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If f(x)=[[x-3 , 2 x^2-18 , 3 x^3-81],[ x...

If `f(x)=[[x-3 , 2 x^2-18 , 3 x^3-81],[ x-5 , 2 x^2-50 , 4 x^3-500],[ 1 , 2 , 3 ]]` then `f(1) . f(3)+f(3) . f(5)+f(5) . f(1)=`

A

`f(1)`

B

f(3)`

C

`f(1)+f(3)`

D

`f(1)+f(3)+f(5)`

Text Solution

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The correct Answer is:
B
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HIMALAYA PUBLICATION-MATRICES AND DETERMINANTS-QUESTION BANK
  1. The value of the determine : Delta=|(1!,2!,3!),(2!,3!,4!),(3!,4!,5!)| ...

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  2. The determinant: |(xp+y,x,y),(yp+z,y,z),(0,xp+y,yp+z)|=0 if :

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  3. If f(x)=[[x-3 , 2 x^2-18 , 3 x^3-81],[ x-5 , 2 x^2-50 , 4 x^3-500],[ 1...

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  4. The value of n for which the determinant |[8 C3 , 9 C5 , 10 C7 ],[8 C4...

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  5. [[ 1 , 1 , 1],[ 4 , 3 , 2],[ 4^2 , 3^2 , 2^2 ]] =

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  6. If Delta= [[0 , x , -y ],[-x , 0 , z],[ y , -z , 0 ]] then

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  7. Let Delta=|(1,sintheta,1),(-sin theta,1,sintheta),(-1,-sintheta,1)| , ...

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  8. If [[ p , q-y , r-z],[ p-x , q , r-z ],[ p-x , q-y , r ]]=0, then (p)/...

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  9. A and B are matrices of order three and |A| =4, |B| =-1 . Then the de...

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  10. If A and P are 3xx3 matrices with integral entries such that P ' AP = ...

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  11. Let A be a matrix of order 3 xx 3, and B is its adjoint matrix. If ...

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  12. IF A is a 3 times 3 matrix, |A| ne 0 and |3A|=k|A|, then write the val...

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  13. IF A is a 3 times 3 matrix, |A| ne 0 and |3A|=k|A|, then write the val...

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  14. If alpha , beta and gammaare roots of the equations x^3+px+q=0 then th...

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  15. Delta=|[x+a,b,c],[b,x+c, a],[c,a, x+b]| which of the following is a fa...

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  16. The value of Delta= [[5^2 , 5^3 , 5^4],[ 5^3 , 5^4 , 5^5],[ 5^4 , 5^6 ...

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  17. [[ 0 , p-q , p-r ],[q-p , 0 , q-r],[ r-p , r-q , 0 ]] =

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  18. With the usual notation in the triangle A B C [[ 1 , 1 , 1 ],[ sin A...

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  19. If A= [[-1 , 2 , 4 ],[ 3 , 1 , 0],[ -2 , 4 , 2 ]] and B= [[-2 , 4 ...

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  20. If [[ a , b , c],[ m , n , p],[ x , y , z ]] =k, then [[ 6 a , 2 b ,...

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