1.
பின்வருவனவற்றுள் எது மெய்யான கூற்றல்ல ?
Correct Answer
A. (1) ஒவ்வொரு சார்பும் ஒரு தொடர்வரிசையினைக் குறிக்கும்
Explanation
Each of the given options provides a statement about a sequence or series. Option (1) states that every term determines a sequence. This means that each term in the given series determines a sequence or series. The other options either discuss the calculation or representation of the terms in the series, but do not specifically address the relationship between the terms and a sequence. Therefore, option (1) is the correct answer.
2.
1,1,2,3,5,8,,.............. என்ற தொடர் வரிசையின் 8- வது உறுப்பு
Correct Answer
A. 21
Explanation
The given sequence is a Fibonacci sequence, where each term is the sum of the two preceding terms. The sequence starts with 1, 1, and then continues with 2, 3, 5, and 8. To find the 8th term, we need to continue the sequence by adding the previous two terms. Therefore, the 8th term is 13.
3.
என்ற தொடர்வரிசையில் , உறுப்பு 1/20 - க்கு அடுத்த உறுப்பு
Correct Answer
A. 1/30
Explanation
The given series is a decreasing sequence where each term is obtained by subtracting 1/20 from the previous term. Therefore, to find the next term, we subtract 1/20 from the current term. By doing so, we get 1/30 as the next term in the series.
4.
A , b,c என்பன ஒரு கூட்டுத்தொடர் வரிசையில் உள்ளன எனில் =
Correct Answer
A. 1
Explanation
The given expression 1/(a/c) simplifies to c/a. Therefore, the correct answer is c/a.
5.
A,b,c,l,m என்பன கூட்டுத்தொடர்வரிசையில் இருப்பின் a-4b+6c-4l+m =
Correct Answer
A. 0
Explanation
The given expression is a-4b+6c-4l+m. Since there is no information given about the values of a, b, c, l, and m, we cannot determine the exact value of the expression. However, if we assume that a, b, c, l, and m are all equal to zero, then the expression simplifies to 0-0+0-0+0=0. Therefore, the answer is 0.
6.
100n+10 என்பது ஒரு தொடர்வரிசையின் n வது உறுப்பு எனில் , அது
Correct Answer
A. ஒரு கூட்டுத்தொடர் வரிசை
Explanation
The given expression, 100n+10, represents a sequence of numbers where each term is obtained by multiplying n by 100 and then adding 10. This is a linear sequence with a common difference of 100. Therefore, the correct answer is "ஒரு கூட்டுத்தொடர் வரிசை" which translates to "an arithmetic sequence" in English.
7.
எனப்ன ஒரு கூட்டுத்தொடர்வரிசையிலுள்ளன . மேலும் எனில் 13 வது உறுப்பு
Correct Answer
A. 0
8.
என்பன ஒரு கூட்டுததொடர்வரிசை எனில் என்ற தொடர் வரிசையானது
Correct Answer
A. ஒரு கூட்டுத்தொடர் வரிசை
Explanation
The correct answer is "ஒரு கூட்டுத்தொடர் வரிசை" because the given sequence follows a pattern where each term is obtained by adding a constant value to the previous term.
9.
ஒரு கூட்டுத்தொடரின் அடுத்தடுத்த மூன்று உறுப்புக்கள் k+2 , 4k-6 , 3k-2 எனில் k -ன் மதிப்பு
Correct Answer
A. 3
Explanation
The given expression consists of three terms: k+2, 4k-6, and 3k-2. We are asked to find the value of k. By comparing the given expression with the answer choices, we can see that the third option, 5, satisfies the expression. When k=5, the three terms become 7, 14, and 13 respectively. Therefore, the value of k is 5.
10.
A,,b,c, l,m,n என்பன கூட்டுத் தொடர்வரிசையில் அமைந்துள்ளன எனில் ,
3a+7 , 3b+7 , 3c+7 , 3l+7 , 3m+7 , 3n+7 என்ற தொடர் வரிசை
Correct Answer
A. ஒரு கூட்டுத்தொடர்வரிசை
Explanation
The given sequence is formed by adding 7 to each element after multiplying it by 3. This is evident from the pattern of the sequence, where each element is obtained by multiplying the corresponding letter by 3 and adding 7. Therefore, the sequence can be classified as a "கூட்டுத்தொடர்வரிசை" (increasing sequence) where each term is obtained by adding a constant value to the previous term.
11.
ஒரு பெருக்குத் தொடர்வரிசையில் 3 -வது உறுப்பு 2 எனில் அதன் முதல் 5 உறுப்புக்களின் பெருக்கற்பலன்
(1) (2) 10 (3) (4) 15
Correct Answer
A. (1)
Explanation
In a geometric progression, each term is obtained by multiplying the previous term by a constant factor. In this case, the common ratio is 3/2. Starting with the first term 5, the second term is obtained by multiplying 5 by 3/2, which gives 7.5. Similarly, the third term is obtained by multiplying 7.5 by 3/2, which gives 11.25. Therefore, the first term in the sequence is 5, the second term is 7.5, and the third term is 11.25. So, the correct answer is (1).
12.
A , b , c என்பன ஒரு பெருக்குத்தொடர்வரிசையில் உள்ளன எனில் , =
Correct Answer
A. A/b
Explanation
The given expression is a/b, which represents the ratio of a to b. In the given sequence, a/b is the only option that represents the ratio between two elements in the sequence. The other options do not represent any ratio between the given elements. Therefore, a/b is the correct answer.
13.
X , 2x+2 , 3x+3 , என்பன ஒரு பெருக்குத்தொடர்வரிசையில் இருப்பின் 5x , 10x+10 , 15x+15 என்ற தொடர் வரிசையானது
Correct Answer
A. ஒரு பெருக்குத் தொடர்வரிசை
Explanation
The given sequence is formed by adding a constant value to each term. The pattern is that each term is obtained by adding (x+1) to the previous term. Therefore, the sequence is an arithmetic sequence with a common difference of (x+1). This type of sequence is known as a "progression" or "பெருக்குத் தொடர்வரிசை" in Tamil.
14.
-3 , -3 , -3 , ....... என்ற தொடர்வரிசையானது
Correct Answer
A. ஒரு கூட்டுத்தொடர்வரிசை மற்றும் பெருக்குத்தொடர் வரிசை
Explanation
The given sequence is repeating the number -3 continuously. This is an example of a periodic sequence where the same number or pattern repeats after a certain interval. In this case, the interval is 1, as the sequence is repeating the number -3 after every term. Therefore, the sequence can be classified as both an arithmetic sequence (as the difference between consecutive terms is 0) and a geometric sequence (as the ratio between consecutive terms is 1).
15.
ஒரு பெருக்குத்தொடர்வரிசையின் முதல் நான்கு உறுப்புக்களின் பெருக்கற்பலன் 256 அதன் பொது விகிதம் 4 மற்றும் அதன் உறுப்பு மிகை எண் எனில் அந்த பெருக்குத்தொடர்வரிசையின் 3-வது உறுப்பு
Correct Answer
A. 16
Explanation
The given arithmetic sequence has a common difference of 4 and the third term is being asked. To find the third term, we can use the formula:
nth term = first term + (n-1) * common difference
Plugging in the values, we get:
3rd term = 16 + (3-1) * 4 = 16 + 2 * 4 = 16 + 8 = 24
Therefore, the answer is 24.
16.
ஒரு பெருக்குத்தொடர் வரிசையில் மற்றும் எனில் பொதுவிகிதம்
Correct Answer
A. 1/3
Explanation
The given sequence of fractions is in ascending order. The numerator of each fraction is 1, while the denominators are 3, 5, 1, and 5 respectively. The fraction 1/3 is the first fraction in the sequence, which is the correct answer.
17.
X # 0 எனில் , +x + =
(1) ()
(2)
(3)
(4)
Correct Answer
A. (2)
18.
என்பது ஒரு கூட்டத்தொடர்வரிசையின் n- வது உறுப்பு எனில் அக் கூட்டுஙததொடர்வரிசையின் முதல் n உறுப்புக்களின் கூடுதல்
(1) (2) (3) (4)
Correct Answer
A. (1)
Explanation
The given answer is (1) because it states that the additional elements in the n-th term of the sequence are the first n elements of the sequence. This means that the sequence is formed by adding the first n terms to the original sequence.
19.
என்ற பெருக்குத்தொடர்வரிசையின் பொது விகிதம்
(1) (2) (3) (4)
Correct Answer
A. (2)
Explanation
The given sequence is (2), (1), (4), (3).
20.
1+2+3+....... +n = k எனில் + +..........+ என்பது
(1) (2) ( 3) (4)
Correct Answer
A. (1)
Explanation
The given question is asking for the correct symbol to fill in the blanks. The equation given is a sum of consecutive numbers from 1 to n. The correct symbol to fill in the blanks is "+". This is because the equation is asking for the sum of all the numbers from 1 to n, and the "+" symbol is used to indicate addition. Therefore, the correct answer is (1).