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The sum of the binomial coefficients in the expansion of (x−3/4 + ax5/4)n lies between 200 and 400 and the term independent of x equals 448. The value of a is
- a)1
- b)2
- c)1/2
- d)for no value of a
Correct answer is option 'B'. Can you explain this answer?
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The sum of the binomial coefficients in the expansion of (x−3/4 ...
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The sum of the binomial coefficients in the expansion of (x−3/4 ...
Explanation:
Given Information:
The given expression is (x-3/4 + ax^5/4)^n.
Constraints:
1. The sum of the binomial coefficients in the expansion lies between 200 and 400.
2. The term independent of x equals 448.
Approach:
1. Use the binomial theorem to expand the given expression.
2. Find the term independent of x in the expansion.
3. Set up the inequality based on the sum of binomial coefficients.
4. Solve for the value of 'a'.
Expanding the Expression:
The general form of the binomial theorem is (a + b)^n = Σ(n choose k)a^(n-k)b^k, where k ranges from 0 to n.
Expanding (x-3/4 + ax^5/4)^n will yield a series of terms involving combinations of x and coefficients.
Term Independent of x:
To find the term independent of x, look for the term where x has a power of 0. This term will be independent of x.
Let the term independent of x be T.
Set T = 448 and solve for 'a'.
Sum of Binomial Coefficients:
The sum of binomial coefficients in the expansion is the sum of all the coefficients in the binomial expansion.
Use the formula for the sum of binomial coefficients in the expansion to set up the inequality.
Solving for 'a':
By satisfying the constraints and solving for 'a', you can determine the value of 'a'.
In this case, the value of 'a' should be 2.
Therefore, the correct answer is option 'B' (a = 2).
Given Information:
The given expression is (x-3/4 + ax^5/4)^n.
Constraints:
1. The sum of the binomial coefficients in the expansion lies between 200 and 400.
2. The term independent of x equals 448.
Approach:
1. Use the binomial theorem to expand the given expression.
2. Find the term independent of x in the expansion.
3. Set up the inequality based on the sum of binomial coefficients.
4. Solve for the value of 'a'.
Expanding the Expression:
The general form of the binomial theorem is (a + b)^n = Σ(n choose k)a^(n-k)b^k, where k ranges from 0 to n.
Expanding (x-3/4 + ax^5/4)^n will yield a series of terms involving combinations of x and coefficients.
Term Independent of x:
To find the term independent of x, look for the term where x has a power of 0. This term will be independent of x.
Let the term independent of x be T.
Set T = 448 and solve for 'a'.
Sum of Binomial Coefficients:
The sum of binomial coefficients in the expansion is the sum of all the coefficients in the binomial expansion.
Use the formula for the sum of binomial coefficients in the expansion to set up the inequality.
Solving for 'a':
By satisfying the constraints and solving for 'a', you can determine the value of 'a'.
In this case, the value of 'a' should be 2.
Therefore, the correct answer is option 'B' (a = 2).
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The sum of the binomial coefficients in the expansion of (x−3/4 + ax5/4)n lies between 200 and 400 and the term independent of x equals 448. The value of a isa)1 b)2 c)1/2 d)for no value of a Correct answer is option 'B'. Can you explain this answer? for Mathematics 2026 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The sum of the binomial coefficients in the expansion of (x−3/4 + ax5/4)n lies between 200 and 400 and the term independent of x equals 448. The value of a isa)1 b)2 c)1/2 d)for no value of a Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the binomial coefficients in the expansion of (x−3/4 + ax5/4)n lies between 200 and 400 and the term independent of x equals 448. The value of a isa)1 b)2 c)1/2 d)for no value of a Correct answer is option 'B'. Can you explain this answer?.
The sum of the binomial coefficients in the expansion of (x−3/4 + ax5/4)n lies between 200 and 400 and the term independent of x equals 448. The value of a isa)1 b)2 c)1/2 d)for no value of a Correct answer is option 'B'. Can you explain this answer? for Mathematics 2026 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The sum of the binomial coefficients in the expansion of (x−3/4 + ax5/4)n lies between 200 and 400 and the term independent of x equals 448. The value of a isa)1 b)2 c)1/2 d)for no value of a Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the binomial coefficients in the expansion of (x−3/4 + ax5/4)n lies between 200 and 400 and the term independent of x equals 448. The value of a isa)1 b)2 c)1/2 d)for no value of a Correct answer is option 'B'. Can you explain this answer?.
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