A physical parameter `a` can be determined by measuring the parameters `b, c, d, and e` using the relation `a=b^(alpha)c^(beta)//d^(gamma)e^(delta)`. If the maximum errors in the measurement of `b, c , d, and e` are `b_(1) %,c_(1)% ,d_(1)% , and e_(1) %`, then the maximum error in the value of `a` determined by the experminent.

Options

A. `(b_(1) + c_(1) + d_(1) + e_(1)) %`
B. `(b_(1) + c_(1) - d_(1) - e_(1)) %`
C. `(alpha b_(1) +beta c_(1) - gamma d_(1) - delta e_(1)) %`
D. `(alpha b_(1) +beta c_(1) + gamma d_(1) +delta e_(1)) %`

Answer

d

Explanation

`a = b^(alpha) c^(beta)//d^(gamma) e^(delta)`
So maximum error in a is given by
`((Delta a)/(a) xx100)_(max) = alpha, (Delta b)/(b) xx 100 + beta.(Delta c)/(c ) xx 100`
`+ gamma.(Delta d)/(d) xx 100+ delta (Delta e)/(e )xx 100`
`= (alpha b_(1) + beta c_(1) + gamma d_(1) + delta e_(1))%`