Physics Q26 – JEE-MAIN 2025

Home Physics Units & MeasurementsQuestion #581

A quantity Q is formulated as

X^{- 2} Y^{\frac{3}{2}} Z^{\frac{2}{5}}

. X, Y and Z are independent parameters which have fractional errors of 0.1, 0.2 and 0.5, respectively in measurement. The maximum fractional error of Q is

Clue 1 of 3: Error Propagation

When quantities are multiplied or divided, their fractional errors add up, weighted by their powers.

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Ninja Strategy•Magnitude Check & Power Awareness

Quickly check if any individual term's contribution exceeds an option, and recognize that powers other than 1 will change the simple sum of fractional errors.

🧠 Full Solution Path

Step 1: Identify the Formula for Q and Fractional Errors✦ Active

The quantity Q is given by the formula $Q = X^{- 2} Y^{\frac{3}{2}} Z^{\frac{2}{5}}$ . The fractional errors for X, Y, and Z are given as $\frac{Δ X}{X} = 0.1$ , $\frac{Δ Y}{Y} = 0.2$ , and $\frac{Δ Z}{Z} = 0.5$ respectively.

Step 2: Apply the Formula for Maximum Fractional Error○ Expand

For a quantity $Q = X^{a} Y^{b} Z^{c}$ , the maximum fractional error is calculated as the sum of the absolute values of the products of each power and its corresponding fractional error. Here, $a = - 2$ , $b = \frac{3}{2}$ , and $c = \frac{2}{5}$ .

\frac{Δ Q}{Q} = | a | \frac{Δ X}{X} + | b | \frac{Δ Y}{Y} + | c | \frac{Δ Z}{Z}

Substituting the values:

\frac{Δ Q}{Q} = | - 2 | (0.1) + | \frac{3}{2} | (0.2) + | \frac{2}{5} | (0.5)

💡 Teacher's Secret Hint

Remember to use the absolute values of the powers to ensure the maximum possible error.

Step 3: Calculate the Maximum Fractional Error○ Expand

Perform the multiplication and summation:

\frac{Δ Q}{Q} = 2 (0.1) + 1.5 (0.2) + 0.4 (0.5)

\frac{Δ Q}{Q} = 0.2 + 0.3 + 0.2

\frac{Δ Q}{Q} = 0.7

The maximum fractional error of Q is $0.7$ .

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Physics Question 26 – JEE-MAIN 2025

Clue 1 of 3: Error Propagation

🧠 Full Solution Path