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|(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-...

`|(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|`

A

`-(a+b+c)`

B

`-2(a+b+c)`

C

`2(a+b+c)`

D

abc

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The correct Answer is:
B
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If |(a-b-c, 2a, 2a),(2b, b-a-c, 2b),(2c, 2c, c-a-b)|=(a+b+c)(x+a+b+c)^2 then the value of x is equal to (A) -2(a+b+c) (B) a+b+c (C) -(a+b+c) (D) 2(a+b+c)

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Using properties of determinants, prove that following |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^3

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Value of |(1,a,a^2),(1,b,b^2),(1,c,c^2)| is (A) (a-b)(b-c)(c-a) (B) (a^2-b^2)(b^2-c^2)(c^2-a^2) (C) (a-b+c)(b-c+a)(c+a-b) (D) none of these

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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE MAIN ARCHIVE
  1. If |(1,1,1),(2,b,c),(4,b^(2),c^(2))| and |A| = in [2, 16]. 2, b, c and...

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  2. If A = [(1,sin theta, 1),(-sintheta, 1, sin theta),(-1, -1sin theta, 1...

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  3. |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|

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  4. Let a(1),a(2),a(3), …, a(10) be in G.P. with a(i) gt 0 for i=1, 2, …, ...

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  5. Let A=[(2,b,1),(b,b^(2)+1,b),(1,b,2)] where b gt 0. Then the minimum v...

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  6. Let d in R, and A[{:(,-2,4+d,(sin theta-2)),(,1,(sin theta)+2,d),(,5,(...

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  7. If B = [{:(5, 2alpha, 1),(0, 2, 1),(alpha, 3, -1):}] is the inver...

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  8. Matrix=[[e^t,e^-t(sint-2cost),e^-t(-2sint-cost)],[e^t,-e^-t(2sint+cost...

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  9. Let A and B be two invertible matrices of order 3xx3. If det. (ABA^(T)...

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  10. If A = [(costheta,-sintheta),(sintheta,costheta)], then the matrix A^(...

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  11. If [x] denotes the greatest integer le x, then the system of liner equ...

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  12. Let lambda be a real number for which the system of linear equations ...

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  13. If the system of linear equation x+y+z=5, x+2y+2z = 6, x+3y + lambda z...

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  14. If the system of equations, 2x + 3y-z = 0, x + ky -2z = 0 " and " 2x-y...

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  15. If the system of linear equations x-2y + kz = 1, 2x + y+ z = 2, 3x-y...

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  16. The greatest value of for which the system of linear equations x-c...

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  17. The set of all values of lambda for which the system of linear equatio...

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  18. An ordered pair (alpha, beta) for which the system of linear equations...

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  19. If the system of linear equations 2x+2y+3z=a 3x-y+5z=b x-3y+2z=...

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  20. The number of possible value of theta lies in (0,pi), such that system...

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