If a + b + c + d = 1, then the maximum value of (1 + a) (1 + b) (1 + c) (1 + d) is

For maximum value,

$a=b=c=d=\frac{1}{4}$

$\therefore(1+a)(1+b)(1+c)(1+d)=\left(\frac{5}{4}\right)^{4}$