Question

For a real number $x\left[x\right]$ denotes the integral part of $x$. The value of $\left[\frac{1}{2}\right]+\left[\frac{1}{2}+\frac{1}{100}\right]+\left[\frac{1}{2}+\frac{2}{100}\right]+......\left[\frac{1}{2}+\frac{99}{100}\right]$ is

• A. $49$
• B. $50$
• C. $48$
• D. $51$

Answer 1

Answer: (B)

$50$

$=\left[\frac{1}{2}\right]+[\frac{1}{2}+\frac{1}{100}]+[\frac{1}{2}+\frac{2}{100}]+.......................+[\frac{1}{2}+\frac{99}{100}]$

till $[\frac{1}{2}+\frac{49}{100}]$ all terms will be zero and after this till $[\frac{1}{2}+\frac{99}{100}]$ all terms will be 1.

$=0+0+0+0+\mathrm{0..........}+1+1+1+........1$

$=50\left(0\right)+50\left(1\right)$

$=50$