Question:
If two distinct non-zero real variables \( x \) and \( y \) are such that \( (x + y) \) is proportional to \( (x - y) \), then the value of \( \frac{x}{y} \) is:
If two distinct non-zero real variables \( x \) and \( y \) are such that \( (x + y) \) is proportional to \( (x - y) \), then the value of \( \frac{x}{y} \) is:
Show Hint
Proportional relationships often simplify to constants. Always isolate terms to identify constants or dependencies.
Updated On: Jan 22, 2025
- depends on \( xy \)
- depends only on \( x \) and not on \( y \)
- depends only on \( y \) and not on \( x \)
- is a constant
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The given condition states that \( (x + y) \) is proportional to \( (x - y) \), which means:
\[
x + y = k (x - y),
\]
where \( k \) is a proportionality constant.
Step 1: Simplify the equation.
Rewriting the equation:
\[
x + y = kx - ky.
\]
Rearranging terms:
\[
x - kx = -ky - y.
\]
Factoring:
\[
x(1 - k) = -y(1 + k).
\]
Step 2: Solve for \( \frac{x}{y} \).
Divide both sides by \( y(1 - k) \) (assuming \( 1 - k \neq 0 \)):
\[
\frac{x}{y} = -\frac{1 + k}{1 - k}.
\]
Step 3: Interpret the result.
Since \( k \) is a constant, \( \frac{x}{y} \) is also a constant. It does not depend on \( x \) or \( y \) individually.
Final Answer:
\[
\boxed{\text{is a constant}}
\]
Was this answer helpful?
0
0
Top Questions on Sequence and Series
- If ‘→’ denotes increasing order of intensity, then the meaning of the words [talk → shout → scream] is analogous to [please → \_\_\_\_\_ → pander]. Which one of the given options is appropriate to fill the blank?
- GATE EE - 2024
- General Aptitude
- Sequence and Series
- Given an input line of numbers and words, a machine rearranges them following particular rule in each step. Here is an illustration of an input and rearrangement sequence (Step 1 to Step 5) :
Input: 61 wb ob 48 45 29 34 sb pb lb
Step 1: lb wb ob 48 45 29 34 sb pb 61
Step 2: lb ob wb 45 29 34 sb pb 61 48
Step 3: lb ob pb wb 29 34 sb 61 48 45
Step 4: lb ob pb sb wb 29 61 48 45 34
Step 5: lb ob pb sb wb 61 48 45 34 29
Step 5 is the last step of the above arrangement.
Based on the rules followed in the above steps, answer the following question :
Input: cb kb eb 58 49 23 38 jb nb gb 69 82
Which of the following represents the position of 58 in the fourth step? (Step-5 is the last step of the arrangement.)- GATE XH-C1 - 2024
- General Aptitude
- Sequence and Series
- Consider the sequence\( t_1 = 1, t_2 = -1 and t_n = \left( \frac{n-3}{n-1} \right) t_{n-2} for n \ge 3. \)Then, the value of the sum \(\frac{1}{t_2}\) + \(\frac{1}{t_4}\) + \(\frac{1}{t_6}\) + ……. + \(\frac{1}{t_{2022}}\) + \(\frac{1}{t_{2024}}\), is
- CAT - 2024
- Quantitative Aptitude
- Sequence and Series
- The sum of the infinite series \( \frac{1}{5} \left( \frac{1}{5} - \frac{1}{7} \right) + \left( \frac{1}{5} \right)^2 \left( \frac{1}{5} - \frac{1}{7} \right)^2 - \left( \frac{1}{7} \right)^2 + \left( \frac{1}{5} \right)^3 \left( \frac{1}{5} - \frac{1}{7} \right)^3 + \dots \) is equal to
- CAT - 2024
- Quantitative Aptitude
- Sequence and Series
- A shopkeeper sells half of the grains plus \(3 \, \text{kg}\) of grains to Customer 1, and then sells another half of the remaining grains plus \(3 \, \text{kg}\) to Customer 2. When the 3rd customer arrives, there are no grains left. Find the total grains that were initially present.
- CAT - 2024
- Quantitative Aptitude
- Sequence and Series
View More Questions
Questions Asked in GATE CS exam
- The number of distinct minimum-weight spanning trees of the following graph is ............ \begin{center} \includegraphics[width=0.5\textwidth]{59.png} \end{center}
- GATE CS - 2024
- Syntax Directed Translation
- Consider a 32-bit system with a 4 KB page size and page table entries of size 4 bytes each. Assume \(1 \, \text{KB} = 2^{10} \, \text{bytes}\). The OS uses a 2-level page table for memory management, with the page table containing an outer page directory and an inner page table. The OS allocates a page for the outer page directory upon process creation. The OS uses demand paging when allocating memory for the inner page table, i.e., a page of the inner page table is allocated only if it contains at least one valid page table entry.
An active process in this system accesses \(2000\) unique pages during its execution, and none of the pages are swapped out to disk. After it completes the page accesses, let \(X\) denote the minimum and \(Y\) denote the maximum number of pages across the two levels of the page table of the process. The value of \(X + Y\) is ............- GATE CS - 2024
- Lexical analysis
- Consider the following augmented grammar, which is to be parsed with an SLR parser. The set of terminals is \(\{a, b, c, d, \#, @\}\). \[ S' \rightarrow S \quad S \rightarrow SS \, | \, Aa \, | \, bAc \, | \, BC \, | \, bBa \quad A \rightarrow d\# \quad B \rightarrow @ \] Let \(I_0 = \text{CLOSURE}(\{S' \rightarrow \cdot S\}\). The number of items in the set \(GOTO(I_0, S)\) is ............
- GATE CS - 2024
- Syntax Directed Translation
- Let \(Z_n\) be the group of integers \(\{0, 1, 2, \dots, n - 1\}\) with addition modulo \(n\) as the group operation. The number of elements in the group \(Z_2 \times Z_3 \times Z_4\) that are their own inverses is ............
- GATE CS - 2024
- Indexed Address
- The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is ............ \begin{center} \includegraphics[width=0.3\textwidth]{60.png} \end{center}
- GATE CS - 2024
- Miscellaneous
View More Questions