A) 1
B) 4
C) \[2+\sqrt{3}\]
D) 5
E) 0
Correct Answer: D
Solution :
\[(1-{{\alpha }_{1}})(1-{{\alpha }_{2}})(1-{{\alpha }_{3}})(1-{{\alpha }_{4}})\] \[=(1+{{\alpha }_{1}}{{\alpha }_{2}}-{{\alpha }_{1}}-{{\alpha }_{2}})(1-{{\alpha }_{3}})(1-{{\alpha }_{4}})\] \[=(1+{{\alpha }_{1}}{{\alpha }_{2}}-{{\alpha }_{1}}-{{\alpha }_{2}}-{{\alpha }_{3}}-{{\alpha }_{1}}{{\alpha }_{2}}{{\alpha }_{3}}\] \[+{{\alpha }_{1}}{{\alpha }_{3}}+{{\alpha }_{2}}{{\alpha }_{3}})(1-{{\alpha }_{4}})\] \[=1+\Sigma {{\alpha }_{1}}{{\alpha }_{2}}-\Sigma {{\alpha }_{1}}{{\alpha }_{2}}{{\alpha }_{3}}-\Sigma {{\alpha }_{1}}+{{\alpha }_{1}}{{\alpha }_{2}}{{\alpha }_{3}}{{\alpha }_{4}}\] \[=1+(2-\sqrt{3})-0-0+2+\sqrt{3}\] \[=-2\sqrt{3}+1+2+\sqrt{3}=5\]
You need to login to perform this action.
You will be redirected in
3 sec
