MCQ
Let $[\alpha]$ denote the greatest integer $\leq \alpha$. Then $[\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}]+\ldots .+[\sqrt{120}]$ is equal to.
- A$824$
- ✓$825$
- C$823$
- D$822$
$\Rightarrow 1+1+1+2+2+2+2+2+3+3+\ldots \ldots .+$
$3=7 \text { times }$
$+4+4+\ldots \ldots .+4=9 \text { times }+\ldots \ldots 10+10+$
$\ldots \ldots+10=21 \text { times }$
$\Rightarrow \sum_{r=1}^{10}(2 r+1) . r$
$\Rightarrow 2 \sum_{r=1}^{10} r^2+\sum_{r=1}^{10} r$
$\Rightarrow 2 \times \frac{10 \times 11 \times 21}{6}+\frac{10 \times 11}{2}$
$\Rightarrow 770+55$
$\Rightarrow 825$
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