Let [x] represent the greatest integer less than or equal to `x` If [`sqrt(n^2+lambda)]=[n^2+1]+2` , where `lambda,n in N ,` then `lambda` can assume `(2n+4)d iffe r e n tv a l u s` `(2n+5)d iffe r e n tv a l u s` `(2n+3)d iffe r e n tv a l u s` `(2n+6)d iffe r e n tv a l u s`

Options

A. `(2n+4)` different values
B. `(2n+5)` different values
C. `(2n+3)` different values
D. `(2n+6)` different values

Answer

B

Explanation

`[sqrt(n^(2)+1)]=n`
or `[sqrt(n^(2)+lambda)]=n+2`
or `n+2 le sqrt(n^(2)+lambda) lt n +3`
or `n^(2)+4 n+4 le n^(2)+lambda lt n^(2) +6n +9`
or `4n +4 le lambda lt 6n +9`
` :. 2n+5` values