A) 1
B) \[-1\]
C) 2
D) \[-2\]
Correct Answer: C
Solution :
[c] \[I=\int\limits_{0}^{3}{[\sqrt{x}].dx}\] \[=\int\limits_{0}^{3}{[\sqrt{x}].dx}\int\limits_{1}^{3}{[\sqrt{x}].dx}\] \[\left[ \begin{align} & \because [\sqrt{x}]=0\,\,\,\,\,\,\,\,when\,0\le x<1 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=1\,\,\,\,\,\,\,\,\,when\,1\le x<3 \\ \end{align} \right]\] \[=\int\limits_{0}^{1}{0.dx}+\int\limits_{1}^{3}{1.dx}=0+[x]_{1}^{3}=(3-1)=2\] Hence, option [c] is correct.
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