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If one variable varies as another, which derived expressions also vary

This type of question, asked 7 times: CDS 1 2020, CDS 2 2020, CDS 1 2021, CDS 2 2022, CDS 2 2023, CDS 1 2024, CDS 1 2026. All 7 questions below, oldest first.

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  1. Question 1

    CDS 1 2020

    24
    If xx varies as yzyz, then yy varies inversely as

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  2. Question 2

    CDS 2 2020

    26
    If xx varies as yy, then which of the following is/are correct ? 1. x2+y2x^2 + y^2 varies as x2−y2x^2 - y^2 2. xy2\frac{x}{y^2} varies inversely as yy 3. x2yn\sqrt[n]{x^2 y} varies as x4y22n\sqrt[2n]{x^4 y^2} Select the correct answer using the code given below :

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  3. Question 3

    CDS 1 2021

    15
    Consider the following statements : 1. If xx is directly proportional to zz and yy is directly proportional to zz, then (x2−y2)(x^2 - y^2) is directly proportional to z2z^2. 2. If xx is inversely proportional to zz and yy is inversely proportional to zz, then (xy)(xy) is inversely proportional to z2z^2. Which of the above statements is/are correct?

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  4. Question 4

    CDS 2 2022

    3
    If (a3+b3)(a^3 + b^3) is proportional to (a2−b2)(a^2 - b^2), then (a2−ab+b2)(a^2 - ab + b^2) is proportional to

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  5. Question 5

    CDS 2 2023

    21
    Consider the following statements : 1. If (a+b)(a + b) is directly proportional to (a−b)(a - b), then (a2+b2)(a^2 + b^2) is directly proportional to ab. 2. If a is directly proportional to b, then (a2−b2)(a^2 - b^2) is directly proportional to ab. Which of the statements given above is/are correct ?

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  6. Question 6

    CDS 1 2024

    58
    If P2P^2 varies as R and Q2Q^2 varies as R, (P≠Q)(P \ne Q), then which of the following are correct ? 1. P2+Q2P^2 + Q^2 varies as R. 2. PQ varies as R. 3. P2−Q2P^2 - Q^2 varies as R. Select the correct answer using the code given below :

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  7. Question 7

    CDS 1 2026

    13
    If x varies directly as y, then which of the following is/are correct ? I. (x2+y2)(x^2 + y^2) varies directly as y2y^2. II. (x3y4)\left(\frac{x^3}{y^4}\right) varies directly as y. Select the answer using the code given below :

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