The correct option is C 12
We divide both the numerator and denominator by x.
Since, from the property of trigonometric functions we know that sinx and cosx can only have their values between −1 and 1
Thus, the expression transforms to,
limx→∞2+7sinxx4+3cosxx
Now applying the limit,
=2+04+0
=12
Hence, option 'C' is correct.