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From an equality of ratios, deduce which relation holds

This type of question, asked 4 times: CDS 2 2019, CDS 2 2020, CDS 2 2021, CDS 2 2022. All 4 questions below, oldest first.

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  1. Question 1

    CDS 2 2019

    38
    If (4a+7b)(4c−7d)=(4a−7b)(4c+7d)(4a + 7b)(4c - 7d) = (4a - 7b)(4c + 7d), then which one of the following is correct ?

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  2. Question 2

    CDS 2 2020

    37
    If xb+c=yc+a=zb−a\dfrac{x}{b + c} = \dfrac{y}{c + a} = \dfrac{z}{b - a}, then which one of the following is correct ?

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  3. Question 3

    CDS 2 2021

    29
    If ay−bxc=cx−azb=bz−cya\dfrac{ay-bx}{c}=\dfrac{cx-az}{b}=\dfrac{bz-cy}{a}, then which of the following is/are correct ? 1. xa=yb\dfrac{x}{a}=\dfrac{y}{b} 2. x+y+za+b+c=zc\dfrac{x+y+z}{a+b+c}=\dfrac{z}{c} Select the correct answer using the code given below :

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  4. Question 4

    CDS 2 2022

    2
    If a+bb+c=c+dd+a\frac{a + b}{b + c} = \frac{c + d}{d + a} where a≠ca \ne c, then which one of the following is correct ?

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