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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): The number of ways of selecting two elements x and y from the set S = {1, 5, 9, 13,...,1093} such that x + y = 1094 is 137.
Reason(R) : The elements of S are in A.P. with common difference 4 and number of terms 274.
Assertion(A): The number of ways of selecting two elements x and y from the set S = {1, 5, 9, 13,...,1093} such that x + y = 1094 is 137.
Reason(R) : The elements of S are in A.P. with common difference 4 and number of terms 274.
- a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- c)Assertion is true but Reason is false.
- d)Assertion is false but Reason is true.
Correct answer is option 'A'. Can you explain this answer?
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In the following question, a Statement of Assertion (A) is given follo...
Assertion(A): The number of ways of selecting two elements x and y from the set S = {1, 5, 9, 13,...,1093} such that x + y = 1094 is 137.
Reason(R): The elements of S are in A.P. with common difference 4 and number of terms 274.
Explanation:
To solve this problem, let's first understand the given set S and its properties.
Properties of Set S:
- Set S contains numbers in an arithmetic progression (A.P.) with a common difference of 4.
- The first term of the A.P. is 1, and the last term is 1093.
- The number of terms in the set S is 274.
Step 1: Finding the sum of the first and last term:
The sum of the first and last term of an A.P. can be calculated using the formula:
Sum = (n/2)(first term + last term)
Using this formula, we can find the sum of the first and last term of S:
Sum = (274/2)(1 + 1093) = 137(1 + 1093) = 137 * 1094
Step 2: Finding the number of ways to select two elements:
To find the number of ways to select two elements x and y from S such that x + y = 1094, we need to consider all possible pairs of elements that sum up to 1094.
Let's consider an example to understand this:
If we select x = 1, then y must be 1093 to satisfy the condition x + y = 1094.
Similarly, if we select x = 5, then y must be 1089.
We can observe that for each element x in the set S, there is a unique element y that satisfies the condition x + y = 1094. Therefore, the number of ways to select two elements is equal to the number of elements in the set S, which is 274.
Step 3: Verifying the Assertion and Reason:
From the above steps, we can see that both the Assertion and Reason are true.
- Assertion: The number of ways of selecting two elements x and y from the set S = {1, 5, 9, 13,...,1093} such that x + y = 1094 is 137.
- Reason: The elements of S are in A.P. with common difference 4 and the number of terms is 274.
Conclusion:
Both the Assertion and Reason are true, and the Reason is the correct explanation of the Assertion. Therefore, the correct answer is option 'A'.
Reason(R): The elements of S are in A.P. with common difference 4 and number of terms 274.
Explanation:
To solve this problem, let's first understand the given set S and its properties.
Properties of Set S:
- Set S contains numbers in an arithmetic progression (A.P.) with a common difference of 4.
- The first term of the A.P. is 1, and the last term is 1093.
- The number of terms in the set S is 274.
Step 1: Finding the sum of the first and last term:
The sum of the first and last term of an A.P. can be calculated using the formula:
Sum = (n/2)(first term + last term)
Using this formula, we can find the sum of the first and last term of S:
Sum = (274/2)(1 + 1093) = 137(1 + 1093) = 137 * 1094
Step 2: Finding the number of ways to select two elements:
To find the number of ways to select two elements x and y from S such that x + y = 1094, we need to consider all possible pairs of elements that sum up to 1094.
Let's consider an example to understand this:
If we select x = 1, then y must be 1093 to satisfy the condition x + y = 1094.
Similarly, if we select x = 5, then y must be 1089.
We can observe that for each element x in the set S, there is a unique element y that satisfies the condition x + y = 1094. Therefore, the number of ways to select two elements is equal to the number of elements in the set S, which is 274.
Step 3: Verifying the Assertion and Reason:
From the above steps, we can see that both the Assertion and Reason are true.
- Assertion: The number of ways of selecting two elements x and y from the set S = {1, 5, 9, 13,...,1093} such that x + y = 1094 is 137.
- Reason: The elements of S are in A.P. with common difference 4 and the number of terms is 274.
Conclusion:
Both the Assertion and Reason are true, and the Reason is the correct explanation of the Assertion. Therefore, the correct answer is option 'A'.
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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A): The number of ways of selecting two elements x and y from the set S = {1, 5, 9, 13,...,1093} such that x + y = 1094 is 137.Reason(R) : The elements of S are in A.P. with common difference 4 and number of terms 274.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer?
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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A): The number of ways of selecting two elements x and y from the set S = {1, 5, 9, 13,...,1093} such that x + y = 1094 is 137.Reason(R) : The elements of S are in A.P. with common difference 4 and number of terms 274.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A): The number of ways of selecting two elements x and y from the set S = {1, 5, 9, 13,...,1093} such that x + y = 1094 is 137.Reason(R) : The elements of S are in A.P. with common difference 4 and number of terms 274.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A): The number of ways of selecting two elements x and y from the set S = {1, 5, 9, 13,...,1093} such that x + y = 1094 is 137.Reason(R) : The elements of S are in A.P. with common difference 4 and number of terms 274.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer?.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A): The number of ways of selecting two elements x and y from the set S = {1, 5, 9, 13,...,1093} such that x + y = 1094 is 137.Reason(R) : The elements of S are in A.P. with common difference 4 and number of terms 274.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A): The number of ways of selecting two elements x and y from the set S = {1, 5, 9, 13,...,1093} such that x + y = 1094 is 137.Reason(R) : The elements of S are in A.P. with common difference 4 and number of terms 274.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A): The number of ways of selecting two elements x and y from the set S = {1, 5, 9, 13,...,1093} such that x + y = 1094 is 137.Reason(R) : The elements of S are in A.P. with common difference 4 and number of terms 274.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer?.
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