CAT 2022 Slot 1 Paper

Question : 66 of 66

Marks: +1, -0

For any real number $x$ , let $[\x]$ be the largest integer less than or equal to $x$ . If $∑^{\N}_n=1 [1/5+n/25]=25$ then $\N$ is

Solution:

It is given,

Σ↙{n=1}↖{N} [{1}/{5}+\;{n}/{25}] =25

Σ↙{n=1}↖{N} [{5+n}/{25}] =25

For

n=1

n=19

, value of function is zero.
For

n=20

n=44

, value of function will be 1 .

44=20+n-1

{\n}=25

which is equal to given value.
This implies

\N=44

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