Question

The sum of the products of the ten numbers $\pm 1,\pm 2,\pm 3,\pm 4,\pm 5$ taking two at a time is

• A. 165
• B. $-165$
• C. 55
• D. $-55$

Answer 1

Answer: (D)

$\therefore \sum ab=\frac{1}{2}\left[{\left(\sum a\right)}^2-\sum a^2\right]$
$=\frac{1}{2}\left[(1-1+2-2+\dots ..+5-5{)}^2-2\left(1^2+2^2+3^2+4^2+5^2\right)\right]$
$=\frac{1}{2}[0-110]=-55$