For z = a 2 x 3 y (1/2), where ' a ' is a constant. If percentage error in measurement of ' x ' and ' y ' are 4 % and 12 %, respectively, then the percentage error for ' z ' will be %.

Question

For z = a 2 x 3 y (1/2), where ' a ' is a constant. If percentage error in measurement of ' x ' and ' y ' are 4 % and 12 %, respectively, then the percentage error for ' z ' will be %. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

z=a2 x3 y1 / 2 (Δ z / z )=(2 Δ a / a )+(3 Δ x / x )+(1/2) (Δ y / y ) a is constant (Δ z / z ) × 100=3(4 %)+(1/2)(12 %)=18 %

Q. For $z = a^{2} x^{3} y^{\frac{1}{2}}$ , where ' $a$ ' is a constant. If percentage error in measurement of ' $x$ ' and ' $y$ ' are $4%$ and $12%$ , respectively, then the percentage error for ' $z$ ' will be $%$ .

$z = a^{2} x^{3} y^{1/2}$
$\frac{Δ z}{z} = \frac{2Δ a}{a} + \frac{3Δ x}{x} + \frac{1}{2} \frac{Δ y}{y}$
$a$ is constant
$\frac{Δ z}{z} \times 100 = 3 (4%) + \frac{1}{2} (12%) = 18%$

Q. For z=a2x3y21​, where ' a ' is a constant. If percentage error in measurement of ' x ' and ' y ' are 4% and 12%, respectively, then the percentage error for ' z ' will be %.

z=a2x3y1/2 zΔz​=a2Δa​+x3Δx​+21​yΔy​ a is constant zΔz​×100=3(4%)+21​(12%)=18%

Q. For $z = a^{2} x^{3} y^{\frac{1}{2}}$ , where ' $a$ ' is a constant. If percentage error in measurement of ' $x$ ' and ' $y$ ' are $4%$ and $12%$ , respectively, then the percentage error for ' $z$ ' will be $%$ .

$z = a^{2} x^{3} y^{1/2}$
$\frac{Δ z}{z} = \frac{2Δ a}{a} + \frac{3Δ x}{x} + \frac{1}{2} \frac{Δ y}{y}$
$a$ is constant
$\frac{Δ z}{z} \times 100 = 3 (4%) + \frac{1}{2} (12%) = 18%$