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).
Quiz-summary
0 of 5 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
Information
Best of Luck! 🙂
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Results
0 of 5 questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 points, (0)
Categories
- Not categorized 0%
- 1
- 2
- 3
- 4
- 5
- Answered
- Review
-
Question 1 of 5
1. Question
If p and q are positive integers such that:
A = 8p + 11
B = 4q + 5then which of the following is definitely true for the value of A + B?
Correct
Answer: (b)
Explanation:
A + B = 8p + 11 + 4q + 5
A + B = 8p + 4q + 16
Now,
8p is divisible by 4.
4q is divisible by 4.
16 is divisible by 4.So,
A + B is always divisible by 4.
But it is not always divisible by 3, 5 or 8.
Hence, the correct answer is (b).
Incorrect
Answer: (b)
Explanation:
A + B = 8p + 11 + 4q + 5
A + B = 8p + 4q + 16
Now,
8p is divisible by 4.
4q is divisible by 4.
16 is divisible by 4.So,
A + B is always divisible by 4.
But it is not always divisible by 3, 5 or 8.
Hence, the correct answer is (b).
-
Question 2 of 5
2. Question
Let p be a prime number greater than 5. Then (p² − 1) i
Correct
Answer: (a)
Explanation:
Any prime number greater than 5 is odd.
So, p − 1 and p + 1 are consecutive even numbers.
Their product is divisible by 8.
Also, p is not divisible by 3.
So, either p − 1 or p + 1 must be divisible by 3.
Therefore,
p² − 1 = (p − 1)(p + 1)
is divisible by 8 and 3.
So, p² − 1 is always divisible by 24.
It is not always divisible by 5.
Example:
p = 7
p² − 1 = 49 − 1 = 48
48 is not divisible by 5.
Hence, the correct answer is (a).
Incorrect
Answer: (a)
Explanation:
Any prime number greater than 5 is odd.
So, p − 1 and p + 1 are consecutive even numbers.
Their product is divisible by 8.
Also, p is not divisible by 3.
So, either p − 1 or p + 1 must be divisible by 3.
Therefore,
p² − 1 = (p − 1)(p + 1)
is divisible by 8 and 3.
So, p² − 1 is always divisible by 24.
It is not always divisible by 5.
Example:
p = 7
p² − 1 = 49 − 1 = 48
48 is not divisible by 5.
Hence, the correct answer is (a).
-
Question 3 of 5
3. Question
Each digit of a 6-digit number is 1. It is multiplied by itself. What is the sum of the digits of the resulting number?
Correct
Answer: (b)
Explanation:
The 6-digit number is:
111111
Now multiply it by itself:
111111 × 111111 = 12345654321
Now find the sum of digits:
1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 36
Hence, the correct answer is (b).
Incorrect
Answer: (b)
Explanation:
The 6-digit number is:
111111
Now multiply it by itself:
111111 × 111111 = 12345654321
Now find the sum of digits:
1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 36
Hence, the correct answer is (b).
-
Question 4 of 5
4. Question
Consider the Question and two Statements given below:
Question: Is p a rational number?
Statement 1: p² is an integer.
Statement 2: p + 4 is a rational number.Which one of the following is correct?
Correct
Answer: (b)
Explanation:
From Statement 1:
p² is an integer.
But p may be rational or irrational.
Example:
p = 3 gives p² = 9.
p = √2 gives p² = 2.
So, Statement 1 alone is not sufficient.
From Statement 2:
p + 4 is rational.
Since 4 is rational, p must also be rational.
So, Statement 2 alone is sufficient.
Hence, the correct answer is (b).
Incorrect
Answer: (b)
Explanation:
From Statement 1:
p² is an integer.
But p may be rational or irrational.
Example:
p = 3 gives p² = 9.
p = √2 gives p² = 2.
So, Statement 1 alone is not sufficient.
From Statement 2:
p + 4 is rational.
Since 4 is rational, p must also be rational.
So, Statement 2 alone is sufficient.
Hence, the correct answer is (b).
-
Question 5 of 5
5. Question
If T is the sum of all three-digit numbers divisible by both 15 and 20, then consider the following statements:
Statement 1: T is divisible by 60.
Statement 2: The value of T/10 is an odd number.Which of the above-mentioned statements is/are correct?
Correct
Answer: (a)
Explanation:
Numbers divisible by both 15 and 20 must be divisible by their LCM.
LCM of 15 and 20 = 60
Smallest three-digit multiple of 60 = 120
Largest three-digit multiple of 60 = 960So, the series is:
120, 180, 240, …, 960
Number of terms:
(960 − 120)/60 + 1
= 840/60 + 1
= 14 + 1
= 15
Now,
T = 15/2 × (120 + 960)
T = 15/2 × 1080
T = 15 × 540
T = 8100
Statement 1:
8100 is divisible by 60.
So, Statement 1 is correct.
Statement 2:
T/10 = 8100/10 = 810
810 is even, not odd.
So, Statement 2 is incorrect.
Hence, the correct answer is (a).
Incorrect
Answer: (a)
Explanation:
Numbers divisible by both 15 and 20 must be divisible by their LCM.
LCM of 15 and 20 = 60
Smallest three-digit multiple of 60 = 120
Largest three-digit multiple of 60 = 960So, the series is:
120, 180, 240, …, 960
Number of terms:
(960 − 120)/60 + 1
= 840/60 + 1
= 14 + 1
= 15
Now,
T = 15/2 × (120 + 960)
T = 15/2 × 1080
T = 15 × 540
T = 8100
Statement 1:
8100 is divisible by 60.
So, Statement 1 is correct.
Statement 2:
T/10 = 8100/10 = 810
810 is even, not odd.
So, Statement 2 is incorrect.
Hence, the correct answer is (a).
