A) 2, 3, 7
B) 1.5, 2.5, 8
C) 1, 5, 6
D) 4, 2, 6
Correct Answer: D
Solution :
\[{{C}_{\text{1}}}+{{C}_{\text{2}}}+{{C}_{\text{3}}}=\text{12}\] ....(i) \[{{C}_{\text{1}}}{{C}_{\text{2}}}{{C}_{\text{3}}}=\text{ 48}\] ....(ii) \[{{C}_{\text{1}}}+{{C}_{\text{2}}}=\text{ 6}\] ....(iii) From equation (i) and (iii) \[{{C}_{\text{3}}}=\text{ 6}\] ....(iv) From equation (ii) and (iv) \[{{C}_{\text{1}}}{{C}_{\text{2}}}=\text{ 8}\] Also \[{{({{C}_{1}}-{{C}_{2}})}^{2}}={{({{C}_{1}}+{{C}_{2}})}^{2}}-4{{C}_{1}}{{C}_{2}}\] \[{{({{C}_{1}}-{{C}_{2}})}^{2}}={{(6)}^{2}}-4\times 8=4\] Þ \[{{C}_{\text{1}}}{{C}_{\text{2}}}=\text{ 2}\] .....(v) On solving (iii) and (v) \[{{C}_{\text{1}}}=\text{ 4},~{{C}_{\text{2}}}=\text{ 2}\]You need to login to perform this action.
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