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If a,b,c are non-zeros, then the system ...

If `a,b,c` are non-zeros, then the system of equations
`{:((alpha+a)x+alphay+alphaz=0),(alphax+(alpha+b)y+alphaz=0),(alphax+alphay+(alpha+c)z=0):}`
has a non-trivial solution if

A

`alpha^(-1) = -(a^(-1) + b^(-1) + c^(-1))`

B

`alpha^(-1) = a +b +c`

C

`alpha + a + b + c = 1`

D

none of these

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Chapter Test
  1. If x, y , z are in A.P., then the value of the det (A) is , where A ...

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  2. The value of |(b +c,a,a),(b,c +a,b),(c,c,a +b)|, is

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  3. If a ,\ b ,\ c are non-zero real numbers and if the system of equat...

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  4. If a!=6,b,c satisfy|[a,2b,2c],[3,b,c],[4,a,b]|=0 ,then abc =

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  5. The value of Delta = |(1^(2),2^(2),3^(2)),(2^(2),3^(2),4^(2)),(3^(2),4...

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  6. Prove: |a a+b a+2b a+2b a a+b a+b a+2b a|=9(a+b)b^2

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  7. If all the elements in a square matrix A of order 3 are equal to 1 or ...

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  8. Sum of real roots of the euation |{:(1,4,20),(1,-2,5),(1,2x,5x^(2)):}|...

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  9. If f(x)=|{:(sinx,cosx,tanx),(x^(3),x^(2),x),(2x,1,x):}|, then lim(xto0...

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  10. If A, B and C are the angles of a triangle and |(1,1,1),(1 + sin A,1...

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  11. If |(x,2,3),(2,3,x),(3,x,2)|=|(1,x,4),(x,4,1),(4,1,x)|=|(0,5,x),(5,x,0...

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  12. Using properties of determinants, solve for x:|a+x a-x a-x a-x a+x a...

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  13. If Delta(1) = |(7,x,2),(-5,x +1,3),(4,x,7)| and Delta(2) = |(x,2,7),(x...

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  14. If Delta1=|{:(10,4,3),(17,7,4),(4,-5,7):}|,Delta2=|{:(4,x+5,3),(7,x+12...

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  15. If |(a,a +d,a +2d),(a^(2),(a + d)^(2),(a + 2d)^(2)),(2a + 3d,2 (a +d),...

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  16. If Delta(k) = |(k,1,5),(k^(2),2n +1,2n +1),(k^(3),3n^(2),3n +1)|, " th...

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  17. If the system of equations bx + ay = c, cx + az = b, cy + bz = a h...

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  18. If a,b,c are non-zeros, then the system of equations {:((alpha+a)x+a...

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  19. If p^(th), q^(th),r^(th) terms an A.P are 1/a,1/b and 1/c respectively...

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  20. If A = |(a,b,c),(x,y,z),(p,q,r)| and B = |(q,-b,y),(-p,a,-x),(r,-c,z)|...

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