If, $$a^2+b^2+c^2+d^2 = 1$$​ what will be the maximum value of the product abcd ?

Correct option is A

Given:
​$$a^2 + b^2 + c^2 + d^2 = 1$$

Solution:

​$$a^2 + b^2 + c^2 + d^2 = 1\\\text{Let } a = b = c = d\\\text{Then, } a^2 + a^2 + a^2 + a^2 = 1\\4a^2 = 1\\a = \pm \frac{1}{2}\\\text{For maximum value, } a = \frac{1}{2}\\\\a = b = c = d = \frac{1}{2}\\\ \\abcd = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}= \frac{1}{16}\\$$​​