A) \[a=0,b=7\]
B) \[a=5,b=2\]
C) \[a=1,b=6\]
D) \[a=3,b=4\]
Correct Answer: D
Solution :
[d] Mean of \[a,b,8,5,10\] is 6 \[\Rightarrow \frac{a+b+8+5+10}{5}=6\Rightarrow a+b=7\] ?. (i) Variance of \[a,b,8,5,10\]is \[6.80\] \[\Rightarrow \frac{{{(a-6)}^{2}}+{{(b-6)}^{2}}+{{(8-6)}^{2}}+{{(5-6)}^{2}}+{{(10-6)}^{2}}}{5}\]\[=6.80\] \[\Rightarrow {{a}^{2}}-12a+36+{{(1-a)}^{2}}+21=34\] [Using eq. (i)] \[\Rightarrow 2{{a}^{2}}-14a+24=0\Rightarrow {{a}^{2}}-7a+12=0\] \[\Rightarrow a=3or\Rightarrow b=4or3\] \[\therefore \] The possible values of a and b are a=3 and b= 4 or, a = 4 and b = 3
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