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Let "f(x)"=|{:(1,x,x+1),(2x,x(x-1),(x+1)...

Let `"f(x)"=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)):}|` then f(100) is equal to

A

0

B

1

C

100

D

`-100`

Text Solution

Verified by Experts

The correct Answer is:
A
We have, `f(x) |(1,x,x +1),(2x,x (x-1),(x+1) x),(3x(x -1),x (x -1) (x -2),(x +1) x (x -1))|` Applying `C_(3) rarr C_(3) - C_(2)`, we get
`f(x) |(1,x,1),(2x,x(x -1),2x),(3x(x -1),x(x -1) (x -2),3x (x -1))| =0`
`:. f(100) = 0
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OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Section I - Solved Mcqs
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  10. The determinant |{:(y^(2),,-xy,,x^(2)),(a,,b ,,c),(a',,b',,c'):}| is ...

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  17. If Dk=|1nn2k n^2+n+2n^2+n2k-1n^2n^2+n+2|a n d sum(k=1)^n Dk=48 ,t h e...

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