QJEEM16Phecb9: JEE Main 2016 Physics - Class 11 JEEM16Phecb9 Solution: A, B, C and D are four different physical quantities having…

Given,

AD = c ln (BD)

As log is dimensionless.

So, [BD] = 1    $\Rightarrow$   [B] = ${1 \over {\left[ D \right]}}$

And  [AD] = [C]

Now checking options one by one

(a)   [B² C²] = [B²] [A² D²] = [A²] [B² D²] = [A²]

$\therefore$    This is meaningful.

(b)    $\left( {{{A - C} \over D}} \right)$ is not meaningful.

As dimension of A $\ne$ dimension of C

Hence (A $-$ C)   is not possible.

(c)    $\left[ {{A \over B}} \right]$ = [AD] = [C]

$\therefore$     ${{A \over B}}$ $-$ C is meaningful.

(d)    $\left[ {{C \over {BD}}} \right]$ = ${{\left[ C \right]} \over {\left[ {BD} \right]}}$ = ${{\left[ C \right]} \over 1}$ = [C]

$\left[ {{{A{D^2}} \over C}} \right]$ = ${{\left[ {AD} \right]\left[ D \right]} \over {\left[ C \right]}}$ = ${{\left[ C \right]\left[ D \right]} \over {\left[ C \right]}}$ = [D]

As dimension of C and D are not same so it is not meaning ful.