Which of the following may be sensible expression? Given that A, B, C and D are all dimensionally different ?

Since A,B,C and D are all dimensionally different, dimensional formula of  $\frac{\mathrm{A}}{\mathrm{B}}$  may be same as that of CD. If  $\frac{\mathrm{A}}{\mathrm{B}}$ and CD represent same physical quantity. They may be added and option–(1) is right. Again CD may be dimensionless. In that case ${\mathrm{e}}^{\mathrm{CD}}$  is mathematically correct. Again ${\mathrm{A}}^2\mathrm{B}$  may be dimensionless, in that case option –(2) is also correct. Since $\frac{\mathrm{A}}{\mathrm{B}}$  and $\frac{\mathrm{C}}{\mathrm{D}}$  can never be dimensionless, option–(3) is meaningless.