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The value of the determinant ∣5C0 5C1 5C...

The value of the determinant ∣5_C_0 5_C_1 5_C_2 5_C_3 5_C_4 5_C_5 1 4 1 1∣ is (A) 0

A

(A) 0

B

(B) −576

C

(C) 80

D

(D) None of these

Text Solution

Verified by Experts

The correct Answer is:
A, C
Since, `f(x) =cos[pi^(2)]x+cos [-pi^(2)]x`
`rArr f(x)=cos(9)x+cos(-10)x`
` " "["using " [pi^(2)]=9 and [-pi^(2)]= -10]`
` therefore f((pi)/(2))="cos" (9pi)/(2) + cos 5pi = -1`
`f(pi)=cos 9pi +cos 10pi= -1+1=0`
`f(-pi)=cos 9pi+cos 10pi= -1+1=0`
`f((pi)/(4))="cos"(9pi)/(4)+"cos"(10pi)/(4)=(1)/(sqrt(2))+0=(1)/(sqrt(2))`
Hence, (a) and (c) are correct options.
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