 ways. i.e., 10 × 9 = 90 Number of ways to form the password = 990 × 90 = 89100 Hence, option (a) is the right answer. Incorrect Answer: Option (a) Explanation: The 11 Letters A, H, I, M, O, T, U, V, W, X and Y are symmetrical. 3 letters can be arranged in 11P3 ways. i.e., 11 x 10 × 9 = 990 2 numbers can be arranged in 10P2 ways. i.e., 10 × 9 = 90 Number of ways to form the password = 990 × 90 = 89100 Hence, option (a) is the right answer.
#### 1. Question
How many 5-digit passwords can be formed without repetition where they start with 3 symmetric alphabets (mirror image) and the rest are numbers?
Answer: Option (a)
Explanation:
The 11 Letters A, H, I, M, O, T, U, V, W, X and Y are symmetrical.
3 letters can be arranged in 11P3 ways. i.e., 11 x 10 × 9 = 990
2 numbers can be arranged in 10P2 ways. i.e., 10 × 9 = 90
Number of ways to form the password = 990 × 90 = 89100 Hence, option (a) is the right answer.
Answer: Option (a)
Explanation:
The 11 Letters A, H, I, M, O, T, U, V, W, X and Y are symmetrical.
3 letters can be arranged in 11P3 ways. i.e., 11 x 10 × 9 = 990
2 numbers can be arranged in 10P2 ways. i.e., 10 × 9 = 90
Number of ways to form the password = 990 × 90 = 89100 Hence, option (a) is the right answer.
• Question 2 of 5 2. Question A student found HCF of two numbers to be 2, instead of the LCM. If the numbers are in the ratio 4 : 7, what is the LCM? (a) 84 (b) 112 (c) 56 (d) 168 Correct Answer: Option © Explanation: A : B = 4 : 7 So, A = 4x, B = 7x HCF = x = 2 (given) Therefore, A = 8, B = 14 LCM (A, B) = 56 Hence, option © is the right answer. Incorrect Answer: Option c Explanation: A : B = 4 : 7 So, A = 4x, B = 7x HCF = x = 2 (given) Therefore, A = 8, B = 14 LCM (A, B) = 56 Hence, option c is the right answer.
#### 2. Question
A student found HCF of two numbers to be 2, instead of the LCM. If the numbers are in the ratio 4 : 7, what is the LCM?
Answer: Option ©
Explanation:
A : B = 4 : 7
So, A = 4x, B = 7x
HCF = x = 2 (given)
Therefore, A = 8, B = 14
LCM (A, B) = 56 Hence, option © is the right answer.
Answer: Option c
Explanation:
A : B = 4 : 7
So, A = 4x, B = 7x
HCF = x = 2 (given)
Therefore, A = 8, B = 14
LCM (A, B) = 56 Hence, option c is the right answer.
• Question 3 of 5 3. Question In a shooting game, there are 7 yellow, 3 red and 4 black balloons on the wall. If Suresh shoots one balloon randomly, then what is probability that the balloon shot by him is not a red balloon? (a) 11/18 (b) 3/11 (b) 3/11 (d) 11/14 Correct Answer: Option (d) Explanation: Total number of balloons = 7 + 3 + 4 = 14 One balloon can be shot out of 14C1 ways A balloon other than a red balloon (7 + 4 = 11) can be shot in 11C1 ways Hence, probability of not shooting a red balloon = 11C1/14C1 = 11/14 Hence, option (d) is the right answer. Incorrect Answer: Option (d) Explanation: Total number of balloons = 7 + 3 + 4 = 14 One balloon can be shot out of 14C1 ways A balloon other than a red balloon (7 + 4 = 11) can be shot in 11C1 ways Hence, probability of not shooting a red balloon = 11C1/14C1 = 11/14 Hence, option (d) is the right answer.
#### 3. Question
In a shooting game, there are 7 yellow, 3 red and 4 black balloons on the wall. If Suresh shoots one balloon randomly, then what is probability that the balloon shot by him is not a red balloon?
Answer: Option (d)
Explanation:
Total number of balloons = 7 + 3 + 4 = 14
One balloon can be shot out of 14C1 ways
A balloon other than a red balloon (7 + 4 = 11) can be shot in 11C1 ways
Hence, probability of not shooting a red balloon = 11C1/14C1 = 11/14 Hence, option (d) is the right answer.
Answer: Option (d)
Explanation:
Total number of balloons = 7 + 3 + 4 = 14
One balloon can be shot out of 14C1 ways
A balloon other than a red balloon (7 + 4 = 11) can be shot in 11C1 ways
Hence, probability of not shooting a red balloon = 11C1/14C1 = 11/14 Hence, option (d) is the right answer.
• Question 4 of 5 4. Question How many 4 digit numbers are there such that the product of the digits is less than 5? (a) 13 (b) 19 (c) 15 (d) 21 Correct Answer: Option (b) Explanation: For the product of a 4-digit number to be lesser than 8, it should comprise of either 1, 2, 3, 4, 5, 6 or 7 in a certain way. Let’s start with Product 1 => Possible in only one way (1111). Product 2 => Possible in 4 ways (2111, 1211, 1121 and 1112). Product 3=> Possible in 4 ways (3111, 1311, 1131 and 1113). Product 4 => Possible in 10 ways (4111, 1411, 1141, 1114, 2211, 2121, 2112, 1122, 1212 and 1221). Total = 1 + 4 + 4 + 10 =19 numbers. Hence, option (b) is the right answer. Incorrect Answer: Option (b) Explanation: For the product of a 4-digit number to be lesser than 8, it should comprise of either 1, 2, 3, 4, 5, 6 or 7 in a certain way. Let’s start with Product 1 => Possible in only one way (1111). Product 2 => Possible in 4 ways (2111, 1211, 1121 and 1112). Product 3=> Possible in 4 ways (3111, 1311, 1131 and 1113). Product 4 => Possible in 10 ways (4111, 1411, 1141, 1114, 2211, 2121, 2112, 1122, 1212 and 1221). Total = 1 + 4 + 4 + 10 =19 numbers. Hence, option (b) is the right answer.
#### 4. Question
How many 4 digit numbers are there such that the product of the digits is less than 5?
Answer: Option (b)
Explanation:
For the product of a 4-digit number to be lesser than 8, it should comprise of either 1, 2, 3, 4, 5, 6 or 7 in a certain way.
Let’s start with
Product 1 => Possible in only one way (1111).
Product 2 => Possible in 4 ways (2111, 1211, 1121 and 1112).
Product 3=> Possible in 4 ways (3111, 1311, 1131 and 1113).
Product 4 => Possible in 10 ways (4111, 1411, 1141, 1114, 2211, 2121, 2112, 1122, 1212 and 1221).
Total = 1 + 4 + 4 + 10 =19 numbers. Hence, option (b) is the right answer.
Answer: Option (b)
Explanation:
For the product of a 4-digit number to be lesser than 8, it should comprise of either 1, 2, 3, 4, 5, 6 or 7 in a certain way.
Let’s start with
Product 1 => Possible in only one way (1111).
Product 2 => Possible in 4 ways (2111, 1211, 1121 and 1112).
Product 3=> Possible in 4 ways (3111, 1311, 1131 and 1113).
Product 4 => Possible in 10 ways (4111, 1411, 1141, 1114, 2211, 2121, 2112, 1122, 1212 and 1221).
Total = 1 + 4 + 4 + 10 =19 numbers. Hence, option (b) is the right answer.
• Question 5 of 5 5. Question A question is given followed by information in two statements. You have to consider the information in the two statements and decide that which of the statement(s) is necessarily required to answer the question. What is the temperature on Tuesday? I. Average temperature for Monday, Tuesday and Wednesday is 340C II. Average temperature for Tuesday, Wednesday and Thursday is 380C (a) Only I is sufficient to answer the question (b) Only II is sufficient to answer the question (c) Either I or II is sufficient to answer the question (d) Both I & II are not sufficient to answer the question Correct Answer: Option (d) Explanation: From I Monday + Tuesday + Wednesday = 340C × 3 = 1020 C From II Tuesday + Wednesday + Thursday = 380C × 3 = 1140 C Here, statement I and statement II together are not sufficient to answer the question. Hence, option (d) is the right answer. Incorrect Answer: Option (d) Explanation: From I Monday + Tuesday + Wednesday = 340C × 3 = 1020 C From II Tuesday + Wednesday + Thursday = 380C × 3 = 1140 C Here, statement I and statement II together are not sufficient to answer the question. Hence, option (d) is the right answer.
#### 5. Question
A question is given followed by information in two statements. You have to consider the information in the two statements and decide that which of the statement(s) is necessarily required to answer the question.
What is the temperature on Tuesday?
I. Average temperature for Monday, Tuesday and Wednesday is 340C
II. Average temperature for Tuesday, Wednesday and Thursday is 380C
• (a) Only I is sufficient to answer the question
• (b) Only II is sufficient to answer the question
• (c) Either I or II is sufficient to answer the question
• (d) Both I & II are not sufficient to answer the question
Answer: Option (d)
Explanation:
Monday + Tuesday + Wednesday = 340C × 3 = 1020 C
Tuesday + Wednesday + Thursday = 380C × 3 = 1140 C
Here, statement I and statement II together are not sufficient to answer the question. Hence, option (d) is the right answer.
Answer: Option (d)
Explanation:
Monday + Tuesday + Wednesday = 340C × 3 = 1020 C
Tuesday + Wednesday + Thursday = 380C × 3 = 1140 C
Here, statement I and statement II together are not sufficient to answer the question. Hence, option (d) is the right answer.
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