Home
Class 12
MATHS
If [] denotes the greatest integer less ...

If `[]` denotes the greatest integer less than or equal to the ral number under consideration, and `-1lt=x<0,0lt=y<1,1lt=a<2,` then the value of the determinant `|[x]+1[y][z][x][y]+1[z][x][y][z]+1|` is `[x]` b. `[y]` c. `[z]` d. none of these

A

`[x]`

B

`[y]`

C

`[z]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`:' -1 le lt 0 :. [x] =-1`
`0le y lt 1 :. [y] =0`
`1 le z lt 2 :. [z] =1`
Hence the given determinant is
`|{:(0,,0,,1),(-1,,1,,1),(-1,,0,,2):}|=1-[z]`
Promotional Banner

Similar Questions

Explore conceptually related problems

If [] denotes the greatest integer less than or equal to the real number under consideration and -1lt=xlt0,0lt=ylt1,1lt=zlt2, the value of the determinant |{:([x]+1,[y],[z]),([x],[y]+1,[z]),([x],[y],[z]+1):}| is

If [x] denotes the greatest integer less than or equal to x, then ["log"_(10) 6730.4]=

The greatest integer less than or equal to (sqrt(2)+1)^(6) is

The greatest integer less than or equal to (sqrt(2)+1)^(6) is

If [x] denotes the greatest integer less than or equal to* then [(1+0.0001)^(1000)] equals

Let f : [-1, 3] to R be defined as {{:(|x|+[x]", "-1 le x lt 1),(x+|x|", "1 le x lt 2),(x+[x]", "2 le x le 3","):} where, [t] denotes the greatest integer less than or equal to t. Then, f is discontinuous at

Let f(x)=[cosx+ sin x], 0 lt x lt 2pi , where [x] denotes the greatest integer less than or equal to x. The number of points of discontinuity of f(x) is