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Delta = |(a +x,b,c),(b,x +c,a),(c,a,x +b...

`Delta = |(a +x,b,c),(b,x +c,a),(c,a,x +b)|`. Which of the following is a factor for the above determinant ?

A

`x -(a + b +c)`

B

`x + (a +b +c)`

C

`a + b + c`

D

`-(a +b +c)`

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`Delta = |(a +x,b,c),(b,x +c,a),(c,a,x + b)|`
`rArr Delta = |(x + a + b + c,b,c),(x +a + b + c,x +c,a),(x + a + b + c,a,x +b)|` Applying `C_(1) rarr C_(1) + C_(2) + C_(3)`
`rArr Delta = (x +a +b +c) |(1,b,c),(1,x +c,a),(1,a,x +b)|`
`rArr (x +a +b +c)` is a factor of `Delta`
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OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Chapter Test
  1. Delta = |(a +x,b,c),(b,x +c,a),(c,a,x +b)|. Which of the following is ...

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  2. STATEMENT-1: The lines a(1)x+b(1)y+c(1)=0a(2)x+b(2)y+c(2)=0,a(3)x+b(3)...

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

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  4. Use properties of determinants to solve for x: |{:(,x+a,b,c),(,c,x+b,a...

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  5. |(sin^(2) x,cos^(2) x,1),(cos^(2) x,sin^(2) x,1),(- 10,12,2)| =

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  6. The system of linear equations x + y + z = 2 2x + y -z = 3 3x + ...

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  7. The roots of the equation |(3x^(2),x^(2) + x cos theta + cos^(2) the...

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  8. |(bc,bc'+b'c,b'c'),(ca,ca'+c'a,c'a'),(ab,ab'+a'b,a'b')| is equal to

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  9. If alpha, beta, gamma are the cube roots of 8 , then |(alpha,beta,gamm...

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  10. One root of the equation |(3x-8, 3, 3),(3,3x-8, 3),(3,3,3x-8)|=0 is ...

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  11. If a,b and c are non- zero real number then prove that |{:(b^(2...

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  12. If x, y , z are in A.P., then the value of the det (A) is , where A ...

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

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

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

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

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

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

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

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

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