The product 

$$\left(1 - \frac{1}{2^2}\right)\left(1 - \frac{1}{3^2}\right)\left(1 - \frac{1}{4^2}\right).....\left(1 - \frac{1}{11^2}\right)\left(1 - \frac{1}{12^2}\right)$$ is equal to

Expression : $$\left(1 - \frac{1}{2^2}\right)\left(1 - \frac{1}{3^2}\right)\left(1 - \frac{1}{4^2}\right).....\left(1 - \frac{1}{11^2}\right)\left(1 - \frac{1}{12^2}\right)$$

= $$\left(1^2 - \frac{1}{2^2}\right)\left(1^2 - \frac{1}{3^2}\right)\left(1^2 - \frac{1}{4^2}\right).....\left(1^2 - \frac{1}{11^2}\right)\left(1^2 - \frac{1}{12^2}\right)$$

= $$\left(1 - \frac{1}{2}\right)(1+\frac{1}{2})\left(1 - \frac{1}{3}\right)(1+\frac{1}{3})\left(1 - \frac{1}{4}\right)(1+\frac{1}{4}).....\left(1 - \frac{1}{11}\right)(1+\frac{1}{11})\left(1 - \frac{1}{12}\right)(1+\frac{1}{12})$$

= $$(\frac{1}{2})(\frac{3}{2})\times(\frac{2}{3})(\frac{4}{3})\times(\frac{3}{4})(\frac{5}{4})\times(\frac{4}{5})(\frac{6}{5})\times.................\times(\frac{10}{11})(\frac{12}{11})\times(\frac{11}{12})(\frac{13}{12})$$

= $$\frac{1}{2}\times\frac{13}{12}=\frac{13}{24}$$

=> Ans - (D)