If 2x2 = 3y2 = 12z2 then

Option c: 2/x2 + 1/y2 = 1/z2. Solution: Let us set the given equal expressions to a constant k (where k > 1 ): 2x2 = 3y2 = 12z2 = k This allows us to express the base numbers 2 , 3 , and $12 in terms of k : 2 = k1/x2 3 = k1/y2 12 = k1/z2 We know the mathematical relation between the numbers $12 , 2 , and 3 is: 12 = 4 × 3 = 22 × 3 Substitute the expressions of these numbers in terms of k into this equation: k1/z2 = (k1/x2)2 × k1/y2 Using the laws of exponents ( xa × xb = xa+b and (xa)b = xab ): k1/z2 = k2/x2 × k1/y2 k1/z2 = k2/x2 + 1/y2 Equating the exponents since the bases are identical: 2/x2 + 1/y2 = 1/z2 This corresponds to Option C. Note: The textbook designates Option B as correct. This discrepancy arises because of a typographical swap of bases in the question text. If the question had been written as 3x2 = 2y2 = 12z2 , then we would have 3 = k1/x2 and 2 = k1/y2 , which yields 1/x2 + 2/y2 = 1/z2 (Option B). However, for the given question text, the correct mathematical derivation leads to Option C. Hence, Option C is the correct answer.

If 2x2 = 3y2 = 12z2 then

The correct answer is Option c: 2/x2 + 1/y2 = 1/z2. Let us set the given equal expressions to a constant k (where k > 1 ): 2x2 = 3y2 = 12z2 = k This allows us to express the base numbers 2 , 3 , and $12 in terms of k : 2 = k1/x2 3 = k1/y2 12 = k1/z2 We know the mathematical relation between the numbers $12 , 2 , and 3 is: 12 = 4 × 3 = 22 × 3 Substitute the expressions of these numbers in terms of k into this equation: k1/z2 = (k1/x2)2 × k1/y2 Using the laws of exponents ( xa × xb = xa+b and (xa)b = xab ): k1/z2 = k2/x2 × k1/y2 k1/z2 = k2/x2 + 1/y2 Equating the exponents since the bases are identical: 2/x2 + 1/y2 = 1/z2 This corresponds to Option C. Note: The textbook designates Option B as correct. This discrepancy arises because of a typographical swap of bases in the question text. If the question had been written as 3x2 = 2y2 = 12z2 , then we would have 3 = k1/x2 and 2 = k1/y2 , which yields 1/x2 + 2/y2 = 1/z2 (Option B). However, for the given question text, the correct mathematical derivation leads to Option C. Hence, Option C is the correct answer.

Ratio, Proportion, Indices, LogarithmMCQPYQ June 19Question 875 of 302

All Questions

If $\displaystyle 2^{x^2} = 3^{y^2} = 12^{z^2}$ then

Select Your Answer (Keyboard: A, B, C, D)

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — $\displaystyle \frac{2}{x^2} + \frac{1}{y^2} = \frac{1}{z^2}$

All Options:

A $\displaystyle \frac{1}{x^2} + \frac{1}{y^2} = \frac{1}{z^2}$
B $\displaystyle \frac{1}{x^2} + \frac{2}{y^2} = \frac{1}{z^2}$
C $\displaystyle \frac{2}{x^2} + \frac{1}{y^2} = \frac{1}{z^2}$
DNone of these

Detailed Solution & Explanation

Let us set the given equal expressions to a constant

\displaystyle k

(where

\displaystyle k > 1

2^{x^2} = 3^{y^2} = 12^{z^2} = k

This allows us to express the base numbers

\displaystyle 2

\displaystyle 3

, and $12$ in terms of $k

\displaystyle \frac{1}{x^2}

\displaystyle 2

, and

\displaystyle 3

is:

12 = 4

Substitute the expressions of these numbers in terms of

\displaystyle k

into this equation:

k^{

Using the laws of exponents (

\displaystyle x^a

and

\displaystyle (x^a)^b = x^{ab}

k^{

k^{

Equating the exponents since the bases are identical:

\frac{2}{x^{2}} + \frac{1}{y^{2}} = \frac{1}{z^{2}}

This corresponds to **Option C**.
Note: The textbook designates **Option B** as correct. This discrepancy arises because of a typographical swap of bases in the question text. If the question had been written as

\displaystyle 3^{x^2} = 2^{y^2} = 12^{z^2}

, then we would have

\displaystyle 3 = k^{1/x^2}

and

\displaystyle 2 = k^{1/y^2}

, which yields

\displaystyle

(Option B). However, for the given question text, the correct mathematical derivation leads to **Option C**.
Hence, **Option C** is the correct answer.

About This Chapter: Ratio, Proportion, Indices, Logarithm

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Ratio, Proportion, Indices, Logarithms

This chapter covers Ratio, Proportion, Indices, Logarithms and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5-7 Marks weightage. Focus on understanding core concepts rather than memorizing.

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If 2x2=3y2=12z2\displaystyle 2^{x^2} = 3^{y^2} = 12^{z^2}2x2=3y2=12z2 then