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Let a,b,c, be any real number. Suppose t...

Let a,b,c, be any real number. Suppose that there are real numbers x,y,z not all zero such that x=cy+bz,y=az+cx and z=bx+ay. Then
`a^(2)+b^(2)+c^(2)` +2abc is equal to

A

1

B

2

C

`-1`

D

0

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The correct Answer is:
A
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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE MAIN ARCHIVE
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  2. Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identity...

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  3. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

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  4. Let A be a square matrix all of whose entries are integers. Which on...

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  5. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

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  6. Let A= [[5,5alpha,alpha],[0,alpha,5alpha],[0,0,5]] . If |A^2|...

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  7. If A and B f are square matrices of size nxxn such that A^(2) - B^(2...

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  8. Let A =((1,2),(3,4))and B= ((a,0),(0,b)), a, bin N. Then,

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  9. If A is a square matrix such that A^2-A+l=0, then the inverse of A is

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  10. If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

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  11. The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1 ...

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  12. if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...

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  13. Let A=[(0,0,-1),(0,-1,0),(-1,0,0)] Then only correct statement about t...

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  14. Let A=[(1,-1,1),(2,1,-3),(1,1,1)] and 10 B=[(4,2,2),(-5,0,alpha),(1,-2...

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  15. If the system of linear equations {:(x+2ay+az=0),(x+3by+bz=0),(x+4cy...

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  16. If A=[{:(a,b),(b,a):}] and A^(2)=[{:(alpha, beta),(beta, alpha):}] the...

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  17. If omega is a non-real cube root of unity and n is not a multiple o...

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  18. if a,b,c are positive and are the pth qth and rth terms respectively ...

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  19. If one of the cube roots of 1 be omega, then |(1,1+omega^2,omega^2),(...

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  20. If A is a symmetric matrix and B is a skew-symmetric matrix such that ...

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